bluuebunny/crossref_metadata_2025 huggingface dataset:
The classification of the Ricci and Plebański tensors in general relativity using Newman–Penrose formalism
Authors: McIntosh C. B. G. , Foyster J. M. , Lun A. W. -C.
Published: March 2003

A list is given of a canonical set of the Newman–Penrose quantities ΦAB, the tetrad components of the trace-free Ricci tensor, for each Plebański class according to Plebański’s classification of this tensor. This comparative list can easily be extended to cover the classification in tetrad language of any second-order, trace-free, symmetric tensor in a space-time. A fourth-order tensor which is the product of two such tensors was defined by Plebański and used in his classification. This has the same symmetries as the Weyl tensor. The Petrov classification of this tensor, here called the Plebański tensor, is discussed along with the classification of the Ricci tensor. The use of the Plebański tensor in a couple of areas of general relativity is also briefly discussed.
Bäcklund transformations in the Hauser–Ernst formalism for stationary axisymmetric spacetimes
Authors: Cosgrove Christopher M.
Published: March 2003

It is shown that Harrison’s Bäcklund transformation for the Ernst equation of general relativity is a two-parameter subset (not subgroup) of the infinite-dimensional Geroch group K. We exhibit the specific matrix u(t) appearing in the Hauser–Ernst representation of K for vacuum spacetimes which gives the Harrison transformation. Harrison transformations are found to be associated with quadratic branch points of u(t) in the complex t plane. The coalescence of two such branch points to form a simple pole exhibits in a simple way the known factorization of the (null generalized) HKX transformation into two Harrison transformations. We also show how finite (i.e., already exponentiated) transformations in the B group and nonnull groups of Kinnersley and Chitre can be constructed out of Harrison and/or HKX transformations. Similar considerations can be applied to electrovac spacetimes to provide hitherto unknown Bäcklund transformations. As an example, we construct a six-parameter transformation which reduces to the double Harrison transformation when restricted to vacuum and which generates Kerr–Newman–NUT space from flat space.
A generalization of the concept of spacetime
Authors: Schaer Carl
Published: March 2003

It is argued that a physically relevant generalization of spacetime should maintain the line element of general relativity. A limited number of spaces can be constructed which satisfy this condition. In addition to the symmetric metric field, three antisymmetric fields naturally arise, and it is shown that, if one of these is interpreted as the electromagnetic field, the other two fields have equal but opposite charges.
Linear wave conversion in a warm, unmagnetized, collisionless plasma
Authors: Kriegsmann Gregory A.
Published: March 2003

In this paper we apply the method of matched asymptotic expansions to study the problem of linear mode conversion in a warm, unmagnetized, collisionless plasma. The plasma is assumed to fill the half space x≳0. At the boundary, x = 0, the transition from free space to plasma is very smooth. Two linear second-order ordinary differential equations govern the electric field within the plasma. Since a very small parameter (ε2) multiplies the highest derivative in one equation, the mathematical problem is singular and not unlike the Orr–Sommerfeld equation. The method of multiple scales decouples the equations which allows us to determine the transverse and longitudinal waves. These results break down in a small neighborhood of the critical point where we develop new expansions. The composite results are computed to second order in ε.
Time-dependent, finite, rotating universes
Authors: Rebouças Marcelo J. , de Lima J. Ademir S.
Published: March 2003

We present three new classes of finite, homogeneous and nonsingular solutions of Einstein’s equations which have time-dependent expansion, shear, and rotation. The t-constant sections are of Bianchi type IX. The source of these geometries is a fluid which has not been thermalized.
Sensitivity theory for nonlinear systems. II. Extensions to additional classes of responses
Authors: Cacuci Dan G.
Published: March 2003

This work extends a recent, functional-analytic formulation of sensitivity theory to include treatment of additional types of responses. There are physical systems where a critical point of a function that depends on the system’s state vector and parameters defines the location in phase-space where the response functional is evaluated. The Gâteaux differentials giving the sensitivities of both the functional and the critical point to changes in the system’s parameters are obtained by alternative formalisms. The foward sensitivity formalism is the simpler and more general, but may be prohibitively expensive for problems with large data bases. The adjoint sensitivity formalism, although less generally applicable and requiring several adjoint calculations, is likely to be the only practical approach. Sensitivity theory is also extended to include treatment of general operators, acting on the system’s state vector and parameters, as response. In this case, the forward sensitivity formalism is the same as for functional responses, but the adjoint sensitivity formalism is considerably different. The adjoint sensitivity formalism requires expanding the indirect effect term, an element of a Hilbert space, in terms of elements of an orthonormal basis. Since as many calculations of adjoint functions are required as there are nonzero terms in this expansion, careful consideration of truncating the expansion is needed to assess the advantages of the adjoint sensitivity formalism over the forward sensitivity formalism.
Resonance poles and Gamow vectors in the rigged Hilbert space formulation of quantum mechanics
Authors: Böhm A.
Published: March 2003

