bluuebunny/crossref_metadata_2025 huggingface dataset:
Variational principles on rth order jets of fibre bundles in field theory
Authors: Aldaya Víctor , de Azcárraga José A.
Published: March 2003

The Hamilton and the modified Hamilton variational principles in classical field theory are studied for physical systems described by Lagrangian and Hamiltonian densities depending on arbitrary order derivatives of the field. These principles are established on the fibre bundles Jr(E), J1(Jr−1(E)), J1*(Jr−1(E)). This is accomplished by defining an appropriate Poincaré–Cartan form. This form is also required in the definition of the associated symmetry problem and in the explicit construction of the Noether currents.
Nuclearity of some spaces of C∞ vectors in induced representations
Authors: Arnal D.
Published: March 2003

We give conditions on irreducible unitary induced representations of inhomogeneous Lie groups ensuring nuclearity of the space of differentiable vectors. We study the consistency of these conditions. Finally we show that our conditions hold almost everywhere with respect to the Plancherel measure for some generalizations of the Poincaré group.
Stochastic quantization of wave fields and its application to dissipatively interacting fields
Authors: Yasue Kunio
Published: March 2003

The stochastic quantization procedure, proposed by Nelson, is further developed to include the problem of field quantization. To maintain the mathematical rigor in treating infinitely many degrees of freedom, basic notions of the nonstandard analysis are adopted. As an application of the present method, a quantum mechanical description of dissipatively interacting fields, such as the laser electric field in the lossy cavity, is investigated.
Energy–momentum tensor symmetries and concomitant conservation laws. I. Einstein-massless-scalar (meson) field
Authors: Katzin Gerald H. , Levine Jack
Published: March 2003

Symmetries of energy–momentum tensors 𝒯 in a Riemannian space–time are defined by infinitesimal mappings x̄i =xi+ξi(x) δa where the mapping vector ξi is determined by the symmetry condition ℒξ(gw/2𝒯) =0, (gw/2𝒯) is a relative tensor of weight w, g≡ absolute value of the metrical determinant, and ℒξ is the Lie derivative with respect to the vector ξi). The existence of such symmetry vectors ξi leads to concomitant conservation laws in the form of conserved vector currents Ji for both special and general relativity. The currents Ji will be explicit functions of the energy momentum tensor 𝒯 and the symmetry vector ξi. The symmetries and conservation laws so obtained will in general differ from the familiar Trautman formulation. The theory is applied to obtain symmetries and conserved currents for a class of conformally flat solutions of the Einstein-massless-scalar (meson) field equations.
Symmetries of the stationary Einstein–Maxwell field equations. III
Authors: Kinnersley William , Chitre D. M.
Published: March 2003

We further investigate the infinite hierarchy of potentials and nonlinear symmetry transformations given in a previous paper. We outline a general method of explicitly calculating the potentials for a given spacetime. We show that some of the transformations can be exponentiated to finite values of their parameters, making them available as a means of generating new solutions. In particular, we show how our transformations may be used to generate all static solutions (including Schwarzschild), starting from nothing but flat space.
Quantization on a manifold with connection
Authors: Underhill J.
Published: March 2003

We give a rule Q which generalizes the Weyl correspondence to systems whose configuration space is equipped with an affine connection. We show that [Q (f), Q (g)]=iQ ({f, g}) for arbitrary f provided g has the form Xipi, where Xi is an affine vector field.
Generalization of the inversionlike integral equations and application to nonlinear partial differential equations. II
Authors: Cornille Henri
Published: March 2003

Using pedestrian algebraic method, in the case of a coupled system of n linear first order differential equations (Δ0−iφΛ −Q) ψ=0, Λ= (δijλi), Δ0 = (δijμi(x)(∂/∂x)), Q= (qij), we deduce inversionlike integral equations (from which we can construct a class of potentials without introducing the data). Assuming, like in the Zakharov–Shabat theory, that the kernels of the linear integral inversion equation satisfy linear partial differential equations, we deduce, for the solution of the integral equation, the corresponding nonlinear partial differential equation. We show that the validity of the whole formalism depends mainly on the set of {λi} of the associated differential linear system. We discuss fully the different possibilities which occur depending on different sets of {λi}.
Quantum dynamical semigroups and multipole relaxation of a spin in isotropic surroundings
Authors: Verri Maurizio , Gorini Vittorio
Published: March 2003

We derive and discuss three different parametrizations of the generator of a dynamical semigroup which describes the Markovian relaxation of a spin j under the influence of isotropic surroundings. The relevant parametrizations that we consider are the strengths of the polarities of the interaction, the relaxation rates of the different multipoles and the transition probabilities per unit time among the Zeeman sublevels. The results are model independent and allow us to derive a set of relations and inequalities for the transition probabilities and for the relaxation rates whose validity is not bound to any specific assumption concerning the mechanisms which govern the relaxation.
On phase-integral quantization conditions for bound states in one-dimensional smooth single-well potentials
Authors: Fröman Nanny , Fröman Per Olof
Published: March 2003

