bluuebunny/crossref_metadata_2025 huggingface dataset:
Unified gauge theory for electromagnetism and gravitation based on twistor bundles
Authors: Luehr C. P. , Rosenbaum M.
Published: March 2003

A unified gauge theory of the combined gravitational and electromagnetic fields is obtained by two different procedures using twistors as a starting point for the construction of the appropriate bundles. One of these formalisms is obtained by relaxing the conditions on the structure of a twistor bundle theory previously developed by the authors for the Poincaré group as the structure group. The other formalism is based on a tensor product bundle and can be readily extended to include structure groups involving direct products of nonabelian groups with the Poincaré group. The results of the theory are compared with those obtained in projective theories of the generalized Jordan–Kaluza–Klein type, and some of the essential differences are pointed out.
The U(6) Λ SU(3) hidden symmetry in collective excitations of many-body systems
Authors: Castaños O. , Frank A.
Published: March 2003

We analyze the problem of an A-nucleon system interacting through harmonic oscillator forces in terms of variables which separate collective and noncollective aspects of the Hamiltonian. To study the symmetry group of the collective Hamiltonian in the limit when A is very large, we carry out a group contraction on the dynamical group generators for the system, which permits the identification of this group as U(6) Λ SU(3). In addition, an explicit realization for the symmetry group generators is given in terms of Bohr- and Mottelson-like variables.
The ballooning spectrum of rotating plasmas
Authors: Hameiri Eliezer , Laurence Peter
Published: March 2003

Ballooning modes are shown to be part of the spectrum by using a ‘‘singular sequence’’ of localized modes. We show that the modes arise from Alfven and slow magnetosonic waves propagating along rays confined inside the plasma. Different ballooning modes are seen, depending on the particular rotating frame of observation, indicating that there are accumulation points of eigenvalues. The effect of rigidly rotating flow is seen to be destabilizing due to an analog of the Rayleigh–Taylor instability associated with density gradients in the presence of a centrifugal force. Flow shear also modifies the stability criterion. A certain component of the flow shear will eliminate the ballooning modes.
Global attractors and global stability for closed chemical systems
Authors: Fernández Ariel , Sinanoǧlu Oktay
Published: March 2003

The structural stability in the sense of Adronov and Pontriaguin for kinetic models of a closed reacting mixture is investigated. Necessary and sufficient conditions for the mass-action kinetics model to be structurally stable are derived.
Higher-dimensional Riemannian geometry and quaternion and octonion spaces
Authors: Moffat J. W.
Published: March 2003

An eight-dimensional Riemannian geometry is shown to be the basis of a nonsymmetric theory of gravitation. A hyperbolic complex structure is imposed and the group structure is GL(8,R)→GL(4,R)⊗GL(4,R)⊇GL(4,R). Octonion and quaternion division algebras are used to represent geometrical quantities and spinors. A Lagrangian is constructed that is related to supersymmetry and supergravity theories. The group structure for a hyperbolic octonion scheme is GL(8,qH)→GL(4,OH)≂GL(4,qH) ⊗GL(4,qH)⊇GL(4,qH), while a simpler scheme based on hyperbolic quaternions is GL(8,C)→GL(4,qH)≂GL(4,C)⊗GL(4,C)⊇GL(4,C).
An exact recursion for the composite nearest-neighbor degeneracy for a 2×N lattice space
Authors: McQuistan R. B. , Hock J. L.
Published: March 2003

A set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest-neighbor degeneracy for simple, indistinguishable particles distributed on a 2×N lattice space. The associated generating functions, as well as the expectation of the resulting statistics are also treated.
Symplectic approach to nonconservative mechanics
Authors: Cantrijn F.
Published: March 2003

The dynamics of autonomous nonconservative systems is studied in terms of Lagrangian submanifolds of a special symplectic manifold. Both the Hamiltonian and Lagrangian description are taken into consideration and the transition between the two descriptions is established by means of the generating function of a symplectic relation.
A unified theory of the point groups. V. The general projective corepresentations of the magnetic point groups and their applications to magnetic space groups
Authors: Kim Shoon K.
Published: March 2003

This paper presents the general expressions of the projective irreducible corepresentations of the 20 homologous sets of the magnetic double point groups from which follow all those of the remaining groups of finite order through isomorphisms (the icosahedral group is excluded). These are explicitly given in terms of the irreducible representations of the unitary double point groups. Their special cases provide all the irreducible corepresentations of all magnetic space groups of wave vector through simple gauge transformations. A method of determining the gauge transformations is discussed through typical examples.
Identities satisfied by the generators of the Dirac algebra
Authors: Nash Patrick L.
Published: March 2003

The geometry of real four-dimensional spinor space and its symmetry groups are reviewed from the perspective of S̄Ō(̄3̄,̄3̄)̄. Two identities that concern the matrix generators of S̄Ō(̄3̄,̄3̄)̄, and which were first proved by Dirac, are generalized.
Infinitesimal symmetry transformations of some one-dimensional linear systems
Authors: Aguirre M. , Krause J.
Published: March 2003