After a summary of the Rigged Hilbert space formulation of quantum mechanics and a brief statement of its advantages over von Neumann’s formulation, a mathematically correct definition of Gamow’s exponentially decaying vectors as generalized energy eigenvectors is suggested. It is shown that exponentially decaying vectors are obtained from the S-matrix poles in the lower half of the second sheet and exponentially growing vectors from the S-matrix poles in the upper half of the second sheet. Decaying ’’state’’ vectors are defined as functionals over half of the space of physical states and growing ’’state’’ vectors are defined as functionals over the other half. On functionals over these subspaces, the dynamical group of time development splits into two semigroups, one for t ≳ 0 and the other for t < 0. The generalized basis system connected with the spectrum of the Hamiltonian is transformed into a new basis system in which the exponentially decaying component of the density matrix is separated.
On the covariant differential of spin direction in the Finslerian deformation theory of ferromagnetic substances
Authors: Ikeda Satoshi
Published: March 2003

In the Finslerian deformation theory of ferromagnetic substances, each point (x) is endowed with the unit vector ( y) called the spin and the line-element (x,y) is taken as the independent variable. The length of y is normalized at each point, so that the direction of y alone is noticed. This is the so-called spin direction. In the case of the magnetization state, each vector y rotates to become parallel, in a Euclidean sense (not a Finslerian sense), to the direction of an applied magnetic field and the magnetostriction occurs there. Within the framework of Finsler geometry, this Euclidean ’’parallelism’’ of y cannot be grasped by the ordinary covariant differential of y (i.e., Dy), so that a new one (i.e., δy) must be introduced, which is nothing but the covariant differential of spin direction. Up to now, however, the geometrical meaning of δy and the relation between δy and Dy have not yet been clarified, so that these problems will be considered in this paper.
Signals and discontinuities in general relativistic nonlinear electrodynamics
Authors: Alarcón Gutiérrez Sabás , Dudley Alan L. , Plebañski Jerzy F.
Published: March 2003

A theory of nonlinear electrodynamics in an arbitrary curved space–time is developed from the fundamental action functional for a charged perfect fluid. The equations for small perturbations on a fixed nonlinear background are then the initial point for a comprehensive study of the characteristic surfaces. The essential distinctions between linear and nonlinear electrodynamic interactions under the influence of gravitation are exhibited. Discontinuities in the first derivatives of small perturbations are encountered (1) which may be of general algebraic types for both the electrodynamic and gravitational fields and (2) which may have spacelike propagation. A specific set of constraints which would permit the propagation of these extraordinary radiative fronts is presented. If the physical organization of a particular problem is presumed to be sufficiently sensitive to the nonlinear nature of the dynamical interactions, then the application of traditional causal concepts may be unreliable when intuition derived from Maxwellian electrodynamics with noninteracting photons is anticipated to provide event horizons.
Nonrelativistic Coulomb Green’s function in parabolic coordinates
Authors: Blinder S. M.
Published: March 2003

The nonrelativistic Coulomb Green’s function G(+)(r1,r2,k) is evaluated by explicit summation over discrete and continuum eigenstates in parabolic coordinates. This completes the derivation of Meixner, who was able to obtain only the r1=0 and r2→∞ limiting forms of the Green’s function. Further progress is made possible by an integral representation for a product of two Whittaker functions given by Buchholz. We obtain the closed form for the Coulomb Green’s function previously derived by Hostler, via an analogous summation in spherical polar coordinates. The Rutherford scattering limit of the Green’s function is also demonstrated, starting with an integral representation in parabolic coordinates.
An example of an ℋ-space
Authors: Sparling G. A. J. , Tod K. P.
Published: March 2003

The good cut equation for a specific asymptotic shear is solved and the metric of the associated ℋ-space is found to be type N, asymptotically flat and positive frequency.
Representations of Osp(2, 1) and the metaplectic representation
Authors: Hughes J. W. B.
Published: March 2003

Shift operator techniques are used to treat the irreducible representations of the superalgebra Osp(2, 1). Apart from obtaining the well known gradestar dispin representations which arise when the even part is the compact SU(2) algebra, the case when the star conditions on the even part are those satisfied by the noncompact SU(1, 1) algebra is also treated. In this case no gradestar representations arise, and the star representations are found to consist of the direct sum of two discrete series representations of SU(1, 1). One of these representations can be realized in terms of functions of a single complex variable, and turns out to be a simple example of a metaplectic representation.
Solution of the unitarity equation with overlapping left and right cuts: A tool for study of the S* and similar systems
Authors: Johnson Porter W. , Warnock Robert Lee
Published: March 2003

The partial-wave unitarity condition is complicated by the presence of overlapping left and right branch cuts when the lowest exchanged mass is small in comparison to the direct-channel mass. A coupled-channel ND−1 method for constructing unitary amplitudes with overlapping cuts is described. The study is motivated in part by the problem of analyzing the ππ−K̄system near the S* resonance.
Representations of the Poincaré group in a K3-basis and the infinite momentum limit
Authors: Quirós M. , Mittelbrunn J. Ramirez
Published: March 2003

