bluuebunny/crossref_metadata_2025 huggingface dataset:
On the two-point functions of some integrable relativistic quantum field theories
Authors: Ruijsenaars S. N. M.
Published: March 2003

Two-point functions associated with the Federbush, massless Thirring, and continuum Ising models and their boson analogs are studied. In the Thirring case it is shown that the fields do not define operator-valued distributions, while temperedness of the two-point Wightman function is proved in the Ising case and in the Federbush case for a certain range of coupling constants. By relating the short-distance singularity of the Schwinger functions to the high-energy behavior of the spectral measures it is shown the fields cannot be made to satisfy the CCR/CAR by a rescaling. In the fermionic Federbush case this breakdown of the CAR occurs in spite of the fact that the fields correspond to a local Lagrangian.
Yang–Mills theory in null-path space
Authors: Kent S. L. , Newman E. T.
Published: March 2003

We define a GL(n,C) matrix-valued function G on a six-dimensional space of null paths in Minkowski space. Such paths are defined to begin at an arbitrary spacetime point xa and end at future null infinity. The space of these paths can thus be parametrized by giving the point xa and null direction. We show how knowledge of G can be used to obtain the GL(n,C) Yang–Mills connection at xa. We also derive a single equation for G, involving characteristic data given on null infinity, which is equivalent to the currentless or vacuum Yang–Mills field equations. The self-dual (anti-self-dual) nonabelian fields and the general abelian cases are described as special examples.
Friedmann universe and superluminal Dirac particles
Authors: Srivastava Sushil K.
Published: March 2003

Superluminal Dirac particles are considered in a Friedmann universe. It is concluded that if such particles were produced at the epoch of the big bang (as assumed by Narlikar and Sudarshan) and also that they survived up to the present time, their metamass should be less than 8.77×10−54 g. It is also concluded that the wavelength of these primordial tachyons (superluminal particles surviving to present time) would be greater than 4.56×10−23 cm. In this paper, expressions for various physical parameters such as probability density and energy and rate of dissipation of energy for these particles are derived.
Analysis of the outer product for the symmetric group
Authors: Somers L. J.
Published: March 2003

Expressions are derived to write the basis vectors for an irreducible representation μ of the symmetric group in terms of basis vectors for irreducible representations whose outer product yields μ.
The Coulomb Jost states in the momentum representation for all partial waves in closed form
Authors: van Haeringen H.
Published: March 2003

We obtain the Coulomb Jost states in the momentum representation for all l in exact closed form. These closed expressions consist of combinations of the function 2F1(1, iγ; 1+iγ; ⋅), Jacobi polynomials, and other polynomials. We also discuss the relation of the Coulomb Jost states with other quantities that are of interest in the theory of charged-particle scattering.
Rotating hollow cylinders: General solution and Machian effects
Authors: Embacher Franz
Published: March 2003

The general solution of the exact gravitational field of a rotating hollow cylinder is derived. It is more general than the solution found by E. Frehland. Machian effects are considered.
Newtonian gravity on the null cone
Authors: Winicour J.
Published: March 2003

For a general relativistic ideal fluid, we analyze the Newtonian limit of the initial value problem set on a family of null cones. The underlying Newtonian structure is described using Cartan’s elegant space–time version of Newtonian theory and a limiting process rigorously based upon the velocity of light approaching infinity. We find that the existence of a Newtonian limit imposes a strikingly simple relationship between the gravitational null data (i.e., the shear of the null cones) and the Newtonian gravitational potential. This result has immediate application to numerical evolution programs for calculating gravitational radiation and might serve as the basis for a post-Newtonian approximation scheme.
Spinors in two dimensions
Authors: Yip Ping
Published: March 2003

The issue of the meanings of ‘‘spinors’’ in two-dimensional Minkowski spacetime is investigated. Spinors in two dimensions are defined and shown to behave like the familiar spinors in four dimensions. Both of them can be interpreted as square roots of vectors, and both of them describe fermions in a quantum field theory. We also show that an analogous version of the spin-statistics theorem holds in two-dimensional Minkowski spacetime.
Self-dual Yang–Mills fields
Authors: Porter John R.
Published: March 2003