The converse problem of similarity analysis is solved in general for the infinitesimal symmetry transformations of any given inhomogeneous ordinary differential equation of the second order ẍ+f2(t)ẋ+f1(t)x=f0(t). The completely general associated Lie algebra is obtained for equations of this kind, which structure constants depend only on the chosen set of initial values  f0(0),  f1(0),  f2(0), and  ḟ2(0). The infinitesimal elements of the dynamical group of a Newtonian one-dimensional linear system are also discussed, and some miscellaneous examples are given.
General indices of representations and Casimir invariants
Authors: Okubo S. , Patera J.
Published: March 2003

A modified definition of the index of degree p of a finite-dimensional representation of a simple Lie algebra is given. The definition applies equally to even and odd p. The correspondence between the earlier definitions of indices (even p) and anomaly numbers (odd p) is pointed out as well as the relation to Casimir invariants of the algebra. A closed formula for the fifth-order index is derived.
On Lie–Bäcklund vector fields of the evolution equations ∂2u/∂x ∂t=f(u) and ∂u/∂t=∂2u/∂x2+f(u)
Authors: Steeb W.-H.
Published: March 2003

For the evolution equations ∂2u/∂x ∂t=f(u) and ∂u/∂t=∂2u/∂x2+f(u) we derive the analytic functions f where Lie–Bäcklund vector fields are admitted.
SU(3) symmetry of the equations of unidimensional gas flow, with arbitrary entropy distribution
Authors: Gaffet B.
Published: March 2003

We have shown in an earlier work that, assuming a particular class of equations of state, the Euler equations of one-dimensional gas flow are invariant under an SU(3) group of transformations, and in fact admit of a Lie group of symmetry of infinite order; they, therefore, possess an infinite number of conservation laws. We show in the present work that the SU(3) symmetrical formalism still brings about tremendous simplification and analytical order in the most general case where the equation of state is arbitrary. The six characteristic equations assume a vector form and relate two conjugate, three-dimensional vectors U and X. The SU(3) symmetry is only broken to a minor extent through the occurrence of a multiplicative factor Γ in the equations. The conservation laws take the form of the Cauchy integrability condition for the elements of a traceless second rank tensor εij and, taken all together, form an SU(3) octet; in the most general case, however, there exist four conservation laws only (five if the gas is monatomic) as a result of the breaking of symmetry. Application of these results to the theory of self-similar flow is also discussed. Finally, we show the invariance of the equations of monatomic gas flow under Lorentz transformations in a three-dimensional Minkowski space; that raises the question of whether a geometrical relation may exist between the Minkowski light cones and characteristics.
The continuous Heisenberg chain and constrained harmonic motion
Authors: Lund Fernando
Published: March 2003

It is shown that the equation describing the evolution of the classical continuous Heisenberg ferromagnet can be regarded as one aspect of quadratically constrained harmonic motion, as it is also the case in a number of other integrable systems. Two ingredients are used: a method to solve the inverse scattering problem for second-order operators using ordinary differential (rather than integral) equations and the equivalence of the Heisenberg chain with the nonlinear Schrödinger equation.
Derivation and application of extended parabolic wave theories. I. The factorized Helmholtz equation
Authors: Fishman Louis , McCoy John J.
Published: March 2003

The reduced scalar Helmholtz equation for a transversely inhomogeneous half-space supplemented with an outgoing radiation condition and an appropriate boundary condition on the initial-value plane defines a direct acoustic propagation model. This elliptic formulation admits a factorization and is subsequently equivalent to a first-order Weyl pseudodifferential equation which is recognized as an extended parabolic propagation model. Perturbation treatments of the appropriate Weyl composition equation result in a systematic development of approximate wave theories which extend the narrow-angle, weak-inhomogeneity, and weak-gradient ordinary parabolic (Schrödinger) approximation. The analysis further provides for the formulation and exact solution of a multidimensional nonlinear inverse problem appropriate for ocean acoustic and seismic studies. The wave theories foreshadow computational algorithms, the inclusion of range-dependent effects, and the extension to (1) the vector formulation appropriate for elastic media and (2) the bilinear formulation appropriate for acoustic field coherence.
Derivation and application of extended parabolic wave theories. II. Path integral representations
Authors: Fishman Louis , McCoy John J.
Published: March 2003

The n-dimensional reduced scalar Helmholtz equation for a transversely inhomogeneous medium is naturally related to parabolic propagation models through (1) the n-dimensional extended parabolic (Weyl pseudodifferential) equation and (2) an imbedding in an (n+1)-dimensional parabolic (Schrödinger) equation. The first relationship provides the basis for the parabolic-based Hamiltonian phase space path integral representation of the half-space propagator. The second relationship provides the basis for the elliptic-based path integral representations associated with Feynman and Fradkin, Feynman and Garrod, and Feynman and DeWitt-Morette. Exact and approximate path integral constructions are derived for the homogeneous and transversely inhomogeneous cases corresponding to both narrow- and wide-angle extended parabolic wave theories. The path integrals allow for a global perspective of the transition from elliptic to parabolic wave theory in addition to providing a unifying framework for dynamical approximations, resolution of the square root operator, and the concept of an underlying stochastic process.
The Doppler effect: Now you see it, now you don’t
Authors: Censor Dan , Le Vine D. M.
Published: March 2003