The Poincaré group is represented taking as a complete set of commuting observables {PT,K3,𝒯3}, where K3 is the boost along the third axis and 𝒯3 the third component of the null plane spin. We name it K3-representation. There appears in it a parameter K, with dimensions of momentum, from which the infinite momentum limit can be implemented in a natural way as the contraction k→∞. K3-states and wavefunctions are well defined in the infinite momentum limit. They are related to null plane states and wavefunctions by a Mellin transformation. The convergence properties of null plane functions translate into analyticity properties of K3-functions in the complex λ (eigenvalue of K3)-plane.
An exact invariant for a class of time-dependent anharmonic oscillators with cubic anharmonicity
Authors: Leach P. G. L.
Published: March 2003

An exact invariant is constructed for a class of time-dependent anharmonic oscillators using the method of the Lie theory of extended groups. The presence of the anharmonic term imposes a constraint on the nature of the time dependence. For a subclass it is possible to obtain an energy-like integral and a condition under which the motion is bounded.
A note on lattice random walks with an excluded point
Authors: Weiss George H.
Published: March 2003

We derive some asymptotic results for the moments of displacement of a random walk on a lattice with a single absorbing point. In one dimension we are able to find an asymptotic expression for the probability distribution of random walks that have not been trapped.
On quantum solitons and their classical relatives: Spin 1/2 approximation of the sine-Gordon system
Authors: Garbaczewski Piotr
Published: March 2003

If gradient terms in the linear Bose chain Hamiltonian couple nearest neighbors only, then in the spin 1/2 approximation they reduce to the spin 1/2 x-y-z Hamiltonian. Hence, spin 1/2 approximation reveals the Thirring model as the one, whose spectrum is completely included in the spectrum of the underlying Bose chain. Relation to the Coleman’s equivalence is discussed.
Liouville dynamics and Poisson brackets
Authors: Marmo G. , Saletan E. J. , Simoni A. , Zaccaria F.
Published: March 2003

We study divergenceless dynamical systems from a differential geometrical point of view. The analogy with Hamiltonian mechanics is pursued even as far as Poisson brackets. In particular, we study Nambu mechanics and its generalizations.
Passivity and equilibrium for classical Hamiltonian systems
Authors: Daniëls H. A. M.
Published: March 2003

For classical continuous n-particle systems equilibrium states are characterized by a condition of passivity.
General solutions to inverse transport problems
Authors: Sanchez R. , McCormick N. J.
Published: March 2003

A new approach is developed for solving time-independent inverse problems for particle or radiation transport described by the monoenergetic linear Boltzmann equation. For a homogeneous plane geometry medium, the approach leads to a set of inverse solutions which can be obtained by purely algebraic means; previously derived methods appear as special cases. All these solutions require only measurements of the angular intensities at the surface. The analysis is extended to time-dependent and energy-dependent problems.
Linear transport in an exponential atmosphere
Authors: Larsen Edward W. , Mullikin Thomas W.
Published: March 2003

Two basic theoretical problems concerning linear transport in a subcritical half-space with an exponential scattering ratio are solved. First, the continuum eigenvolutions developed by Mullikin and Siewert are shown to be half-range complete. Second, the singular integral equation developed by Martin for the angular flux exiting the half-space is shown to possess a unique solution.
The role of noncompact Lie algebras in relativistic wave equations. I
Authors: Cant A.
Published: March 2003

The role of real Lie algebras in the study of relativistic wave equations of the form (αμ∂μ+iκ)ψ(x) = 0 is considered. To a finite-dimensional equation there corresponds a Lie algebra S containing so(4,C) and a vector operator {αμ}. The importance of finding all possible real forms of S containing the Lorentz Lie algebra so(3,1) is discussed. This problem is solved in detail for certain ’’generic’’ cases, namely S = sp(n,C), so(n,C), and sl(n,C). The exceptional algebras G2, F4, and E6 are also considered.
On the Killing surface—event horizon relation
Authors: Krisch J. P.
Published: March 2003

A projective transformation on the scalar norm and twist of a timelike killing vector can be used to generate new space-times. The effect of the transformation on the new Killing surface and its relation to the lcoal event horiozn is discussed. It is shown that the Geroch transformation will only connect spaces where this relation is the same.
A further note on the Hénon–Heiles problem
Authors: Leach P. G. L.
Published: March 2003

The method of the Lie theory of extended groups is applied to the Hénon–Heiles problem. Only one generator for a one-parameter group is found. The corresponding first integral is the energy. It is inferred that no other exact integral exists.
Functional methods in random classical field theory
Authors: Willemsen Jorge F.
Published: March 2003

A functional which generates N distinct point solutions to a classical wave equation with random coefficients in the presence of external sources is constructed. Statistical averaging over the random coefficients is then implemented using replica and/or anticommuting field techniques.
4-space formulation of field equations for multicomponent eigenfunctions
Authors: Fanchi John R.
Published: March 2003

Beginning with the assumptions employed in the development of the 4-space formulation (FSF) for spinless particles, a formalism for multicomponent eigenfunctions is constructed. The primary result is a general expression for the field equations of multicomponent eigenfunctions. The ’’Relativistic Dynamics’’ of Horwitz, Piron, and Reuse for spin-0 and spin- 1/2 particles is shown to be consistent with the FSF. Expectation values are defined and briefly discussed in the appendix.
Partial-range completeness and existence of solutions to two-way diffusion equations
Authors: Beals Richard
Published: March 2003