The realization of self-dual Yang–Mills fields as nonlinear superpositions of plane waves is treated in analogy with electromagnetism. Despite the nonlinear nature of the fields, there is a complete correspondence between the two theories. The asymptotic behavior of asymptotically flat fields is examined and the plane wave components are shown to decouple on ℐ− and on ℐ+ for such fields and to exibit the character of linear fields when viewed as propagating from ℐ− to ℐ+.
Local S-matrix symmetries in Galilean field theories
Authors: Garber Wolf-Dieter
Published: March 2003

A symmetry of the S-matrix S is an operator that commutes with S and is additive, i.e., transforms an incoming n-particle state as a sum of its constituent one-particle states. For field theories with the Galilei group as a symmetry group and with nonvanishing elastic two-particle scattering amplitude, all S-matrix symmetries Q are determined that are local, i.e., transform local asymptotic fields into local ones. For scalar fields, Q is a linear combination of the ten generators of the Galilei group G, internal symmetries, and, possibly, two other generators C and D. By Galilean invariance, the generators of G are S-matrix symmetries in all field theories. In contrast, it depends on the specific field theory if C and D occur. If C is a symmetry, then D is, too, and vice versa. All scattering amplitudes are given that admit C and D as S-matrix symmetries.
Off-shell T matrix for Coulomb plus simple separable potentials for all l in closed form
Authors: van Haeringen H.
Published: March 2003

We derive simple exact analytic expressions for the off-shell T matrices associated with potentials consisting of the sum of the Coulomb potential and any so-called simple separable potential, for all partial waves. Such potentials play an important role in model calculations for the description of the interaction between charged particles, e.g., protons. We also derive some interesting properties of the Coulomb-modified form factors associated with the form factors of the separable potentials. The analytic expressions obtained are useful for theoretical and numerical applications.
On a generalized F. Riesz problem
Authors: Diţă P.
Published: March 2003

The description of the pion–pion partial waves which are analytic and crossing symmetric is equivalent to solving a generalized Riesz problem. A continuous family of solutions of this problem is constructed.
Generalized Hooke groups and the mass-spectrum problem
Authors: Beau Daniel
Published: March 2003

We briefly recall the notion of internal structure and the relativistic covariant method [introduced in Beau and Horchani, J. Math. Phys. 20, 1700 (1979)] of unifying external and internal structures leading to a kinematical Lie algebra. In this framework we propose a concept of dynamical development of the physical systems defined by this Lie algebra. So we obtain some Lie algebras, a generator of which (the Hamiltonian) gives rise to various mass formulas capable of describing the hadron spectrum; we make use of both unitary irreducible global representations and partially integrable, Schur-irreducible, symmetric local representations.
Interaction of a spin-1/2 tachyon with a spin-1/2 bradyon and a tachyon–bradyon model
Authors: Srivastava Sushil K.
Published: March 2003

Interaction of a spin-1/2 tachyon with the gravitational field of a spin-1/2 bradyon is investigated in the background of Schwarzschild geometry. A tachyon–bradyon bound system (PTBBS) is proposed. In PTBBS, a tachyon revolves around a bradyon in a circular orbit. It is found that as the tachyon goes away from the bradyon, it emits energy under a certain condition; but if this condition is not satisfied, the tachyon gains energy while going away from the bradyon. Also, PTBBS is compared with Bohr’s hydrogen atom model. In the end, the possibility of formation of PTBBS is discussed.
Stability analysis of the neutron transport equation with temperature feedback
Authors: Pao C. V.
Published: March 2003