Previous work by the present authors on phase-integral quantization conditions for single-well potentials is extended and generalized. Exact as well as approximate quantization conditions are considered and investigated more fully than previously. Not only their necessity but also their sufficiency is treated. An improvement of the estimate of the error of the generalized quantal Bohr–Sommerfeld quantization condition is also given.
The tensor virial theorem in quantum mechanics
Authors: Cohen Leon
Published: March 2003

A quantum mechanical generalization of the scalar virial theorem is derived and specialized to atoms and molecules in the Born–Oppenheimer approximation. The theorem is the quantum mechanical counterpart to Chandrasekhar’s classical tensor virial theorem. The usual scalar virial equation follows by tensor contraction. One possible application is the introduction of more than one scale factor in a trial wavefunction. The scaling method proposed involves different stretchings for the different spatial coordinates. This is in contrast to the standard method of using the scalar virial theorem where the stretching is the same in all directions. An example is given where the introduction of multiple scale factors and the imposition of the tensor virial theorem yields a better result than the usual procedure of subjecting the wavefunction to a single scale transformation and imposing the scalar virial theorem.
Search for periodic Hamiltonian flows: A generalized Bertrand’s theorem
Authors: Onofri E. , Pauri M.
Published: March 2003

A complete classification is given of the two-dimensional Hamiltonian systems (whose Hamilton–Jacobi equation separates in Cartesian or polar coordinates) which admit strictly periodic motions for open sets of initial conditions (completely degenerate systems). Any of the systems which are separable in Cartesian coordinates turn out to be canonically equivalent to some anisotropic harmonic oscillator. In the polar case our results provide a generalization of a celebrated theorem of Bertrand. It is proven that all the completely degenerate systems fall into two families. These families are characterized by the semiclassical inverse ’’spectral functions’’ n1J1+n2J2=ℱ (H) =α (−H)−1/2−β, n1J1+n2J2=ℱ (H) =αH−β (α, β real positive constants) and contain, as central symmetric cases, the Kepler system and the isotropic harmonic oscillator, respectively. Qualitative and higher symmetry properties of these systems are also discussed.
Spherical delta functions and multipole expansions
Authors: Rowe E. G. Peter
Published: March 2003

The Cartesian–Taylor series for an analytic function in three dimensions is rewritten as a series of solid spherical harmonics. A discussion of the distribution theory definition of singular spherical harmonics is given, which leads to a definition of spherical delta functions. An expansion of source functions in spherical delta functions and their derivatives leads to multipole expansions for the fields which, in a distribution theory sense, are valid everywhere.
A time dependent generalization of the multiple scattering formalism
Authors: Gersten Joel I.
Published: March 2003

The multiple scattering formalism is generalized to include the restricted class of time dependent potentials in which each scattering center is moving with an arbitrary, but constant, velocity.
Polynomial tensors for double point groups
Authors: Desmier P. E. , Sharp R. T.
Published: March 2003

Generating functions for (Γr,Γm) tensors for each pair of irreducible representations Γr and Γm are calculated for each double point group. A (Γr,Γm) tensor transforms according to Γr and its components are polynomials in another tensor transforming by Γm. The actual tensors are given for the groups (d)Cn, (d)Dn, (d)T and for some representations Γm of (d)0. Certain of the polynomial tensors provide polynomial SU(2) bases reduced according to the double point group in question.
Wigner coefficients for SU(6) ⊇ SU(3) ⊗ SU(2)
Authors: So S. I. , Strottman D.
Published: March 2003

A technique for evaluating the Wigner coeficients for SU(6) with the physically interesting subgroups SU(3) ⊗SU(2) is outlined. Coefficients appropriate for coupling a single quark to a many quark wavefunction are tabulated for functions of nine or fewer quarks.
Solutions of the generalized nonlinear Schrödinger equation in two spatial dimensions
Authors: Cornille Henri
Published: March 2003

Recently, from two independent methods, the generalized nonlinear Schrödinger evolution equation in two spatial dimensions has been derived both by Ablowitz and Haberman and by Morris. Here the same extension of the Schrödinger cubic equation is obtained from a two-dimensional spatial inversionlike integral equation when a suitable time dependence is introduced. We investigate the solutions (corresponding to degenerate kernels of the inversion equation) in both cases, where the nonlinear part reduces or not to a cubic term. While in the first case, the solutions are not confined, on the contrary in the second case, we show explicitly for any finite time, that there exists an infinite number of solutions which are confined in the two-dimensional coordinate space.
Geometry of homothetic Killing trajectories and stationary limit surfaces
Authors: Dyer C. C. , Honig E.
Published: March 2003

We investigate the intrinsic geometry of timelike and null homothetic Killing trajectories. We do this through the use of two different Frenet–Serret formalisms developed by Synge and Bonnor. The curvature of such a nongeodesic timelike curve passing through a spacetime point is a direct measure of the expansion of the congruence at that point. Moreover, the rotation of this congruence is directly related to the torsions of its individual curves. For both classes of curves, timelike and null, the intrinsic scalars can be expressed as exponential functions of suitable parameters. We prove the following theorem twice, first by using the timelike formalism, and then through the null one. A homothetic stationary limit surface (where the homothetic Killing vector becomes null) is a null geodesic hypersurface if and only if the rotation of the homothetic Killing congruence vanishes on that hypersurface. The second, ’’null’’ approach allows us to derive this theorem directly on the hypersurface. Finally, we note that by setting a parameter equal to zero we recover all of the corresponding results for ordinary Killing vectors.
Application of Altman’s contractor techniques to nonlinear integral equations for Green’s functions of augmented quantum field theory
Authors: Nouri-Moghadam M. , Yoshimura Tetz
Published: March 2003