Separating variables to solve a two-way diffusion equation leads to a nonstandard eigenvalue problem in one variable. It is shown that the eigenfunctions having negative eigenvalues are complete on the part of the domain where initial conditions are imposed, while those with positive eigenvalues are complete where final conditions are imposed. The corresponding exponentially growing and exponentially decaying solutions may be used to expand arbitrary solutions on semi-infinite intervals in the ’’time’’ variable. A natural iterative procedure for obtaining solutions on finite intervals is shown to converge. In some cases a linearly growing solution must also be taken into account.
On Euler characteristics of compact Einstein 4-manifolds of metric signature (++−−)
Authors: Matsushita Yasuo
Published: March 2003

In the present paper, the Euler characteristic is studied for a compact oriented Einstein 4-manifold of signature (++−−). For such a manifold, there are three types of normal forms of the curvature tensor. It is shown that for each type the Euler characteristic is nonnegative and even. Several new inequalities are obtained concerning the Euler characteristic and the volume of the manifold. The second Betti number is even, and if it is zero, then the first Betti number also vanishes. The arguments developed here are based upon the famous work of Chern about the Gauss–Bonnet formula for a pseudo-Riemannian manifold.
Integral inequalities for optical constants
Authors: King Frederick W.
Published: March 2003

Some upper bound integral inequalities are derived for various optical constants. Weight functions which damp out the high frequency spectral domain are given special emphasis. The implications for testing experimental data are discussed.
Schrödinger equation with time-dependent boundary conditions
Authors: Munier A. , Burgan J. R. , Feix M. , Fijalkow E.
Published: March 2003

A Schrödinger equation for a well potential with varying width is studied. Generalized canonical transformations are shown to transform the problem into a time-dependent harmonic oscillator problem submitted to fixed boundary conditions. This transformed problem is solved by a perturbation technique and gives the evolution of the average energy of the system according to the motion of the well. Motions corresponding to a renormalization or compaction group are shown to be solvable by separation of variables.
Exterior spacetimes for rotating stars
Authors: Xanthopoulos Basilis C.
Published: March 2003

The algorithms are studied which construct stationary axisymmetric asymptotically flat spacetimes. The multipole moment structure of the resulting spacetimes is determined. The static metric and the transformations which generate any stationary metric are obtained.
On quantum solitons and their classical relatives: II. ‘‘Fermion–boson reciprocity’’ and classical vs quantum problem for the sine-Gordon system
Authors: Garbaczewski Piotr
Published: March 2003

Both quantum and classical sine–Gordon fields can be built out of the fundamental free neutral massive excitations, which quantally obey the Bose–Einstein statistics. At the roots of the ’’boson-fermion reciprocity’’ invented by Coleman, lies the spin 1/2 approximation of the underlying Bose system. By generalizing the coherent state methods to incorporate non-Fock quantum structures and to give account of the so-called boson transformation theory, we construct the carrier Hilbert space ℋSG for quantum soliton operators. The h/→0 limit of state expectation values of these operators among pure coherentlike states in ℋSG reproduces the classical sine–Gordon field. The related (classical and quantum) spin 1/2 xyz Heisenberg model field is built out of the fundamental sine–Gordon excitations, and hence can be consistently defined on the appropriate subset of the quantum soliton Hilbert space ℋxyz . A correct classical limit is here shown to arise for the Heisenberg system: phase manifolds of the classical Heisenberg and sine–Gordon systems cannot be then viewed independently as a consequence of the quantum relation.
Dynamically variable internal symmetries
Authors: Ahner Henry F.
Published: March 2003

The mathematical consequences of the ansatz that the generators of internal transformations, as well as the parameters, may be space–time-dependent is investigated. In addition to the Yang–Mills type fields, a transformation changing field must be introduced. The formalism developed is consistent. An appendix contains a derivation of the Fock–Ivanenko coefficient for the Dirac equation in general relativity that shows a connection between the ideas developed here and gauge fields.
Inverse scattering—exact solution of the Gel’fand-Levitan equation
Authors: Pechenick Kay R. , Cohen Jeffrey M.
Published: March 2003

One formulation of inverse scattering theory involves the Gel’fand–Levitan equation. We present a procedure for finding exact solutions to this equation; this procedure can be applied whenever the reflection coefficient is a rational function of the wave number k, with an arbitrary number of poles. We present graphs of the potential as a function of distance, for several cases with 3, 4, 5, and 6 poles. Prior to this paper, no 4-, 5-, or 6-pole case had ever been treated successfully.
Equivalent Lagrangians: Multidimensional case
Authors: Hojman S. , Harleston H.
Published: March 2003

We generalize a theorem known for one-dimensional nonsingular equivalent Lagrangians (L and ?) to the multidimensional case. In particular, we prove that the matrix Λ, which relates the left-hand sides of the Euler–Lagrange equations obtained from L and ?, is such that the trace of all its integer powers are constants of the motion. We construct several multidimensional examples in which the elements of Λ are functions of position, velocity, and time, and prove that in some cases equivalence prevails even if detΛ = 0.
Comments on a paper by L. L. Lee [J. Math. Phys. 2
1, 1055 (1980)]
Authors: Whitehead R. R.
Published: March 2003