Two main classes of problems are identified in the theory of electromagnetic scattering in velocity-dependent systems. The first involves transformation of space and time coordinates and field components from the laboratory system of reference to the comoving system of the scatterer, solution of the scattering problem, and inverse transformations. In general, this method displays the Doppler frequency shifts. The second class involves the substitution of Minkowski’s constitutive relations into Maxwell’s equations for harmonic time variation, heuristically stipulating the absence of Doppler frequency shifts. The interrelation between the two methods is investigated here. It is argued that the second method is a limiting case for very low, as well as very high frequencies, and provided the mean square fluctuation of the dielectric constant is small, and the geometrical boundaries defining the scatterers are fixed. Canonical problems of plane, cylindrical, and spherical stratification are discussed and analytical results for the scattered fields are derived. If the parameters of the problem do not meet the above conditions, the first method should be used, giving rise, in general, to a whole spectrum of frequencies due to the Doppler effect.
A note on fluctuations of weak gravitational radiation and the classical Hanbury Brown–Twiss effect
Authors: Mallett Ronald L.
Published: March 2003

We comment on the possible application of the Hanbury Brown–Twiss method to the study of the classical statistical properties of weak gravitational radiation from chaotic microscopic sources.
A class of shear-free perfect fluids in general relativity. I
Authors: White A. J. , Collins C. B.
Published: March 2003

It has been conjectured that shear-free perfect fluids in general relativity, with an equation of state p=p(μ) and satisfying μ+p≠0, necessarily have either zero expansion or zero vorticity. We prove that this result holds in the restricted case when the fluid’s vorticity and acceleration are parallel. Specifically, we prove that if the vorticity is nonzero, the fluid’s volume expansion must vanish.
The gravitational fields of some rotating and nonrotating cylindrical shells of matter
Authors: Stachel John
Published: March 2003

The exterior and flat interior metrics of an infinite cylindrical shell (surface layer) of matter are studied, for nonrotating and rigidly rotating shells. Relations between the parameters characterizing the exterior metric and the components of the shell’s stress-energy tensor are established. It is shown that one of these parameters, characterizing the ‘‘conicality’’ of the exterior field, is related to the energy density of the source; while another, characterizing local nonflatness, is related to certain components of the stress tensor. A one-parameter family of locally flat but conical exterior metrics generated by a particular type of massive cylindrical shell is exhibited. The globally stationary but locally static exterior field of a rigidly rotating shell is studied. The (nonlocal) parameter of the exterior field characterizing the rotation is related to the rate of rotation of the shell as defined by the flat interior metric.
Null strings and Hertz potentials
Authors: Torres del Castillo G. F.
Published: March 2003

A covariant expression for the massless spinor fields in terms of Hertz potentials is given, assuming that the space-time admits a congruence of null strings defined by a multiple Debever–Penrose spinor. The metric of these spaces is also given in a covariant form.
Accelerating black hole in a magnetic field
Authors: Krori K. D. , Chaudhury Sumita , Dowerah S.
Published: March 2003

This paper presents an investigation of the geometrical properties of an accelerating black hole embedded in a magnetic field.
The metric dependence of four-dimensional formulations of electromagnetism
Authors: Post E. J.
Published: March 2003

The following is a comment on a recent paper by Birss [R. R. Birss, J. Math. Phys. 23, 1153 (1982)] under the above title. The objective is to supplement the conclusion arrived therein and to confront an ensuing conflict between flux quantization and the recently revived hypothesis of magnetic charge quantization.
Borchers algebra formulation of an indefinite inner product quantum field theory
Authors: Jakȯbczyk Lech
Published: March 2003

Formulation of an indefinite inner product quantum field theory in terms of so-called Strocchi–Wightman states is investigated. In particular, the reconstruction theorem for such states is discussed. We consider also general properties of field theory reconstructed from a Strocchi–Wightman state.
Spin-1/2 quantum field theory in nonstatic space-times. I. Construction of states
Authors: Najmi Amir-Homayoon
Published: March 2003

The problem of constructing states for a Hermitian spin- (1)/(2) quantum field in a nonstatic background geometry is considered and the solution corresponding to the extremization of the total energy at an initial time is obtained.
On zeta function regularization for operators with continuous spectra
Authors: Gallatin G. M.
Published: March 2003

We present the generalization of the method of zeta function regularization for operators with continuous spectra where one cannot interchange the order of integration and limit processes. A sample calculation is presented.
A possible approach to the construction of the :exp ξ:d quantum field theory in a finite volume
Authors: Osipov Edward P.
Published: March 2003

Using a solution of some Euclidean invariant problem of moments, we construct a Euclidean realization (= a Euclidean field) for the Wightman–Jaffe quantum field :exp φ(x):d, where φ(x) is the free quantum field. With the help of this Euclidean realization we propose a new nonperturbative mathematically rigorous approach to the construction of the quantum field theory with the exponential interaction in a finite volume of d-dimensional space-time (d≥2) and without ultraviolet cutoffs. In particular, for pure imaginary values of the coupling constant the generating functional for Schwinger functions is constructed. The expansion of the theory which is constructed by using this method in powers of the coupling constant gives the renormalized perturbation series.
Separable systems for the Dirac equation in curved space-times
Authors: Rüdiger Roland
Published: March 2003