This paper discusses the stability and instability of neutron transport in a reactor system where positive temperature feedback is taken into consideration. The feedback effect is considered only through the multiplication factor in the neutron transport equation. This consideration leads to a coupled system of nonlinear partial integrodifferential equations of neutron transport and heat conduction. The investigation of this coupled nonlinear initial boundary-value problem is based on the existence-comparison theorem established in an earlier paper in which an iterative scheme for the determination of the solution is given. It is shown in this paper that by constructing a suitable pair of the comparison functions, called upper and lower solutions, as two distinct initial iterations, the corresponding sequences converge monotonically from above and below, respectively, to a unique solution of the system. Under certain conditions on the multiplication factor, the property of upper and lower solutions determines the asymptotic behavior of the solution and leads to stability or instability of the system. A stability region for the zero steady state and an instability region of the system are also given.
Symmetry of the complete second-order nonlinear conductivity tensor for an unmagnetized relativistic turbulent plasma
Authors: Brandt Howard E.
Published: March 2003

A new exact symmetry is proved for the complete second-order nonlinear conductivity tensor of an unmagnetized relativistic turbulent plasma. The symmetry is not limited to principal parts. If Cerenkov resonance is ignored, the new symmetry reduces to the well-known symmetry related to the Manley–Rowe relations, crossing symmetry, and nondissipation of the principal part of the nonlinear current. Also, a new utilitarian representation for the complete tensor is obtained in which all derivatives are removed and the pole structure is clearly exhibited.
Nonscalar extension of shift operator techniques for SU(3) in an O(3) basis. III. Shift operators of second degree in the tensor components
Authors: Van der Jeugt J. , De Meyer H. E. , Vanden Berghe G.
Published: March 2003

Shift operators Qkl (−2≤k≤2) of second degree in the tensor components qμ (−2≤μ≤2) are constructed. Relations connecting quadratic shift operator products of the type Ojl+k Qkl or Qkl+j Ojl , and of the type Qjl+k Qkl are derived. The usefulness of these relations is demonstrated by the example of the OOl - and QOl -eigenvalue calculation for various irreducible respresentations (p,q) of SU(3).
Indecomposable representations for para-Bose algebra
Authors: Gruber B. , Santhanam T. S.
Published: March 2003

A general study of the representations of the graded Lie algebra of para-Bose oscillators is given. Besides realizing the standard representations, we also find some interesting indecomposable (not fully reducible) representations.
Harmonic polynomials invariant under a finite subgroup of O(n)
Authors: Ronveaux A. , Saint-Aubin Y.
Published: March 2003

In this paper, an algorithm is described which allows a systematic computation of harmonic polynomials of a given degree invariant under a finite subgroup of the group O(n). An application of the algorithm to the octahedral (cubic) subgroup is given.
A Galerkin method and nonlinear oscillations and waves
Authors: Chen Fengsu , Hsieh D. Y.
Published: March 2003

A Galerkin method is developed as a generalization of the variational averaging method to deal with problems with dissipation. Some nonlinear oscillations, nonlinear waves, and nonlinear stability problems are studied to illustrate the application of the new method. It is demonstrated that when the dissipative parameter is small, the solutions agree with those obtained by other established methods.
A simple proof of a transformation formula for elliptic integrals
Authors: Bassetti B. , Montaldi E. , Raciti M.
Published: March 2003

A very simple proof of a quadratic transformation formula for elliptic integrals found by Carlson in 1977 is given.
Superposition principles for matrix Riccati equations
Authors: Harnad J. , Winternitz P. , Anderson R. L.
Published: March 2003

A superposition rule is obtained for the matrix Riccati equation (MRE) Ẇ=A+WB+CW+WDW [where W(t), A(t), B(t), C(t), and D(t) are real n×n matrices], expressing the general solution in terms of five known solutions for all n≥2. The symplectic MRE (W=WT, A=AT, D=DT, C=BT) is treated separately, and a superposition rule is derived involving only four known solutions. For the ‘‘unitary’’ and GL(n,R) subcases (with D=A and C=BT, or D=−A and C=BT, respectively), superposition rules are obtained involving only two solutions. The derivation of these results is based upon an interpretation of the MRE in terms of the action of the groups SL(2n,R), SP(2n,R), U(n), and GL(n,R) on the Grassman manifold Gn(R2n).
Manifestly covariant, coordinate-free dyadic expression for planar homogeneous Lorentz transformations
Authors: Fahnline Donald E.
Published: March 2003