Analytic expressions are given for the eigenvalues of some matrices arising in connection with Feynman path integrals.
Matrix orthogonal polynomials on the unit circle
Authors: Geronimo Jeffrey S.
Published: March 2003

The properties of matrix orthogonal polynomials on the unit circle are investigated beginning with their recurrence formulas. The techniques of scattering theory and Banach algebras are used in the investigation. A matrix generalization of a theorem of Baxter is proved.
Adjoints of nondensely defined Hilbert space operators
Authors: Pfeifer Peter
Published: March 2003

To each linear operator T acting in a Hilbert space ℋ, an adjoint operator T* is assigned which coincides with the usual adjoint whenever the domain of T is dense in ℋ. General properties of T* are: If ℋ is countably infinite-dimensional, then the set of all closed operators equals the set of all adjoints; if the domain (range) of T is closed, then so is the domain (range) of T*; T is closable (bounded) if and only if T* is densely (everywhere) defined. Noteworthy corollaries are the closed graph and the closed range theorems, as well as basic crosslinks between adjoints and inverses. Applications to the problem of extending formally self-adjoint operators are given.
Representations and Clebsch–Gordan coefficients of Z-metacyclic groups
Authors: Bovier A. , Lüling M. , Wyler D.
Published: March 2003

We investigate finite groups of the form ZmsZn and give all irreducible representations and Clebsch–Gordan coefficients in analytic form. Two subclasses are considered which seem to be inportant for applications: the M-metacyclic groups which are important for spin systems, and the K-metacyclic groups which are the smallest finite groups that have an irreducible representation of dimension p−1, where p is prime.
Sturm–Liouville eigenproblems with an interior pole
Authors: Boyd John P.
Published: March 2003

The eigenvalues and eigenfunctions of self-adjoint Sturm–Liouville problems with a simple pole on the interior of the interval [A, B] are investigated. Three general theorems are proved and it is shown that as n→∞, the eigenfunctions more and more closely resemble those of an ordinary Sturm–Liouville problem and λn ∼−m2π2/(B−A)2, just as if there were no singularity. The low-order modes, however, differ drastically from those of a nonsingular eigenproblem in that (i) both eigenvalues and eigenfunctions are complex (despite the fact the problem is self-adjoint), (ii) the real and imaginary parts of the nth eigenfunction may both have ever-increasing numbers of interior zeros as B→∞, instead of just (n−1) zeros, and (iii) as B→∞, the eigenvalues for all small n may cluster about a common value in contrast to the widely separated eigenvalues of the corresponding nonsingular problem. These results are general, but in order to present quantitative solutions for the low-order modes, too, special attention is given to the particular case   u″+(1/x−λ)u = 0, (1) with u(A) = u(B) = 0 where λ is the eigenvalue and A and B are of opposite signs. For small n, one can obtain the approximation   λn∼exp[(1+31/2i)dn/(2B1/3)]/B, (2) where dn is the nth root of the Airy function Ai(−z). The imaginary part of (2) shows explicitly how profoundly the interior pole has modified the structure of the eigenproblem. The WKB method, which was used to derive (2), is shown to be accurate for all n. The WKB analysis is of some interest in and of itself. Although the number of WKB ’’transition’’ points is the same as for the half-century old quantum harmonic oscillator (two), the substitution of the interior pole for one of the turning points has a profound (and fascinating) impact on both the WKB formalism and the numerical results. Thus, although this problem was motivated by the physics of hydrodynamic waves, it is also an extension to both classical Sturm–Liouville theory and to the WKB treatment of eigenvalue problems.
On a ‘‘conformal’’ Kepler problem and its reduction
Authors: Iwai Toshihiro
Published: March 2003

A ’’conformal’’ Kepler problem is defined in order to associate the Kepler problem with the harmonic oscillator. The four-dimensional conformal Kepler problem which shares an energy surface with the four-dimensional harmonic oscillator reduces to the ordinary three-dimensional Kepler problem. By use of the reduction the symmetry group SO(4) of the Kepler problem is brought out from a symmetry subgroup SU(2)×SU(2) of the conformal Kepler problem; the subgroup is the same as a subgroup of the symmetry group SU(4) of the harmonic oscillator.
Invariant inner products on spaces of solutions of the Klein–Gordon and Helmholtz equations
Authors: Steinberg Stanly , Wolf Kurt Bernardo
Published: March 2003

We construct sesquilinear forms which are invariant under the similarity groups of the Klein–Gordon and Helmholtz equations. These give rise to positive definite inner products on subspaces of solutions of these equations. For the Klein–Gordon case, the known Poincaré-invariant inner product for positive-energy solutions is recovered. For the Helmholtz case, a new Euclidean-invariant inner product is presented which involves the function and its normal derivative to a line, integrated nonlocally over that line.
Fluctuations of P (φ) random fields
Authors: Haba Z.
Published: March 2003

We discuss measures of certain sets in 𝒮′(Rd) related to the behavior of supx ‖φ(g(⋅−x))‖ (fluctuations of φ) for large ‖x‖ in an ultraviolet regularized infinite volume P(φ)d. We investigate also whether the measure of a set is preserved, when the ultraviolet cut-off is removed.
Representations of supergroups
Authors: Balantekin A. Baha , Bars Itzhak
Published: March 2003