Altman’s theory of contractors and contractor directions is applied to equations for connected irreducible Green’s functions of Klauder’s augmented quantum field theory in the φ4 model, and sufficient conditions for existence of solutions are discussed.
Independence of the free energy for one-dimensional systems of fermions
Authors: Campanino M. , Del Grosso G.
Published: March 2003

In this paper we prove the independence of the free energy of a one-dimensional system of fermions in a box from the boundary conditions by using the Wiener integral techniques.
An angle-dependent lower bound on the solution of the elastic unitarity integral and a new uniqueness condition resulting from it
Authors: Sakmar I. A.
Published: March 2003

Through an iteration process we construct, from the angle-dependent upper bound to the unitarity integral, an angle-dependent lower bound and use this result to derive a uniqueness condition on the solution of the integral equation.
Relativistic scattering of model particles
Authors: Snellman Håkan , Tengstrand Göran
Published: March 2003

Relativistic scattering of particles belonging to an irreducible representation (irrep) of the 11-parameter Weyl Lie algebra w is studied. The irrep of w is realized on a manifold R3×T where T=[0,π]. From the corresponding wavefunctions a local relativistic field is constructed which is coupled to itself in such a way that w is respected. Scattering is studied in the Born approximation.
Topological solitons and graded Lie algebras
Authors: Poénaru V. , Toulouse G.
Published: March 2003

This paper is an extension of our previous investigation on the crossing of defects in ordered media. We provide a general mathematical framework, in which the obstructions for crossing p-dimensional defects with q-dimensional defects in a (p+q+1) -dimensional sample are the brackets of a certain graded Lie algebra (connected with homotopy theory). This ’’confinement mechanism’’ brings together the mathematical structures of two not yet related themes in present-day physics: solitons and supersymmetry.
Spherically symmetric static conformally flat solutions in Brans–Dicke and Sen–Dunn theories of gravitation
Authors: Reddy D. R. K.
Published: March 2003

Vacuum field equations for the static spherically symmetric conformally flat metric are obtained in Brans–Dicke and Sen–Dunn scalar-tensor theories of gravitation. Closed form exact solutions to the field equations are presented and studied in both the theories.
Group theory of the interacting Boson model of the nucleus
Authors: Castaños O. , Chacón E. , Frank A. , Moshinsky M.
Published: March 2003

Recently Arima and Iachello proposed an interacting boson model of the nucleus involving six bosons, five in a d and one in an s state. The most general interaction in this model can then be expressed in terms of Casimir operators of the following chains of subgroups of the fundamental group U(6): U(6) ⊆U(5) ⊆O(5) ⊆O(3) ⊆O(2), U(6) ⊆O(6) ⊆O(5) ⊆O(3) ⊆O(2), U(6) ⊆SU(3) ⊆O(3) ⊆O(2). To determine the matrix elements of this interaction in, for example, a basis characterized by the irreducible representations of the first chain of groups, then we only need to evaluate the matrix elements of the Casimir operators of O(6) and SU(3) in this basis as the others are already diagonal in it. Using results of a previous publication for the basis associated with U(5) ⊆O(5) ⊆O(3), we obtain the matrix elements of the Casimir operators of O(6) and SU(3). Furthermore, we obtain explicitly the transformation brackets between states characterized by irreducible representations of the first two chains of groups. Numerical programs are being developed for these matrix elements from the relevant reduced 3j symbols for the O(5) ⊆O(3) chain of groups that were programmed previously.
Variational formalism for spinning particles
Authors: Horváthy P.
Published: March 2003

We relate here the geometric formulation of Hamilton’s principle presented in our previous paper to the usual one in terms of a Lagrangian function. The exact conditions for their equivalence are obtained and a method is given for the construction of a Lagrangian function. The formalism is extended to spinning particles and a local Lagrangian is constructed in this case also. However, this function cannot be extended to a global one.
Nonlinear approach to inverse scattering
Authors: Weston V. H.
Published: March 2003

The inverse scattering problem for the scalar wave equation associated with propagation through a medium whose index of refraction differs from that of free space in a region of compact support is treated when the scattered data is given for diverse directions of (plane wave) incidence, scattered directions, and frequencies. The problem is formulated in terms of the minimization of a nonlinear functional which is bounded below, subject to constraints. It is shown that the conditional-gradient method may be employed, the iteration process converging to stationary points. The linearized version (corresponding to the perturbed wave equation with only the linear perturbed terms retained) of the nonlinear functional is considered as a special case. In particular the linearized version related to the Born approximation leads to some additional new results.
Formal quark binding and geometric strings
Authors: Lloyd-Evans D. J. R.
Published: March 2003