Parametrizing a planar homogeneous Lorentz tranformation P by any timelike or spacelike vector b lying in the transformation plane and its transform a≡Pb yields a dyadic expression for P with several advantages: It provides an immediate solution to the problem of finding a homogeneous Lorentz transformation converting a given timelike or spacelike vector into a second similar vector. Its manifestly covariant, coordinate-free form is valid in any Lorentz frame and reduces easily to coordinate form. It unifies timelike (including boosts), spacelike (including pure spatial rotations), and null planar transformations and also orthochronous and nonorthochronous planar transformations into a single form; these classifications depend on the vectors a and b. Only if a=−b does the expression fail, but then its limit as a→−b still exists and provides a valid expression for P.
Transfer matrices for one-dimensional potentials
Authors: Peres Asher
Published: March 2003

The one-dimensional Schrödinger equation can be written as a first-order multicomponent equation by considering ψ and dψ/dx, or combinations thereof, as independent variables. A potential barrier is then represented by a matrix belonging to one of the homomorphic groups SU(1,1), SO(2,1), Sp(2,R), or SL(2,R). The relationship between these groups is clarified. In various applications, one of them may turn out more convenient than others. In particular, SO(2,1), which is obtained by using as a basis some bilinear combinations of ψ and dψ/dx, leads to remarkable results: The Schrödinger wavefunction is represented by a trajectory on a unit hyperboloid; a periodic potential corresponds to a pseudorotation around a fixed axis; a random potential gives a random walk on the hyperboloid. This method can also be used to calculate bound states (in potential wells) and may have many other interesting applications.
Extended continued fractions and energies of the anharmonic oscillators
Authors: Znojil M.
Published: March 2003

We describe the analytic solution to the Schrödinger eigenvalue problem for the class of the central potentials V(r)=∑δ∈Zaδrδ, where a−2>−1/4, amax δ >0, Z is an arbitrary finite set of the integer or rational exponents, −2≤δ1<δ2<⋅⋅⋅<δI, and the couplings aδ satisfy only one auxiliary (formal, ‘‘superconfinement’’) restriction of the type aδI−1 >0. The formalism is based on an analysis of the asymptotic behavior of the explicit regular solution ψ(r) and issues in the formulation of the ‘‘secular’’ equation 1/L1(E)=0 which determines the binding energies. The main result is the rigorous construction of L1(E) as a generalized (‘‘extended’’) and convergent continued fraction. The method cannot be applied to the aδI−1 <0 cases—this disproves the closely related Hill-determinant approach as conjectured recently by Singh et al. for the simplest potentials with Z={−2,2,4,6} and Z={−2,−1,1,2}.
On the number of unnatural parity bound states of the H− ion
Authors: Grosse H. , Pittner L.
Published: March 2003

We show rigorously that the H− ion possesses exactly one (three times degenerate) bound state in the unnatural parity sector.
The multipole structure of stationary space-times
Authors: Simon Walter , Beig Robert
Published: March 2003

A definition of multipole moments for stationary asymptotically flat solutions of Einstein’s equations is proposed. It is shown that these moments characterize a given space-time uniquely. Conversely, they can be arbitrarily prescribed, i.e., they generate power series for the field variables which satisfy the field equations to all orders. Despite their apparently rather different origin, they are shown to be identical with the Geroch–Hansen ones.
Charged spinning mass field involving rational functions
Authors: Chen Y. , Guo D. S. , Ernst F. J.
Published: March 2003

Using a microcomputer, we have derived a new nine-parameter charged spinning mass field. This solution is the simplest member of an infinite sequence of rational function solutions of the coupled Einstein–Maxwell field equations.
Magnetization of all stationary cylindrically symmetric vacuum metrics
Authors: Iyer B. R. , Vishveshwara C. V.
Published: March 2003