An explicit construction of representations of supergroups is given in terms of direct products of covariant and contravariant fundamental representations. The rules of supersymmetrization are characterized by extended Young supertableaux. This constructive approach leads to explicit transformation properties of higher representations as well as to closed explicit formulas for characters from which other invariants such as dimensions and eigenvalues of all Casimir operators can be calculated. We have applied this approach so far to the supergroups SU(N/M), OSP(N/2M), P(N), for which we have obtained all the representations constructible as direct products of the fundamental (defining) representations. An argument is presented toward the irreducibility of all these representations.
Decomposition of the natural representation of the U(2) color charge algebra in the three-quark sector
Authors: Van Hieu Nguyen
Published: March 2003

It was shown that the natural 16-dimensional representation ψa1a2a3a,an = 1,2,n = 1,2,3,0, of the three-quark U(2) color charge algebra proposed by Adler, contains five irreducible representations (1,0), three irreducible representations (3̄,0), and one irreducible representation (1, 1/2 ) of the SU(3)⊕SU(2) subalgebra.
Symmetry of time-dependent Schrödinger equations. I. A classification of time-dependent potentials by their maximal kinematical algebras
Authors: Truax D. Rodney
Published: March 2003

Potentials for the time-dependent Schrödinger equation [− 1/2 ∂xx +V(x,t)]Ψ(x,t) = i∂tΨ(x,t) are classified according to their space–time or kinematical algebras in a search for exactly solvable time-dependent models. In addition, it is shown that their dynamical algebras are isomorphic to their kinematical algebras on the solution space of the Schrödinger equation.
Faddeev’s equations in differential form: Completeness of physical and spurious solutions and spectral properties
Authors: Evans J. W. , Hoffman D. K.
Published: March 2003

Faddeev type equations are considered in differential form as eigenvalue equations for non-self-adjoint channel space (matrix) Hamiltonians HF. For these equations in both the spatially confined and infinite systems, the nature of the spurious (nonphysical) solutions is obvious. Typically, these together with the physical solutions (given extra technical assumptions) generate a regular biorthogonal system for the channel space. This property may be used to provide an explicit functional calculus for the then real eigenvalue scalar spectral HF, to show that ±iHF generate uniformly bounded C0 semigroups and to simply relate HF to self-adjoint Hamiltonian-like operators. These results extend to the four-channel Faddeev type equations where the breakup channel is included explicitly.
Memory function approach to nonlinear deterministic systems: An exact linear equation
Authors: Nishigori Takeo
Published: March 2003

A set of nonlinear evolution equations is cast into an exact linear non-Markovian equation with the memory kernel reflecting the nonlinearity and coupling with irrelevant variables. The equation is deterministic in contrast to the generalized Langevin equation derived in a similar way. The solution to the nonlinear equations is expressed by a sum of exponential functions. A simple illustrative example is treated to show the effectiveness of the present approach.
On the gravitational phase transition in the Thomas–Fermi model
Authors: Messer J.
Published: March 2003

The first order phase transition in an infinite system of gravitating fermions is analyzed in the canonical ensemble. Except for the question of nonmonotonicity of the mass distribution as a function of the chemical potential, we give an analytical proof for the existence of the phase transition. A single phase region is shown to exist for temperatures high compared to the gravitational energy.
Time development of Bose systems
Authors: Majewski W. A.
Published: March 2003

We investigate the dynamics of an infinite Bose system in C*-algebraic description. The free time development is constructed under some conditions which are natural from a physical point of view. The properties of locally perturbed dynamics are discussed.
Numerical representation and identification of graphs
Authors: Chen H. H. , Lee Felix
Published: March 2003

A method to represent each linear graph by a single number, the determinant of its modified incidence matrix, is introduced. The isomorphism of graphs can be determined by comparing the determinants of their incidence matrices. Although it is not proved that different graphs can always be distinguished by the determinants of their modified incidence matrices, the proposed method provides a good practical algorithm for the identification of graphs. Applications of the single-number representation of graphs are discussed.
Exact invariants for a class of time-dependent nonlinear Hamiltonian systems
Authors: Lewis H. Ralph , Leach P. G. L.
Published: March 2003

A method of generalizing a class of invariants for a time-dependent linear oscillator is developed for the motion of a mass point in one dimension with a general time-dependent nonlinear potential. Formulas are derived for the allowable time-dependent potentials and for the corresponding invariants. The method by which these conclusions are reached is interesting theoretically and is explained in detail.
Current responses of first and second order in a collisionless plasma. II. Three-wave interaction
Authors: Larsson Jonas
Published: March 2003

The three-wave interaction in a possibly strongly inhomogeneous plasma is considered. Coupled mode equations are derived with coefficients expressed in terms of the response operators treated in part I of this paper.
The equivalence of the Feshbach and J-matrix methods
Authors: Yamani Hashim A.
Published: March 2003

It is shown, by takcing P to be the projection operator on the subspace of function space in which the potential is truncated, that the exact solution of the scattering problem for the truncated potential using the Feshbach formalism is identical to the J-matrix solution.
The asymptotic form of the continuum wavefunctions and redundant poles in the Heisenberg condition
Authors: Terry Paul
Published: March 2003