In this paper, the consequences of the existence of a Killing–Yano tensor for the separability of the general relativistic Dirac equation in an exterior electromagnetic field are investigated. Those properties of Killing–Yano tensors, which are relevant for the subject of this work, are reviewed; it is then shown that for any class of metrics admitting this type of tensor the Dirac equation can be separated at least once. Furthermore, all separable systems which are obtained in this way are stated explicitly. Finally, for the special case of the Kerr solution, the formalism of the present paper is compared with Chandrasekhar’s work on the separability of the Dirac equation.
On the Weyl group, its little groups, and associated massless particle descriptions
Authors: Hussin V. , Beckers J.
Published: March 2003

The Weyl or similitude group of space-time is studied in order to get invariant (free) wave equations for massless particles. We deduce the extended Wigner little groups of the Weyl group and define new operators related to the generators of these little groups in order to get wave equations for arbitrary (but nonzero) helicity particles. The Maxwell theory is also discussed through the action of our operators on electromagnetic tensors.
Bifurcation and the magnetic multipole solutions of the Yang–Mills equations with sources
Authors: Oh C. H.
Published: March 2003

It is shown that any Sikivie–Weiss-type magnetic multipole solution possesses a bifurcation point and it has the corresponding abelian Coulomb solution as its partner branch, which is unstable. The magnetic multipole solution is the stable branch.
Bäcklund transformations for spherically symmetric solutions to the self-dual Yang–Mills equations
Authors: Dodd Roger K. , Morris Hedley C.
Published: March 2003

Prolongation techniques are used to derive a linear deformation problem for self-dual spherically symmetric solutions of the SU(2) Yang–Mills equations. Bäcklund transformations are then obtained which generate solutions to these equations. We use the transformations to generate some new solutions to the equations.
Compact gauge group representations without triangular anomalies
Authors: Saliu L. , Tătaru L.
Published: March 2003

By formulating the anomaly-free condition in terms of the fully symmetric third-order Casimir operators, we find all safe algebras and the algebraic equations satisfied by the highest weights of the anomaly-free representations of the only nonsafe algebras An, n≥2. By solving these equations for the irreducible representations of An−1 [SU(n)], n=3, 4, 5, and 6, we obtain the generating formulas of the highest weights for all anomaly-free representations of these groups. It turns out that for SU(n), n≥5 there is an infinite set of anomaly-free complex irreducible representations grouped as infinite series of such representations. Using the same technique, the infinite series of complex anomaly-free representations containing the lowest-dimension ones for SU(n), n=7, 8, 9, and 10 are determined.
The theory of superselection rules. II. Sectors of the free electromagnetic field
Authors: Ekhaguere G. O. S.
Published: March 2003

In the first part of this study [J. Math. Phys. 19, 1751 (1978)], a wide class of inequivalent irreducible *-representations of the C*-algebra 𝔄 of quasilocal observables of the free electromagnetic field was constructed and analyzed. A *-representation π is called positive if it satisfies the spectrum condition, i.e., if space-time automorphisms are implemented in π by a strongly continuous unitary representation of Minkowski space M4 whose infinitesimal generator has spectrum contained in the forward light cone. Here, we characterize the subclass of the class of *-representations constructed in Ref. 1, which consists of positive *-representations. This then leads to the exhibition of new superselection sectors, i.e., equivalence classes of positive *-representations.
Coulomb-modified scattering parameters for Coulomb-plus-separable potentials for all l
Authors: de Maag J. W. , Kok L. P. , van Haeringen H.
Published: March 2003

For three different separable-potential models, closed analytical expressions are presented for the Coulomb-modified scattering length and effective range for all values of the angular-momentum quantum number, l=0,1,2,... . In the derivation of these results, use is made of the regular and irregular Coulomb wave functions that are entire analytic in k2. It is shown that the Coulomb-modified effective-range function can be written as a simple expression involving these entire-analytic functions.
Relativistic motion of a charged particle, the Lorentz group, and the Thomas precession
Authors: Salingaros Nikos
Published: March 2003

The equation of motion of a classical charged particle in a homogeneous, static electromagnetic field is solved exactly in terms of a Lorentz transformation. All higher-order corrections to the motion follow from the Baker–Campbell–Hausdorff formula. Some of these terms, as well as corrections to the Thomas precession, are calculated here for the first time. The derivation is based on an intrinsic formulation of the Lorentz group using
Theory of nonlocal piezoelectricity
Authors: Eringen A. Cemal
Published: March 2003

Constitutive equations are derived for nonlinear and linear, nonlocal piezoelectric elastic solids. Restrictions arising from the second law of thermodynamics are determined. The theory of nonlocal em elastic solids is introduced and applied to the discussion of Debye screening of an electron in an elastic solid with defect and dispersion of optical and piezoelectric waves.
Non-self-adjoint Zakharov–Shabat operator with a potential of the finite asymptotic values. II. Inverse problem
Authors: Asano Naruyoshi , Kato Yusuke
Published: March 2003

The inverse spectral and scattering problem of the Zakharov–Shabat (ZS) operator is studied. The similarity transformation between ZS operators is examined when their potentials Q(x) have the common nonvanishing asymptotic values Q± at the infinity. The Marchenko equation is derived from the Parseval equation. We give the necessary as well as the sufficient condition of the scattering data for the potential of the specified class.
Continued fraction expansions for the complete, incomplete, and relativistic plasma dispersion functions
Authors: Peratt Anthony L.
Published: March 2003