New exact solutions of the Einstein–Maxwell equations are obtained by a Harrison-type transformation applied to the most general stationary cylindrically symmetric vacuum spacetime. These solutions include generalizations of the well-known Melvin Magnetic Universe, and the Weyl–Levi-Cività magnetic solution in addition to a new class of magnetic stationary axisymmetric spacetimes.
Summational invariants in the mechanics of mass points
Authors: Amigó J. M. , Reeh H.
Published: March 2003

For systems of point particles, summational invariants (the analog to symmetries of the S-matrix, and in general depending on momenta and coordinates of the particle and explicitly on time) are defined. For systems with interaction, their most general form is derived.
Fluctuation properties of the imperfect Bose gas
Authors: Buffet E. , Pulè J. V.
Published: March 2003

The fluctuations of the occupation numbers of the different levels of the imperfect Bose gas are computed. They are neither normal, Gaussian, nor independent of the way the infinite volume limit is taken. The fluctuations of the overall density are on the contrary normal, Gaussian, and shape independent.
An equation of Hammerstein type arising in particle transport theory
Authors: Boffi V. C. , Spiga G.
Published: March 2003

An equation of Hammerstein type arising in particle transport theory is derived. A sufficient condition for the existence of a solution to it is obtained via a simple application of the contracting mapping principle.
Potential densities for quantum field theories in the scattering picture
Authors: Farrukh M. O.
Published: March 2003

We introduce causality into the general field theory in the scattering picture, introduced in a previous paper, by expanding the effective potential density, which is constructed in analogy with local nonrelativistic potentials and which is shown not to be microcausal. Thus the usual divergencies of conventional quantum field theory could be avoided. In the nonrelativistic limit, the expansion of the U matrix reduces to the conventional time-ordered expansion, which shows that the theory is, in a sense, macrocausal.
Nonlinear Schrödinger-type field equation for the description of dissipative systems. I. Derivation of the nonlinear field equation and one-dimensional example
Authors: Schuch D. , Chung K.-M. , Hartmann H.
Published: March 2003

Based on three principles taken from empiricism we establish a new nonlinear field theory which allows us to describe frictional effects in dissipative systems with the aid of a Schrödinger-type field equation with logarithmic nonlinearity. This nonlinear field equation corresponds to the classical Langevin equation and can be interpreted in different ways, taking the view of classical undulatory theory or probabilistic theories, respectively. Because of formal similarities, calculations can be performed independently of the accepted interpretation; only the occurring quantities have to be provided with the corresponding meaning. As an example, the nonlinear field equation for the damped harmonic oscillator is solved exactly. The solutions, a wavefunction and a wavepacketlike solution, a solution with Gaussian shape, exhibit reasonable properties, contain the correct reduced frequency Ω=(ω20−γ2/4)1/2 and are different from the solutions of the undamped problem. The properties of our nonlinear friction term are discussed and compared with those of similar nonlinear friction terms used by other authors. Finally, we derive a nonlinear friction term equivalent to our logarithmic nonlinearity but involving only combinations of suitably defined operators of position and linear momentum and mean values of these operators.
Wobbling kinks in φ4 and sine-Gordon theory
Authors: Segur Harvey
Published: March 2003

When the φ4 model admits a kink solution, it also admits a wobbling kink, which satisfies the boundary conditions of a kink, but possesses an internal degree of freedom. In this paper we develop a formal perturbation series for the wobbling kink in φ4 theory, and give the first two terms in the series explicitly. Then we prove that the formal series actually is asymptotic for a rather long time [O(K ln(1/ε)) for a certain K]. Finally, we construct an exact 3-soliton solution of the sine-Gordon equation that also has the properties of a wobbling kink. For the sine-Gordon equation, the wobbling kink seems to be mildly unstable.
Sufficient conditions for weak minimum of a functional depending on n functions and their derivatives
Authors: Ray Alak
Published: March 2003

The sufficient condition for positive definiteness of a quadratic form involving unsymmetric matrix operators is given in terms of a global criterion. This determines the sufficient condition for the weak minimum of a functional depending on n-functions and their derivatives. The criterion is formulated in terms of the absence of conjugate points in the interval of the variational integral and is a generalization of a similar criterion due to Newcomb in problems of hydromagnetic stability in plasma physics.
The fundamental identity for iterated spherical means and the inversion formula for diffraction tomography and inverse scattering
Authors: Beylkin G.
Published: March 2003