Geometric quantization is applied to a line bundle over spacetime with structure group GL(2,C)/SL(2,C) and curvature form determined by the Ricci tensor. The Ricci form is interpreted as the Hamiltonian form for a particle moving on a string associated with a harmonic oscillator spectrum. Strings are characterized as minimal surfaces, and quarks as the gradients of minimal immersions of surfaces in a three-dimensional spatial hypersurface, leading to a model of a baryon as the intersection of three such surfaces, and their associated quarks.
Clebsch–Gordan coefficients of finite magnetic groups
Authors: van den Broek P. M.
Published: March 2003

A detailed method is given for the calculation of Clebsch–Gordan coefficients of finite magnetic groups. This method is a generalization of a new method for the calculation of Clebsch–Gordan coefficients of finite nonmagnetic groups which makes use of the fact that the Clebsch–Gordan coefficients may be arranged into vectors which are eigenvectors of certain projection matrices.
Gel’fand–Levitan equations with comparison measures and comparison potentials
Authors: Moses H. E.
Published: March 2003

Using an abstract form of the Gel’fand–Levitan equation, it is shown how a solution of the equation corresponding to a given weight operator can be found in terms of a solution for the equation with a different weight operator. The resulting Gel’fand–Levitan equation is a generalization of the original one. To achieve our result, an analog of a canonical transformation for direct scattering is used. The effect of the use of the transformation is to include part of the scattering potential (the comparison potential) in the unperturbed Hamiltonian. The generalized Gel’fand–Levitan equation has the advantage that if the weight operator for a given Gel’fand–Levitan equation is close to that for an already solved Gel’fand–Levitan equation, the solution of the first can be obtained from the second by using the solution of the second as a first approximation in an iteration procedure or as a trial function in a variational procedure. The method is illustrated by considering the inverse problem for the one-dimensional Schrödinger equation, a generalized radial Schrödinger equation, and the Marchenko equation for the zero angular momentum radial Schrödinger equation. Though the use of a comparison weight function for some of the cases above has been given by others, the work of the present paper represents a systematic approach to the problem. The role of a variational principle will also be discussed.
Gauge theory in Hamiltonian classical mechanics : The electromagnetic and gravitational fields
Authors: Boisseau B. , Barrabès C.
Published: March 2003

Gauge potentials are directly defined from Hamiltonian classical mechanics. Gauge transformations belong to canonical transformations and are determined by a first order development of generating functions. The electromagnetic and gravitational fields, and they only, are obtained.
Quasiprobability distributions and the analysis of the linear quantum channel with thermal noise
Authors: Helstrom Carl W.
Published: March 2003

The quasiprobability distributions (QPD) introduced by Cahill and Glauber much simplify calculating the density operator of the output of a linear quantum channel from the density operator of the input when the channel attenuates and is corrupted by thermal noise. This channel models, for instance, an attenuator viewed as a simple harmonic oscillator in contact with a heat bath, or the relation between the radiating field mode in the aperture of a transmitter and the field mode it excites at the aperture of a distant receiver. It is shown how the attenuation and the noise in the channel modify the dependence of the QPD on the ordering parameter s. The form of the QPD at the output indicates that the greater the attenuation, the more nearly the state of the output resembles a classical state. Indeed, the addition of thermal noise contributing on the average only one photon suffices to convert an arbitrary unimodal state into a classical state. The principal result of the paper is applied to determining the output of a quantum channel whose input mode is in a generalized coherent state.
Deformations and spectral properties of merons
Authors: Gidas Basilis
Published: March 2003

We consider a meron–antimeron pair located at a, b, ∈ R4, and show that the spectrum of its stability operator is not bounded below [in precise mathematical terms: The stability operator defined on C∞0(R4−{a,b}) has a self-adjoint extension, possibly many, all of which are unbounded below]. We regularize a single meron located at the origin by replacing it inside a sphere of radius R0 and outside a sphere of radius R by ’’half instantons,’’ and show that for R≫R0 the regularized configuration continues to be unstable. For R0 finite and R=∞, we show that the spectrum of the stability operator continues to extend to −∞. We employ a singular transformation to embed R4 into S3×R where the meron pair takes a simple form and its stability operator ℒ becomes ℒ=−d2/dτ2+V, where τ∈R, and the potential V can be diagonalized in terms of the angular momenta, spin, and isospin of the vector field. The spectrum of ℒ is continuous and extends from −2 to +∞. We determine the number of (generalized) zero eigenmodes of ℒ, and calculate its spectrum explicitly.
A note on Sommerfeld’s diffraction problem
Authors: Sastry V. V. S. S. , Chakrabarti A.
Published: March 2003

A direct transform technique is found to be most suitable for attacking two-dimensional diffraction problems. As a first example of the application of the technique, the well-known Sommerfeld problem is reconsidered and the solution of the problem of diffraction, by a half-plane, of a cylindrical pulse is made use of in deducing the solution of the problem of diffraction of a plane wave by a soft half-plane.
Analysis of the dispersion function for anisotropic longitudinal plasma waves
Authors: Arthur M. D. , Bowden R. L. , Zweifel P. F.
Published: March 2003