In our investigation of the linear theory of waves in plasma and the stability of relativistic beam-plasma systems, we have been led to consider methods for the evaluation of integrals of the form ∫dχ(χ−ζ)−1 exp(−χ2) and ∫dχ(χ−ζ)−1 exp[(1−χ2)−1/2] for complex ζ. In this work, we report on the evaluation of this integral and its derivative by means of continued fraction expansions. The expressions derived allow the precise calculation of these integrals in previously inaccessible regions. Additionally, applications to non-Maxwellian particle distributions, such as those found in the analysis of plasma diodes, are included.
Scattering by a penetrable body
Authors: Ramm A. G.
Published: March 2003

An integral equation equivalent to the interface problem is derived. A numerical scheme for its solution is given. Convergence of the scheme is established.
Three-term recursion relations for hydrogen wave functions: Exact calculations and semiclassical approximations
Authors: de Prunelé E.
Published: March 2003

Three-term recursion relations with respect to the angular momentum l are given for the normalized hydrogen wave functions associated with r, pr, p (r is the radial polar coordinate in configuration representation, pr is the momentum conjugated to r, p is the radial polar coordinate in momentum representation). These three-term recursion relations [Eqs. (4), (6), (16)] are found numerically stable in the order of decreasing l values, even for large quantum numbers. The three-term recursion relations in r and p are used to derive semiclassical approximations for the radial wave functions Pn,l( p) and Rn,l(r). These semiclassical approximations [Eqs. (67) and (84)] are valid even at the classical turning points and are still markedly good at small quantum numbers.
Explicit integrability for Hamiltonian systems and the Painlevé conjecture
Authors: Dorizzi B. , Grammaticos B. , Ramani A.
Published: March 2003

We analyze a class of Hamiltonian systems in two dimensions for which we proved that a second constant of motion exists. It is shown that, using the two first integrals, the equations of motion can be written in a form which allows their integration by quadratures. An analysis of the equations of motion in this reduced form establishes the behavior of the solutions in the complex-time plane. It is shown explicitly that the systems belonging to this class possess the ‘‘weak Painlevé’’ property, i.e., their solutions in complex time can present singularities of a specific algebraic type.
Lightlike contractions on Minkowski space-time
Authors: Robinson Ivor , Rózga Krzysztof
Published: March 2003

The lightlike contractions of electromagnetic fields are discussed. In particular Dirac’s delta type behavior on null hyperplanes is established and the lightlike limit of the electromagnetic field of a spinning, charged particle is obtained.
On the anomaly number of the classical groups
Authors: Karadayi Hasan R.
Published: March 2003

The Adler–Bell–Jackiw (ABJ) anomalies for all representations of the classical groups are calculated with the aid of a technique proposed recently for the representation theory of these groups. The method presented here is useful also for the calculations of the eigenvalues of Casimir invariants with rank higher than 3.
Algebras with anticommuting basal elements, space-time symmetries, and quantum theory
Authors: Wene G. P.
Published: March 2003

A collection 𝒜 of algebras with anticommuting basal elements is investigated. It is shown that the collection 𝒜 includes the quaternions, the octonions, the ‘‘algebra of color,’’ as well as other algebras familiar to the physicist. Each algebra 𝒜 is a quadratic, Jordan-admissible algebra and possesses a norm that is a generalization of the Minkowski metric. Using a Cayley–Dickson-like process, each such algebra A in 𝒜 can be embedded into a larger algebra Â that is also in the collection 𝒜. These algebras should provide candidates for models to describe observables, color, and other phenomena encountered in particle physics.
Double-Gel’fand boson polynomials and the permutation group
Authors: Nikam R. S. , Sarma C. R.
Published: March 2003

Double Gel’fand polynomials of boson operators spanning the irreducible representation [m] of U(n) in U(n)*U(n) have been obtained using symmetrized linear combinations of Wigner operators of the permutation group. The normalized coefficients which occur in the polynomial representation have been expressed as linear combinations of the Young orthogonal representation matrix elements.
Infinitesimal operators and structure of the representations of the groups SO*(2n) and SO(2n) in a U(n) basis and of the groups SU*(2n) and SU(2n) in an Sp(n) basis
Authors: Klimyk A. U. , Gavrilik A. M.
Published: March 2003

The infinitesimal operators of the most degenerate representations of the groups SO*(2n) and SU*(2n) are found in a discrete basis. The structure (composition series) of these representations is studied. The classification of unitary irreducible representations of these groups which belong to most degenerate series is given. The infinitesimal operators of irredicuble unitary representations of SO(2n) in a U(n) basis and of SU(2n) in an Sp(n) basis are found for the cases of highest weights (M, M, 0, ..., 0), M≥0.
Dyson representation of SU(3) in terms of five boson operators
Authors: Dündarer Resit , Gürsey Feza
Published: March 2003

A representation of SU(3) in terms of five boson operators is proposed. It is a generalization of the Dyson–Maleev type representation used in nuclear physics with two boson operators related to the integers that label the irreducible representation of SU(3).
Charge operators in simple Lie groups
Authors: Taormina A.
Published: March 2003

Charge operators for representations of dimension less than or equal to 16 are computed in all simple Lie groups. The representations for which the charge operator reproduces the charge spectrum of leptons and quarks of one family are analyzed from a GUT point of view.
Cohomology of Lie algebras with a nontrivial center
Authors: Mitra Bani , Sitaram B. R. , Tripathy K. C.
Published: March 2003