The derivation of the Heisenberg condition is re-examined to show why it is not an identity for potentials possessing redundant poles. Consideration of several such potentials for which exact solutions are known reveals that, in the process of taking an asymptotic limit, the usual derivation of the Heisenberg condition improperly neglects a set of terms. These terms are just those necessary to make the Heisenberg condition an identity; more importantly, it is demonstrated that these terms, providing information on the redundant poles, i.e., the sum of the residues of S(k) at the redundant poles, come from the asymptotic expansion of the continuum wavefunction. By this we are able to give the details of the nature of the asymptotic expansion of the continuum wavefunction and the information contained therein.
Jordan–Kaluza–Klein type unified theories of gauge and gravity fields
Authors: Bradfield T. , Kantowski R.
Published: March 2003

We investigate the generalized Jordan–Kaluza–Klein type scalar tensor theories of gravity with gauge fields present for the purpose of restricting the spacetime dependence of the scalar fields. These scalars are essential in building Lagrangians for fields with internal degrees of freedom. By one rather simple consistency restriction on covariant differentiation we are able to show that the scalar fields must be spacetime constants.
Initial-boundary-value problem for diffusion of magnetic fields into conductors with external electromagnetic transients
Authors: Wilhelm H. E.
Published: March 2003

The initial-boundary-value problem for the diffusion of an initially homogeneous magnetic field into a slab of conductivity σ<∞ and width Δx=2a is solved, under consideration of the electromagnetic wave pulses generated at the surfaces of the conductor by its interaction with the external magnetic field, which propagate into the surrounding vacuum. The analytical solutions show that (i) the external electromagnetic transients are necessary in order to correctly satisfy the boundary conditions for the tangential electric and magnetic field components, and (ii) the spatial and temporal development of the electromagnetic field and electric current in the conductor is quantitatively determined by a new dimensionless parameter group ℛ=μ0σac[c=(μ0ε0)−1/2]. This ‘‘magnetic Reynolds number of the vacuum’’ determines the coupling between the transient fields in the conductor σ>0 and the ambient space (σ=0).
Constructing measures for spin-variable path integrals
Authors: Klauder John R.
Published: March 2003

By exploiting the overcompleteness of the spin-coherent states we derive expressions for spin-kinematics path integrals (specifically for spin 1/2 and spin 1) in terms of genuine (Wiener) measures on continuous paths lying on the unit sphere and for certain dynamical systems which when projected onto the subspace spanned by the proper spin-coherent-state matrix elements yield the appropriate quantum-mechanical propagator.
Perturbative technique as an alternative to the WKB method applied to the double-well potential
Authors: Mansour H. M. M. , Müller-Kirsten H. J. W.
Published: March 2003

We give an explicit and complete perturbation theoretical analysis of the solutions and the eigenvalues of the Schrödinger equation for the double-well potential. In particular we demonstrate the matching of various branches of the solutions over the entire range of the independent variable, and we calculate the splitting of eigenvalues due to the finite height of the central hump of the potential.
Maxwell’s equations in axiomatic quantum field theory. II. Covariant and noncovariant gauges
Authors: Bongaarts P. J. M.
Published: March 2003

The outlines of a general formalism for the description of the Maxwell field in the framework of axiomatic quantum field theory were given in a preceding paper. It was based on the use of locally convex topological spaces connected in a natural way with the distribution properties of the n-point functions of both the Aμ(x) and Fμν(x) fields. In this paper this approach is developed further. We discuss in particular aspects of the reconstruction theorem, gauges and their equivalence, and symmetries and gauge transformations. Finally a systematic and unified derivation is given of the various Lorentz covariant and noncovariant free field gauges together with the properties of the associated Aμ(x) operator field theories.
Moving frames and prolongation algebras
Authors: Estabrook Frank B.
Published: March 2003

We consider differential ideals generated by sets of 2-forms which can be written with constant coefficients in a canonical basis of 1-forms. By setting up a Cartan–Ehresmann connection, in a fiber bundle over a base space in which the 2-forms live, one finds an incomplete Lie algebra of vector fields in the fibers. Conversely, given this algebra (a prolongation algebra), one can derive the differential ideal. The two constructs are thus dual, and analysis of either derives properties of both. Such systems arise in the classical differential geometry of moving frames. Examples of this are discussed, together with examples arising more recently: the Korteweg–de Vries and Harrison–Ernst systems.
Lagrangians for spherically symmetric potentials
Authors: Henneaux Marc , Shepley L. C.
Published: March 2003

Two Lagrangians are s-equivalent (s for ‘‘solution’’) if they yield equations of motion having the same set of solutions. We consider Lagrangians s-equivalent to T−V, where T is flat space kinetic energy and V is a spherically symmetric potential. We show that for n=dimension of space ≥3, there are many s-equivalent Lagrangians which cannot be formed from T−V by multiplication by a constant or addition of a total time derivative. In general these s-equivalent Lagrangians lead to inequivalent quantum theories in the sense that the energy spectra are different.
Geometrical perturbation theory: action-principle surface terms in homogeneous cosmology
Authors: Gowdy Robert H.
Published: March 2003