An analysis of the zeros of the dispersion function for longitudinal plasma waves is made. In particular, the plasma equilibrium distribution function is assumed to have two relative maxima and is not necessarily an even function. The results of this analysis are used to obtain the Wiener–Hopf factorization of the dispersion function. A brief analysis of the coupled nonlinear integral equations for the Wiener–Hopf factors is also presented.
First-stage magnetization and metastable migration field in a type I superconducting slab
Authors: Fortini André , Hairie Alain , Girard Jean-Pierre
Published: March 2003

The penetration of the field in the edge of a type I superconducting slab, placed in a uniform magnetic field, perpendicular to its plane, is analyzed by means of a suited complex potential, derived from general methods used in Dirichlet’s type problems. The way of taking into account the singularities of the field distribution at the ends of the edge structure in the intermediate state, and the boundary conditions are discussed. A computational method is described for calculating the potential and flux profiles along the edges and thereby, the thermodynamic potential of the system. The first stage magnetization law together with the equilibrium dimensions of the edge structure and the previously defined migration threshold are deduced from the theory.
A new approach to inhomogeneous cosmologies: Intrinsic symmetries. II. Conformally flat slices and an invariant classification
Authors: Szafron D. A. , Collins C. B.
Published: March 2003

We continue our analysis of space–times with intrinsic symmetries, by specializing to the case where the matter moves orthogonally to a family of conformally flat hypersurfaces. In so doing, we obtain a characterization of the Szekeres inhomogeneous cosmological models as being those (perfect fluid) solutions of Einstein’s equations with conformally flat comoving slices whose second fundamental form and Ricci tensor possess two equal eigenvalues. An invariant characterization of these models is thereby obtained, and they are then classified in an invariant way.
A new approach to inhomogeneous cosmologies: Intrinsic symmetries. III. Conformally flat slices and their analysis
Authors: Collins C. B. , Szafron D. A.
Published: March 2003

We have already obtained an invariant characterization and classification of the Szekeres inhomogeneous cosmological models. In the present paper, we present a detailed study of the hierarchy of solutions. The approach adopted suggests simple generalizations of the Szekeres models, and we present a number of results and ideas for further study.
A new method of matrix transformation. I. Matrix diagonalizations via involutional transformations
Authors: Kim Shoon K.
Published: March 2003

It is shown that two matrices A and B of order n×n which satisfy a monic quadratic equation with two roots λ1 and λ2 are connected by ATAB=TABB where TAB=A+B−(λ1+λ2) I with I being the n×n unit matrix (Theorem 1). The condition for TAB to be involutional is that the anticommutator of ?=A−(1/2)(λ1+λ2) I and ?=B−(1/2)(λ1+λ2) is a c number (Theorem 2). A 2m×2m matrix Q(2m) is introduced as a typical form of a matrix which can be diagonalized by an involutional transformation. These theorems are further extended through the matrix representation of the group of the general homogeneous linear transformations, GL(n). IUH (involutional, unitary, and Hermitian) matrices are introduced and discussed. The involutional transformations are shown to play a fundamental role in the transformations of Dirac’s Hamiltonian and of the field Hamiltonians which are quadratic in particle creation and annihilation operators in solid state physics.
An application of the maximum principle to the study of essential self-adjointness of Dirac operators. I
Authors: Landgren J. J. , Rejto P. A.
Published: March 2003

We formulate a theorem saying that the Dirac operator corresponding to a one-electron atomic ion is essentially self-adjoint on the usual domain, provided that the nuclear charge Z is less than 118. Furthermore, for such nuclear charges the domains of the closure of the free particle and total Dirac operators are equal. In the present part I of this paper we prove this theorem for the part of the operator over each of the usual reducing subspaces.
Borel multipliers for the Bondi–Metzner–Sachs group
Authors: Cattaneo U.
Published: March 2003

It is shown that there exist only two cohomology classes of Borel multipliers for the Bondi–Metzner–Sachs group B when the subgroup of ’’supertranslations’’ is the additive group of a separable real Hilbert space. This implies that all Borel multipliers for the universal covering group ? of B are coboundaries and so every continuous unitary projective representation of B can be obtained from a continuous unitary (ordinary) representation of ?.
Deformations of gauge groups. Gravitation
Authors: Fang J. , Fronsdal C.
Published: March 2003

This is a review, and an attempt at completion, of the ’’Gupta program,’’ the ultimate goal of which is either to show that Einstein’s theory of gravitation is the only self-consistent field theory of interacting, massless, spin-2 particles in flat space or to discover interesting alternatives. It is useful to notice that the gauge group of general relativity is a deformation (in a mathematically precise sense) of the gauge group associated with the massless, spin-2 free field. The uniqueness of Einstein’s theory depends on the stability of its gauge group with respect to a class of differentiable deformations. A generalized Gupta program for massless fields of arbitrary spins is proposed.
Unitarity and renormalized ’t Hooft identities
Authors: Naito Seichi
Published: March 2003

With the help of the generalized Slavnov identities in a spontaneously broken gauge model, we compactly and explicitly prove renormalized ’t Hooft identities which lead to the unitarity of the renormalized S matrix.
Generalized method of a resolvent operator expansion. II
Authors: Znojil M.
Published: March 2003

The second part of the present series is devoted to the rearrangement of the Born series in the model space. An application is found in pion–nucleus scattering. We present a generalization of the ’’extended schematical model’’ suggested recently by Hirata et al.
On the Lorentz–Dirac equation
Authors: Sanz J. L.
Published: March 2003