A uniform derivation of the inversion formula for diffraction tomography and inverse scattering from the fundamental identity for iterated spherical means is presented.
The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative
Authors: Weiss John
Published: March 2003

In this paper we investigate the Painlevé property for partial differential equations. By application to several well-known partial differential equations (Burgers, KdV, MKdV, Bousinesq, higher-order KdV and KP equations) it is shown that consideration of the ‘‘singular manifold’’ leads to a formulation of these equations in terms of the ‘‘Schwarzian derivative.’’ This formulation is invariant under the Moebius group (acting on dependent variables) and is shown to obtain the appropriate Lax pair (linearization) for the underlying nonlinear pde.
The Hamiltonian structure of the nonabelian Toda hierarchy
Authors: Bruschi M. , Ragnisco O.
Published: March 2003

We show that a subset of the whole class of nonlinear differential-difference equations, associated with the discrete analog of the matrix Schrödinger operator, is endowed with a Hamiltonian structure and exhibits an infinite number of integrals of motion in involution. We also establish the relation between these integrals of motion and the transmission coefficient of the underlying linear problem, and show that such a relation implies that, for the whole class previously introduced, there exists an infinite number of conserved quantities.
On the expansion of integrals containing Fermi distributions
Authors: Åberg Sven
Published: March 2003

We derive an expansion of integrals containing a general function multiplied by a Fermi function raised to an arbitrary power ν. When ν is an integer, direct expressions for the expansion coefficients are given. The expansion is found to converge quite rapidly if the diffuseness of the Fermi distribution is small, and when ν≳1.
Generalized linear inversion and the first Born theory for acoustic media
Authors: Keys R. G. , Weglein A. B.
Published: March 2003

A procedure is derived which incorporates a generalized linear inverse viewpoint within a multidimensional Born inversion method. The method we present is a more general Born theory which can accommodate insufficient and inaccurate data. This general method reduces to the ordinary Born procedure when the data requirements of the latter technique are satisfied.
Continuity statements and counterintuitive examples in connection with Weyl quantization
Authors: Daubechies Ingrid
Published: March 2003

We use the properties of an integral transform relating a classical function f with the matrix elements between coherent states of its quantal counterpart Q f, to derive continuity properties of the Weyl transform from classes of distributions to classes of quadratic forms. We also give examples of pathological behavior of the Weyl transform with respect to other topologies (e.g., bounded functions leading to unbounded operators).
Schrödinger spectral kernels: High order asymptotic expansions
Authors: Osborn T. A. , Wong R.
Published: March 2003

The large energy behavior of the spectral kernel for the N-body Schrödinger Hamiltonian is obtained. In a setting of a d-dimensional Euclidean space without boundaries, the Schrödinger Hamiltonian H is the sum of the negative Laplacian plus a real-valued local potential v(x). The class of potentials studied is the family of bounded and continuous functions that are formed from the Fourier transforms of complex bounded measures. These potentials are suitable for the N-body problem, since they do not necessarily decrease as ‖x‖→∞. Let {e(x,y;λ): λ∈R} be the family of spectral kernels generated by H. In the λ→∞ limit, explicit higher order asymptotic expansions are obtained for e(x,y;λ) and its associated Riesz means. The asymptotic expansion is uniform in x and y and is accompanied by estimates of the error term.
Inverse scattering theory for systems of the Zakharov–Shabat type
Authors: de Castro Helena M. A. , Wreszinski Walter F.
Published: March 2003

We present a mathematically rigorous inverse scattering theory for systems of the Zakharov–Shabat type. A qualitative spectral analysis of a class of non-self-adjoint operators, which is necessary for the construction, is also provided.
Irreversible quantum dynamics and the Hilbert space structure of quantum kinematics
Authors: Gisin N.
Published: March 2003