Let g be a Lie algebra and assume X∈ Z(g) (the center of g). Let φ: g→End V  be such that φ(X)=1V. We show that Hnφ(g, V)=0 for all n>0. The result applies to the nonrelativistic Poincaré, harmonic oscillator and Heisenberg algebras, and also to g⊕u(1) where g is a semisimple Lie algebra. We also give here the cohomology groups for the first three algebras with the adjoint action, giving explicit computations of H1 and H2, respectively, for the first two algebras.
Supermanifolds and automorphisms of super Lie groups
Authors: Cianci Roberto
Published: March 2003

The geometrical theory of supermanifolds is developed and applied to the super Lie groups. The resulting structural equations and the adjoint representation are studied and used to find the automorphisms of super Lie groups. The N=1 supergravity symmetry group (the so-called graded Poincaré group) is explicitly studied and possible applications are outlined.
Quantization, symmetry, and natural polarization
Authors: Aldaya V. , de Azcárraga J. A. , Wolf K. B.
Published: March 2003

We discuss the notion of polarization, as defined in a geometric quantization scheme recently introduced, in terms of the role played by the evolution operator of the quantum system. The analysis uses an integral transform representation of the group WSp(2,R). This clarifies the group theoretic origin of the natural polarizations and the meaning of the polarization changing transformations.
Orthogonality and orthocomplementations in the axiomatic approach to quantum mechanics: Remarks about some critiques
Authors: Cattaneo Gianpiero , Nistico’ Giuseppe
Published: March 2003

The logic approach to axiomatic quantum mechanics via orthocomplemented partial ordered sets of yes–no measurements, which constitute the observing part of a concretely realizable experiment on microworld, has been criticized from the empirical point of view by Mielnik, which on the contrary privileges the convex scheme linked to the preparing part. In this work we do assume that a description of quantum phenomenology must take into account both these two parts in which every elementary experiment can be decomposed. According to this predecision, we develop an axiomatic approach based on indistinguishability principles of a quantum information system. The very general concept of yes–no measurement or ‘‘question’’ is accepted, and then the set of all questions is classified according to the behavior with respect to a phenomenological orthogonality relation. In particular, we single out the set F of fuzzy events or effects and the set E⊆F of exact events. The Mielnik critique is then refused since it regards the order structure of E using counterexamples which pertain to F/E. The notions of physical property and noperty are then introduced and an axiomatic foundation of quantum mechanics based on a pre-Hilbert space is discussed.
Sharpening an inequality in quantum ergodic theory
Authors: Pechukas Philip
Published: March 2003

The fundamental inequality of quantum ergodic theory, which bounds the ensemble-averaged dispersion of a time-averaged occupation probability, is due to von Neumann and to Bocchieri and Loinger. Here this inequality is strengthened by combining the ensemble averaging of von Neumann and Bocchieri and Loinger. In this sharper form, the inequality says that the time average of an occupation probability is liable to be much closer to the statistical expectation than is its instantaneous value, the more so the less degenerate is the spectrum of the Hamiltonian.
The effective potential in quantum mechanics
Authors: Curtright T. L. , Thorn C. B.
Published: March 2003

General properties of the effective potential are discussed for quantum mechanical systems with a single degree of freedom. These properties are illustrated using specific one-dimensional potential models. In particular, it is stressed that the ground state for a system can exist even when the effective potential decreases monotonically towards a unique finite minimum at infinite 〈x〉.
Instantons in quantum mechanics: Numerical evidence for a conjecture
Authors: Zinn-Justin J.
Published: March 2003

In previous articles, we have given a proper definition of multi-instanton contributions in quantum mechanics and calculated these contributions to leading order. We have also presented a conjecture about the form of the expansion of these multi-instanton contributions to all orders in powers of the coupling constant. We give here some numerical results which support this conjecture.
Perturbative solutions in two-channel Schrödinger and Klein–Gordon equations
Authors: Iyer V. P. , Sharma L. K.
Published: March 2003

Perturbative method has been applied for solving one- and two-channel Schrödinger and Klein–Gordon equations for general even power potentials, which can be expanded around a minimum. The eigenvalues and solutions have been derived up to and including the second order. Finally, this method has been applied for calculating the eigenvalues of the one-channel equations for the general even power potential and hence for its different particular cases.
Stochastic formulation of Feynman path integrals from the least action point of view
Authors: Papiez Lech
Published: March 2003

It is shown that solutions of Schrödinger equation may be represented by the action of a stochastically perturbed classical system. In a sense this means that quantum mechanics could be regarded as being a consequence of a variational principle applied to randomly disturbed dynamical systems. A comparison with the Feynman–Kac formula is made and the classical limit is discussed.
On some theorems of Geroch and Stiefel
Authors: Parker Phillip E.
Published: March 2003

Modern proofs of two theorems of Geroch (spinor spacetimes and globally hyperbolic spacetimes are parallelizable) and a theorem of Stiefel (orientable 3-manifolds are parallelizable) are given, using the computationally efficient obstruction theory of algebraic topology. These techniques also easily show that, in fact, Geroch’s second theorem is a corollary of Stiefel’s theorem.
Harmonic functions and matrix elements for hyperspherical quantum field models
Authors: Cutkosky R. E.
Published: March 2003