We study the problem of a charged particle affected by an external electromagnetic field, adopting the point of view that its evolution is governed by an autonomous ordinary second order system of differential equations on M4 whose acceleration can be expanded into a power series of the charge e and assuming the acceleration satisfies the Lorentz–Dirac equation. Thus, we locate the dynamics of the system in a symplectic structure up to order e3 for external fields satisfying certain weak conditions. This is applied to obtain conserved quantities associated to symmetries of the external field that are also isometries.
A new approach to inhomogeneous cosmologies: Intrinsic symmetries. I
Authors: Collins C. B. , Szafron D. A.
Published: March 2003

After briefly discussing systematic ways of studying inhomogeneous cosmologies, we propose the technique of ’’intrinsic symmetries,’’ in which restrictions are placed on submanifolds of space–time. This leads to a broad classification of inhomogeneous cosmologies, and to an associated specialization diagram. By enforcing additional restrictions we obtain a further useful specialization.
Classical non-Abelian gauge theories in the space of reference frames
Authors: Cognola G. , Soldati R. , Vanzo L. , Zerbini S.
Published: March 2003

Classical non-Abelian gauge theories in presence of gravitation are reformulated in the language of the space of local reference frames. The geometric structure of this space, the transformation properties of the fields, and the possibility of introducing a covariant derivative are not assumed a priori, as in the usual classical theory, but they are deduced from a Lagrangian form and an action principle. Some examples of Lagrangian forms and the related equations of motion for the gauge fields and the matter fields are discussed.
Reduction of the two-dimensional O(n) nonlinear σ-model
Authors: Pohlmeyer K. , Rehren K.-H.
Published: March 2003

We reduce the field equations of the two-dimensional O(n) nonlinear σ-model to relativistic O(n−2) covariant differential equations involving n−2 scalar fields.
Normal form for mirror machine Hamiltonians
Authors: Dragt Alex J. , Finn John M.
Published: March 2003

A systematic algorithm is developed for performing canonical transformations on Hamiltonians which govern particle motion in magnetic mirror machines. These transformations are performed in such a way that the new Hamiltonian has a particularly simple normal form. From this form it is possible to compute analytic expressions for gyro and bounce frequencies. In addition, it is possible to obtain arbitrarily high order terms in the adiabatic magnetic moment expansion. The algorithm makes use of Lie series, is an extension of Birkhoff’s normal form method, and has been explicitly implemented by a digital computer programmed to perform the required algebraic manipulations. Application is made to particle motion in a magnetic dipole field and to a simple mirror system. Bounce frequencies and locations of periodic orbits are obtained and compared with numerical computations. Both mirror systems are shown to be insoluble, i.e., trajectories are not confined to analytic hypersurfaces, there is no analytic third integral of motion, and the adiabatic magnetic moment expansion is divergent. It is expected also that the normal form procedure will prove useful in the study of island structure and separatrices associated with periodic orbits, and should facilitate studies of breakdown of adiabaticity and the onset of ’’stochastic’’ behavior.
Continuum theory of nematic liquid crystals subject to electromagnetic fields
Authors: Eringen A. Cemal
Published: March 2003

A continuum theory is presented for the nematic liquid crystals subject to electromagnetic interactions. Complete field equations, jump conditions, and constitutive equations are obtained. The thermodynamic restrictions are studied. The field equations obtained are employed to examine the problem of Fredericksz’ transition.
The growth of wave discontinuities in piezoelectric semiconductors
Authors: McCarthy M. F. , Tiersten H. F.
Published: March 2003

The reference coordinate description of the general nonlinear differential equations describing the interaction of finitely deformable, polarizable, n-type semiconductors with the quasistatic electric field is applied in the study of acceleration waves in piezoelectric semiconductors. As a consequence, the mechanical and dielectric nonlinearities are included in the treatment as well as the semiconduction nonlinearity. The general equation for the propagation velocity of the disturbance is obtained as a function of the state of the material immediately ahead of the wavefront. In the special case of plane waves entering a homogeneous steady state, the growth equation for the amplitude of the acceleration wave is determined and, of course, the propagation velocity and coefficients in the growth equation depend on the propagation direction, but otherwise are constant. The relation between acceleration waves and the formation and propagation of acoustoelectric domains is indicated. The solutions of the growth equation indicate the formation of a shock in a finite time for conditions conducive to domain formation except in certain unusual cases possibly occurring with purely transverse acceleration waves. In the course of the treatment the condition for the threshold field for domain formation is determined under quite general circumstances. When the electrical conduction equation, which can be quite general in this treatment, is specialized to the simple form usually employed for anisotropic semiconductors, the aforementioned more general condition reduces to the anisotropic generalization of the well-known elementary result. In addition, the behavior of weak waves is discussed.
Solution of the wave equation for the logarithmic potential with application to particle spectroscopy
Authors: Müller-Kirsten H. J. W. , Bose S. K.
Published: March 2003