The coordinate-independent formulation of spacetime perturbation theory is applied to the analysis of surface terms which appear in variations of the Einstein Action of general relativity. Restricted variations of the type used to study the dynamics of homogeneous universes require a corrected action functional. A general expression for the correction is found.
Joint distribution indicated by the wave equations of quantum mechanics
Authors: Sutherland Roderick I.
Published: March 2003

By using the notion of conditional mean values and assuming that the classical relationship between momentum and energy remains valid, it is shown that both the Schrödinger and Klein–Gordon equations suggest a particular joint distribution expression for quantum mechanics, namely the Margenau and Hill distribution.
Functional integration treatment of one-dimensional ionic mixtures
Authors: Lugrin Ch. , Martin Ph. A.
Published: March 2003

The classical one-dimensional jellium with several ionic components is treated exactly by the method of functional integration. It is found that ionic demixion does not occur and that the state is crystalline at all temperatures. The period is determined by the greatest common divisor of the ionic charges. The structure of low temperature states of some binary mixtures is investigated in detail by means of the conditional particle distribution densities.
Complete set of states for microscopic nuclear collective models
Authors: Castaños O. , Frank A. , Chacón E. , Hess P. , Moshinsky M.
Published: March 2003

For several years the authors have been interested in determining complete sets of states for macroscopic nuclear collective models, such as the Bohr–Mottelson one (BM) and the interacting boson approximation (IBA), as well as in their use in nuclear structure calculations. In the present paper we obtain a complete set of states for microscopic nuclear collective models such as those of Vanagas and of Filippov and Smirnov. For calculations in these models, one requires a set of states for the A nucleon system, in appropriate coordinates which include the ones related with collective degrees of freedom. As is customary in nuclear physics, the complete set of states is derived more conveniently if one assumes an oscillator interaction between the nucleons. We obtain explicitly this set of states when A≫1, showing that it can be expressed in terms of wavefunctions whose dependence on the collective coordinates is similar to those appearing in the BM model and in the IBA. We briefly indicate how this set of states can be used in microscopic collective model calculations.
Generating functions for IR multiplicities
Authors: Bodine C. , Gaskell R. W.
Published: March 2003

The construction of generating functions for multiplicities of irreducible representations from generating functions for compound characters is examined. Weyl reflection symmetry is used to simplify the procedure. Two examples involving the enumeration of SU(3) irreducible representations are discussed.
Decomposition of the finite-dimensional fermion algebra into irreducible spaces
Authors: Bose A. K. , Navon A.
Published: March 2003

The 22n -dimensional operator algebra constructed on n single-fermion states is decomposed into irreducible tensor operator spaces with respect to three Lie subalgebras of physical interest: (i) the Lie subalgebra associated with the group SU(n) used in Hartree–Fock theory, (ii) the Lie subalgebra associated with the group SO(2n) used in Hartree–Bogoliubov theory, and (iii) the Lie subalgebra associated with the group SO(2n+1) introduced by Wybourne in atomic applications.
The lifting of an İnönü–Wigner contraction at the level of universal coverings
Authors: Fernández Ariel , Sinanoğlu Oktay
Published: March 2003

It is shown that, when the Borel cohomology of a connected Lie group G is such that all projective representations can be lifted to unitary representations of the universal covering group, then any contraction of G corresponds to a contraction of its universal covering. Three theorems are stated and proved. The results apply also to the İnönü–Wigner contraction of the Poincaré group into the Galilei group.
Renormalized Lie perturbation theory
Authors: Rosengaus E. , Dewar R. L.
Published: March 2003

A Lie operator method for constructing action-angle transformations continuously connected to the identity is developed for area preserving mappings. By a simple change of variable from action to angular frequency, a perturbation expansion is obtained in which the small denominators have been renormalized. The method is shown to lead to the same series as the Lagrangian perturbation method of Greene and Percival, which converges on KAM surfaces. The method is not superconvergent but yields simple recursion relations which allow automatic algebraic manipulation techniques to be used to develop the series to high order. It is argued that the operator method can be justified by analytically continuing from the complex angular frequency plane onto the real line. The resulting picture is one where preserved primary KAM surfaces are continuously connected to one another.
Observables measured simultaneously with the potential
Authors: Nasr A. H.
Published: March 2003

The general form of the observables measured simultaneously with some class of potentials is given.
Pre-atlas manifolds and coordinate-free general relativity
Authors: Kloster S. , Das A.
Published: March 2003

Einstein’s equations can be expressed in the tetrad form so that coordinates do not appear explicitly. Tetrads, however, are usually defined on a manifold, which means that coordinates have been introduced. The notion of a manifold without coordinates (a preatlas manifold) is described here and it is shown that Einstein’s equations can be expressed in this setting without introducing coordinates at any stage. Conditions on a preatlas manifold are given which ensure that a C0 atlas can be generated. The motivation for this formulation is the desire to incorporate the philosophy of relativity, which asserts that the mathematical laws of nature are essentially independent of observers or coordinates. ’’The introduction of numbers as coordinates...is an act of violence.’’—H. Weyl