Scalar and vector harmonic functions on the surface of a four-dimensional sphere are discussed. These functions are of use for numerical calculations in a hyperspherical formulation of quantum gauge field models. Formulas are derived for derivatives and integrals involving these functions.
Solving the Schrödinger equation with use of 1/N perturbation theory
Authors: Mlodinow Leonard D. , Shatz Michael P.
Published: March 2003

The large N expansion provides a powerful new tool for solving the Schrödinger equation. In this paper, we present simple recursion formulas which facilitate the calculation. We do some numerical calculations which illustrate the speed and accuracy of the technique
Time delay and dilation properties in scattering theory
Authors: Narnhofer Heide
Published: March 2003

We show the identity of the Eisenbud–Wigner time delay and that of Lavine for potentials V=V1+V2, V1∼1/‖x‖1+ε, x∇V1∼1/‖x‖1+ε, V2∼1/‖x‖2+ε for x→∞. Finally we show the additivity of time delay for the same class of potentials.
The total effective mass of the Kerr–Newman metric
Authors: Cohen Jeffrey M. , de Felice F.
Published: March 2003

We find the total effective gravitational mass which acts on a particle moving in the Kerr–Newman metric. We also identify the contribution to that mass by the electric field energy which is stored in any given portion of the space surrounding the metric source.
Shear-free perfect fluids with zero magnetic Weyl tensor
Authors: Collins C. B.
Published: March 2003

Rotating, shear-free general-relativistic perfect fluids are investigated. It is first shown that, if the fluid pressure, p, and energy density, μ, are related by a barotropic equation of state p=p( μ) satifying μ+p≠0, and if the magnetic part of the Weyl tensor (with respect to the fluid flow) vanishes, then the fluid’s volume expansion is zero. The class of all such fluids is subsequently characterized. Further analysis of the solutions shows that, in general, the space-times may be regarded as being locally stationary and axisymmetric (they admit a two-dimensional Abelian isometry group with timelike orbits, which is in fact orthogonally transistive), although various specializations can occur, with the ‘‘most special’’ case being the well-known Gödel model, which is space-time homogeneous (it admits a five-dimensional isometry group acting multiply transitively on the space-time). all solutions are of Petrov type D. The fact that there are any solutions in the class at all means that a theorem appearing in the literature is invalid, and the existence of some special solutions in which the fluid’s vorticity vector is orthogonal to the acceleration reveals the incompleteness of a previous study of a class of space-times, in which there are Killing vectors parallel to the fluid four-velocity and to the vorticity vector.
Infinitely many commuting symmetries and constants of motion in involution for explicitly time-dependent evolution equations
Authors: Oevel W. , Fokas A. S.
Published: March 2003

The existing symmetry approach to exactly solvable time-evolution equations in one spatial dimension is extended to the case that the equation depends explicitly on the time and space coordinates. In this context (commuting) symmetries, constants of motion (in involution), strong and hereditary symmetries (squared-eigenfunction operators), and Hamiltonian structures are discussed. The cylindrical Korteweg–de Vries equation is used as an illustrative example.
Bradyons and tachyons in an expansion of the spherical wave exp[i(ω/c)(r−c
t)]/r into cylindrical waves
Authors: Agudin J. L. , Platzeck A. M.
Published: March 2003

A resolution of the spherical wave exp[i(ω/c)(r−ct)]/r into (evanescent plus outgoing) cylindrical waves, valid everywhere except at ρ=0 is given. This expansion, being the exp[i(ω/c)(r−ct)]/r solution of an inhomogeneous wave equation, turns out to be wholly equivalent to the expansion of the corresponding source into uniformly moving δ-line densities, which includes bradyonic as well as tachyonic contributions. When applied to the electromagnetic potentials produced by a charged particle in an arbitrary one-dimensional motion, it provides an alternative derivation of the decomposition of the fields of the charge into their bradyonic and tachyonic parts.
The geometric foundations of the integrability property of differential equations and physical systems. II. Mechanics on affinely-connected manifolds and the work of Kowalewski and Painlevé
Authors: Hermann Robert
Published: March 2003

In the 1880’s Sophie Kowalewski proposed to study ‘‘integrability’’ of differential equations in terms of the analyticity properties of their solutions. The model she studied, the spinning top moving under gravity, has an interesting geometric and algebraic structure, which will be generalized. The differential geometric properties of such models will be investigated in terms of the theory of affinely-connected manifolds and Lie theory.
The Schrödinger–Langevin equation: Special solutions and nonexistence of solitary waves
Authors: Brüll L. , Lange H.
Published: March 2003

Two types of solutions of the Schrödinger–Langevin equation are investigated. It is proved that a special type of Gaussian solutions exist globally in time for the harmonic oscillator Hamiltonian. Furthermore, it is shown that the Schrödinger–Langevin equation can have no solitary wave type solutions in the damped free-particle case which lie in L2.
Symmetry reduction for nonlinear relativistically invariant equations
Authors: Grundland A. M. , Harnad J. , Winternitz P.
Published: March 2003