We present an almost complete solution of the Schrödinger equation for a logarithmic potential. In particular we obtain two pairs of high-energy asymptotic expansions of the boundstate eigenfunctions together with a corresponding expansion of the eigenvalue determined by the secular equation. We also obtain a pair of uniformly convergent solutions and a pair of uniform asymptotic expansions. Various properties of the solutions and eigenvalues are examined, including the scattering problem of the cut-off potential and the behavior of Regge trajectories. Finally the relevance of these investigations to the spectroscopy of heavy quark composites is discussed. In particular we point out that the relevance of the logarithmic potential can be tested only if more than two consecutive energy levels are known. In a separate paper the methods outlined here are applied to quark-confining potentials of the generalized power type.
The radial reduced Coulomb Green’s function
Authors: Johnson Bruce R. , Hirschfelder Joseph O.
Published: March 2003

The reduced Green’s function, gnl(r,r′), of the radial hydrogenic Schrödinger equation is simplified for all values of n and l, l⩽n−1, to a closed form appropriate for analytic treatments of Rayleigh–Schrödinger perturbation theory. Integral moments of the form ∫0∞dr′ gnl(r,r′) (r′)k+2exp(−Zr′/n) are given. It is also shown how gnl is connected to gn,l±1 by the ladder operators of the factorization method. Recursion relations are derived between integrals that arise in perturbation theory. The above results are generalized to the case l⩾n, which occurs in the Green’s functions required for the Rayleigh–Schrödinger perturbation treatment even though it does not arise for the eigenfunctions. As an example of the use of the reduced Green’s functions, the first-order wave function and second-order energy corresponding to the spin-orbit interaction is evaluated for any bound state.
A representation of multiparticle scattering operators satisfying unitarity and crossing properties
Authors: Klink W. H.
Published: March 2003

A representation for multiparticle scattering operators satisfying unitarity and crossing properties is presented. The representation is given in terms of a set of functions that satisfy orthogonality, completeness and analyticity conditions. It is shown that integrals over these functions yield inclusive cross sections.
On the multiplicity-free Wigner and Racah coefficients of U(n)
Authors: Wong M. K. F.
Published: March 2003

A necessary and sufficient condition is found for the tensor operators of U(n) to be multiplicity-free. At present all matrix elements for the multiplicity-free tensor operators of U(n) are known explicitly in closed form. The phase convention given by Wong in a previous paper is modified slightly. Some inconsistencies in the equations found in the two previous papers of Wong regarding phase factors are corrected. The present phase convention for the multiplicity-free Wigner and Racah coefficients of U(n) is the most general extension of the Condon–Shortley phase convention from U(2) to U(n).
Meromorphic solutions of nonlinear partial differential equations and many-particle completely integrable systems
Authors: Chudnovsky D. V.
Published: March 2003

Complete description of meromorphic solutions of several two-dimensional equations with algebraic laws of conservation is obtained. Among them are Zakharov–Shabat systems and, e.g., the Kadomtsev–Petiashvili equation.
A guiding center Hamiltonian: A new approach
Authors: Littlejohn Robert G.
Published: March 2003

A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B (x,y) ? is studied. Lie transforms are used to carry out the perturbation expansion.
Off-shell scattering by Coulomb-like potentials
Authors: van Haeringen H.
Published: March 2003

We derive closed expressions for and interrelationships between off-shell and on-shell scattering quantities for Coulomb plus short-range potentials. In particular we introduce off-shell Jost states and show how the transition matrices are obtained from these states. We discuss some formulas connecting the coordinate and momentum representatives of certain quantities. For the pure Coulomb case we derive analytic expressions for the Jost state and the off-shell Jost state for l=0 in the momentum representation.
Symmetries of the stationary Einstein–Maxwell field equations. V
Authors: Hoenselaers C.
Published: March 2003

This paper shows that the field equations and the hierarchy of potentials for static electrovac fields can be formulated in close analogy to the stationary vacuum ones. A list of transformations, some of them previously unknown, will be given for the later case.
Symmetries of the stationary Einstein–Maxwell equations. VI. Transformations which generate asymptotically flat spacetimes with arbitrary multipole moments
Authors: Hoenselaers C. , Kinnersley William , Xanthopoulos Basilis C.
Published: March 2003

A new series of transformations is presented for generating stationary axially symmetric asymptotically flat vacuum solutions of Einstein’s equations. The application requires only algebraic manipulations to be performed. Several examples are given of new stationary axisymmetric solutions obtained in this way. It is conjectured that the transformations, applied to the genral Weyl metric, can be used to generate systematically all stationary metrics with axial symmetry.
Charged fluid sphere in general relativity
Authors: Pant D. N. , Sah A.
Published: March 2003

An analytic solution of the relativistic field equations is obtained for a static, spherically symmetric distribution of charged fluid. The arbitrary constants are determined by matching it with the Reissner–Nordström solution over the boundary. The distribution behaves like a charged perfect gas. As a particular case a solution for a spherical distribution of charged incoherent matter is deduced where the charge density and the mass density are equal in magnitude. In the absence of the charge, the solution reduces to Tolman’s solution VI with B=0.
Covariant perturbed wave equations in arbitrary type-D backgrounds
Authors: Dudley Alan L. , Finley J. D.
Published: March 2003