General dynamics compatible with the Hilbert space structure of quantum kinematics are considered. The general form of dynamics which preserve the set of closed linear submanifolds (i.e., properties) is deduced. Since the orthogonality relation is not necessarily preserved, the result generalizes Wigner’s theorem and provides a model of some irreversible phenomena like spin relaxation, damped oscillator, etc. Connections with quantum logic and with statistical mechanics are presented.
Non-Grassmann quantization of the massive Thirring model
Authors: Garbaczewski Piotr
Published: March 2003

A direct quantization of the c-number (semi) classical massive Thirring model in the inverse scattering formalism leads to the Bose massive Thirring model, which is equivalent to the conventional Fermi one, both having identical S-matrices and bound-state spectra.
Dirac gravitational magnetic monopoles do not exist
Authors: Ross D. K.
Published: March 2003

We show that the gravitational analog of the Dirac magnetic monopole does not exist for a gauge theory of gravitation with either a T4 or an SL(2, C) × T4 gauge group.
Response to gravitational probes and induced Newton’s constant
Authors: Brown L. S. , Zee A.
Published: March 2003

We study the response of the action functional to external probes and derive a representation for Newton’s constant without specializing to conformally flat space, as is normally done in standard discussions of induced gravity.
The nonsymmetric Kaluza–Klein theory
Authors: Kalinowski M. W.
Published: March 2003

This paper is devoted to a five-dimensional unification of Moffat’s theory of gravitation and electromagnetism. We found ‘‘interference effects’’ between gravitational and electromagnetic fields which appear to be due to the skew-symmetric part of the metric of Moffat’s theory. Our unification called the nonsymmetric Kaluza–Klein theory becomes the classical Kaluza–Klein theory if the skew-symmetric part of the metric is zero. The possible generalization to an arbitrary gauge group is discussed.
Character generators for unitary and symplectic groups
Authors: Baclawski Kenneth
Published: March 2003

Combinatorial algorithms for computing the character generators of U(n), SU(n), and Sp(2n, C) are described. These algorithms produce relatively compact, nested expressions for the character generators. Moreover, the terms appearing in these expressions all have positive coefficients. This feature is not shared by the expression for the character generator which uses the Weyl character formula.
Missing label operators in the reduction 𝒪(p)↓𝒪(p−2)×𝒪(2)
Authors: Bincer Adam M.
Published: March 2003

I consider the ‘‘missing label’’ problem for basis vectors of an 𝒪(p) representation corresponding to a group reduction chain with links 𝒪(p)↓𝒪(p−2)×𝒪(2). A chain with these links is required if the basis vectors are to be of definite weight. I obtain two different sets of missing label operators, which together with the Casimir operators of group and subgroups from a complete set of labeling operators whose eigenvectors provide a canonical basis in the 𝒪(p) representation space. The problem is solved for both the even- and odd-dimensional orthogonal groups.
Construction of N-dimensional indecomposable representations for scale and special conformal transformations
Authors: Shintani Meiun
Published: March 2003

The theories of N-dimensional indecomposable representations for the group of semidirect products of D (dilatation group) and K (special conformal group) are investigated through the studies on space-time inversions.
Characterization of canonical Bose–Fermi systems by ‘‘anti-Hermitian’’ symplectic forms
Authors: Nakajima Hideo
Published: March 2003

A complexification of graded manifold theory is given, following Kostant’s procedure, but with a reality concept defined by ‘‘classical’’ correspondent to Hermitian conjugation in quantum mechanics. Presented herein are definitions of graded manifolds with ‘‘Hermite’’ coordinates and of ‘‘Hermiticity’’ on graded differential forms and graded vector fields, all in the coordinate independent way, and characterization of ‘‘classical’’ Bose–Fermi systems by graded symplectic forms ω which are, here, ‘‘anti-Hermitian’’ nonsingular closed 2-forms of z2 grading 0. Also given are Frobenius’ theorem on the graded manifold with ‘‘Hermiticity,’’ and Darboux’s theorem, ω=∑kdpkΛdqk+i∑j +i∑j(εj/2)dsjΛdsj, where all coordinates are ‘‘Hermite,’’ pk† =pk, qk†=qk, sj† =sj. Naive quantization procedures fit in with these systems.
Application of Benson’s inequalities to the atomic electronic density
Authors: King Frederick W.
Published: March 2003