Symmetry reduction is studied for the relativistically invariant scalar partial differential equation H(⧠u,(∇u)2,u)=0 in (n+1)-dimensional Minkowski space M(n,1). The introduction of k symmetry variables ξ1, ... ,ξk as invariants of a subgroup G of the Poincaré group P(n,1), having generic orbits of codimension k≤n in M(n,1), reduces the equation to a PDE in k variables. All codimension-1 symmetry variables in M(n,1) (n arbitrary), reducing the equation studied to an ODE are found, as well as all codimension-2 and -3 variables for the low-dimensional cases n=2,3. The type of equation studied includes many cases of physical interest, in particular nonlinear Klein–Gordon equations (such as the sine–Gordon equation) and Hamilton–Jacobi equations.
Representation of solutions to Helmholtz’s equation
Authors: Ramm A. G.
Published: March 2003

It is proved that any potential of a single layer v is identically equal to a potential of a double layer w in the bounded domain, 𝒟, and a necessary and sufficient condition for v≡w in Ω=R3/𝒟, the exterior domain, is given.
An integral transformation in Lobachevsky space
Authors: Verdiyev Yi. A.
Published: March 2003

The integral formulas of the one-to-one correspondence between the one-particle state Fsλ( p) with nonzero mass p2=E2−p̄2, helicity (−s≤λ≤s), and the state Fν(k)(ν=±s,±(s−1),...,0 or ±( 1/2 ) with mass equal to zero (k2=ω2−k̄2=0) is obtained.
General transformation matrix for Dirac spinors and the calculation of spinorial amplitudes
Authors: Nam Kiwon , Moravcsik Michael J.
Published: March 2003

A general transformation matrix T( p̃,s̃;p,s) is constructed which transforms a Dirac spinor ψ( p,s) into another Dirac spinor ψ( p̃,s̃) with arbitrarily given momenta and polarization states by exploiting the so-called Stech operator as one of generators for those transformations. This transformation matrix is then used in a calculation to yield the spinorial matrix element M=ψ̄( p̃,s̃)Γψ( p,s) for any spin polarization state. The final expressions of these matrix elements show the explicit structure of spin dependence of the process described by these spinorial amplitudes. The kinematical limiting cases such as very low energy or high energy of the various matrix elements can also be easily displayed. Our method is superior to the existing one in the following points. Since we have a well-defined transformation operator between two Dirac spinor states, we can evaluate the necessary phase factor of the matrix elements in an unambiguous way without introducing the coordinate system. This enables us to write down the Feynman amplitudes of complicated processes in any spin basis very easily in terms of previously calculated matrix elements of ψ̄Γψ which are building blocks of those Feynman amplitudes. In contrast, in the existing method, one has to figure out the suitable multiplication factor for each individual case. Furthermore, in the previous method one needs a coordinate system to evaluate phase factors, thus making the calculation more cumbersome. Also, the expression of the matrix element in the previous method is in the fractional form whose denominator may have a singularity structure (and not always an isolated one at that), while the spinorial amplitudes in our method take a much simpler form, free of coordinate systems in any spin basis. The usefulness of the results is illustrated on Compton scattering and on the elastic scattering of two identical massive leptons where the phase factor is important. It is also shown that the Stech operator as a polarization operator is simply related to the operator K=β(Σ⋅L+1)/2, which is often used in bound state problems.
Orthogonal decompositions of certain finite-dimensional vector spaces
Authors: Hässelbarth Werner
Published: March 2003

The vector space of real functions, defined on the set of all mappings of a finite set P into another finite set L, splits into a sum of orthogonal subspaces, one for each subset of P. The orthogonal projections onto these subspaces merely involve averaging operations. Certain linear functional identities are equivalents of k-representability, i.e., of location in the span of those subspaces that belong to subsets of cardinality k. Potential applications refer to complex systems where these results could be used to analyze empirically how their properties depend on properties of their components as well as on the interactions between them. Roughly this amounts to estimating the internal structure of a ‘‘black box’’ from measured properties.
Generalized supermanifolds. I. Superspaces and linear operators
Authors: Hoyos J. , Quirós M. , Ramírez Mittelbrunn J. , de Urríes F. J.
Published: March 2003

Generalized superspaces are defined taking as a starting point the concept of Grassmann–Banach algebra. The category of B-spaces with LB -maps as morphisms is introduced. This allows one to discuss linear and tensor algebra on generalized superspaces.
Quantization of spinor fields. IV. Joint Bose–Fermi spectral problems
Authors: Garbaczewski Piotr
Published: March 2003

In this continued study of the connection between classical c-number spinor models and their quantized Fermi partners, we elaborate further necessary consequences of the bosonization. The genuine (c-number) path integral representation of tr exp(−iHt) is derived for the Fermi oscillator and simple lattice Fermi models. We find that the underlying Hamiltonian of the Fermi system HF can be equivalently written as PHBP, where HB is the related Bose Hamiltonian, P is an appropriate projection in the state space of the Bose system, and [P, HB]−=0, HF=PHBP. Grassmann algebras are not used. We prove further that both for the massive Thirring model (MT) and the chiral invariant Gross–Neveu model (CN), the Bethe ansatz eigenstates for the Fermi Hamiltonians are exact eigenstates of the Bose MT and CGN Hamiltonians, so introduced that HF=PHBP, [P, HB]−=0. As a consequence, through studying the c-number path integral representation for tr exp(−iHFt), we establish a class of classical (c-number) spinor solutions of the underlying field equations, which at the same time stationary both the c-number Bose and c-number Fermi actions.