We present an approach to the fundamental tensorial quantities of general relativity which is inherently covariant and based on the irreducible representations of the Lorentz group, O(3,1). Using this technique, the wave equations appropriate to perturbing, massless, D(0,s), fields in an arbitrary curved background are studied and a relationship between the decoupling of (at least) one of the equations and the algebraic degeneracy of the spacetime is shown. It is then found that sufficient conditions for decoupling the equations determining both of the radiative components (the extremal helicities) are that the space be of type D. Using Plebański–Demiański coordinates to describe such an arbitrary vacuum spacetime (of type D), we separate the (decoupled) perturbation equations for the radiative components corresponding to spin s=0, 1/2, 1, and 2.
On the completeness of the natural modes for quantum mechanical potential scattering
Authors: Hoenders B. J.
Published: March 2003

The set of natural modes, associated with quantum mechanical scattering from a central potential of finite-range is shown to be complete. The natural modes satisfy a non-Hermitian homogeneous integral equation, or alternatively, are solutions of the time independent Schrödinger equation subject to a recently formulated nonlocal boundary condition (the quantum mechanical extinction theorem). An expansion theorem similar to that of Hilbert–Schmidt is formulated, valid for values of the solution of the scattering integral equation inside the range of the potential. The boundary conditions generated by the quantum mechanical extinction theorem are shown to be closely connected with the Jost function.
Invariant operators of IU(n) and IO(n) and their eigenvalues
Authors: Wong M. K. F. , Yeh Hsin-Yang
Published: March 2003

A systematic explicit evaluation of the invariant operators of IU(n) and IO(n) has been carried out. It is found that the invariant operators of IU(n) and IO(n) can be obtained from those of U(n,1) and O(n,1) by simple substitution. Similarly the eigenvalues of the invariant operators of IU(n) and IO(n) can be obtained from those of U(n,1) and O(n,1) by simple substitution. Since the invariant operators and their eigenvalues of U(n,1) and O(n,1) are closely related to those of U(n+1) and O(n+1) our results can be expressed in explicitly closed and simple form.
Conformal Killing horizons
Authors: Dyer C. C. , Honig E.
Published: March 2003

We introduce the concept of a conformal stationary limit surface as the boundary where a conformal Killing vector admitted by a spacetime becomes null. This hypersurface is an infinite frequency shift surface for conformal Killing observers and sources. We derive the local conditions under which it can be an event horizon in the sense that it be a null geodesic hypersurface. In particular, we show that it is null and geodesic if and only if the rotation of the conformal Killing congruence has a vanishing norm on this hypersurface. Finally, we discuss the surface gravity associated with such a conformal Killing horizon.
Constrained Hamiltonian formulation for interacting fields: Stable particlelike solutions
Authors: Rosen Gerald , Jakubowicz Oleg , Tatoian Vahe
Published: March 2003

It is observed that singularity-free localized particlelike solutions to certain essentially nonlinear classical field equations are dynamically stable in a constrained free-field Hamiltonian formulation. Being rather novel, the variational principle for such a theory pertains to an arbitrary pair of neighboring solutions to the field equations, with δφ specified as the difference between neighboring solutions.
Lie algebras associated with motion in axisymmetric electromagnetic fields
Authors: Mitchell Thomas P.
Published: March 2003

The existence and analytical form of a vector constant of the classical relativistic planar motion of a point charge in an arbitrary time-independent axisymmetric electromagnetic field are established. The components of the vector are utilized, in conjunction with the angular momentum, to construct realizations of the Lie algebras of the Euclidean group E(2), of the special unitary group SU(2), and of the Ladder operators of the harmonic oscillator. The charge is assumed to move in an externally prescribed field. The formulation is gauge invariant.
Representations of a para-Bose algebra using only a single Bose field
Authors: Jagannathan R. , Vasudevan R.
Published: March 2003

Representations of a para-Bose algebra are given entirely in terms of the operators of a single Bose field. Incidentally some types of boson representations of a nonsemisimple graded Lie algebra of the three-dimensional Lorentz group are obtained.
Computation of a class of 3j-coefficients
Authors: Sage Martin L. , Wali Kameshwar C.
Published: March 2003

We give an analytical procedure to calculate 3j-coefficients (lm l−m 2j0) for arbitrary integer l.
Semiclassical perturbation expansion of the multichannel scattering matrix
Authors: Bosanac S.
Published: March 2003

A semiclassical perturbation method for the inelastic S matrix is described. The channels are transformed into a set of the eigenstates and it is assumed that the transition between them is small. The perturbation is the matrix which diagonalizes the coupling matrix. It is shown that such a series is independent of h/; hence the limit h/ →0 of the S matrix can be calculated. A special case of the weak coupling is also discussed.
Linearization stability of gravitational and gauge fields
Authors: Arms Judith M.
Published: March 2003

Conditions are given for the linearization stability of the Yang–Mills and the Einstein–Yang–Mills equations on a spacetime with a compact Cauchy surface. There are sufficient conditions on the Cauchy surface, and necessary and sufficient conditions on the spacetime; the latter are identified with global infinitesimal symmetries of the principal fiber bundle associated with the Yang–Mills (gauge) field. For each system a splitting theorem for the initial data is given and the Cauchy problem is discussed.