In this work, several upper bound estimates for the atomic electronic density are derived by making use of Benson’s inequalities. In some cases, it has been possible to compare the results obtained using Benson’s inequalities with some bounds recently derived by other workers.
Critical behavior of the spin van der Waals model
Authors: Pathria R. K.
Published: March 2003

Thermodynamic behavior in the critical region of the spin van der Waals model is considered when the number of spins in the system is large but finite (1≪N<∞). The specific heat curve is shown to possess a steep, yet smooth, maximum which turns into a singularity as the number of spins becomes infinite. In the case of the finite system, this maximum occurs at ε=ε*=O(N−1/3), where ε=(T−Tc)/Tc, Tc being the critical temperature of the infinite system.
A two-parameter matrix Riccati equation pair for a class of nonlinear sigma models based on a symmetric space
Authors: Snyder M. A.
Published: March 2003

It is shown that the infinitesimal action of a group on one of its associated symmetric spaces is, in the case of a classical off-diagonal symmetric space, in the form of a matrix Riccati equation. A two-parameter Riccati equation is then found for the nonlinear sigma model based on a symmetric space G/H.
Radiation gauge covariance. II. Quantization of the free electromagnetic field
Authors: Krause Jorge
Published: March 2003

The ‘‘substratum’’ of the electromagnetic field is defined as a two-dimensional duality isovector, satisfying the homogeneous wave equation. The components of the substratum are two Lorentz scalar fields that carry the two degrees of freedom of the field. It is then shown that the free Maxwell field becomes effectively quantized by the canonical quantization of the substratum. The equal-time canonical commutator thus obtained is precisely the same commutator one gets while quantizing the electromagnetic field within the Coulomb gauge. The whole approach is manifestly relativistic.
Fermion currents in 1+1 dimensions
Authors: Carey A. L. , Hurst C. A. , O’Brien D. M.
Published: March 2003

Let ℱ denote the Fock space for a free massless fermion field in two space-time dimensions. If Q and Q5 denote the charge and chiral charge operators, then ℱ=⊕n1,n2ℱn1,n2, where ℱn1,n2 is the joint eigenspace of Q and Q5 with corresponding eigenvalues n1 and n2. The smeared time-zero free fermion currents formally given by Jμ( f) =∫:ψ̄(x)γμψ(x): f(x) dx [μ=0,1; f∈𝒮(R)] are in fact self-adjoint densely defined operators on ℱ and their exponentials generate a C* algebra which leaves each subspace ℱn1,n2 invariant. If a periodic box cutoff for the fermions is introduced, Uhlenbrock has shown that this C* algebra acts irreducibly in each ‘‘sector’’ ℱn1,n2. We prove this same result without any cutoffs and determine the properties of the representations in each sector. The importance of this result for the problem of constructing fermion fields from ‘‘observables’’ in two-dimensional models, such as those of Thirring and Schwinger, is discussed.
Current responses of first and second order in a collisionless plasma. IV. Applications
Authors: Larsson Jonas
Published: March 2003

The purpose of this paper is to illustrate with a few concrete examples how the general formulas given in the preceding papers I–III may be used. We consider three different background plasmas: a homogeneous static magnetized plasma, a homogeneous magnetized plasma in an oscillating electric field, and a semi-infinite homogeneous static magnetized plasma. The coupled mode equations governing resonant three-wave interaction are given in each case.
Comparison of the extended boundary condition method and perturbation method for scattering from a sinusoidal sea surface
Authors: Ott R. H. , Fang D. J.
Published: March 2003

Scattering from a lossy sinusoidal surface is examined by using two methods: extended boundary condition (EBC) and perturbation. The range of applicability of the perturbation approach is established by comparison with EBC. The range of applicability of EBC is established through numerical examples. A convergence criterion based on the sequence of partial sums of the scattered energy is suggested for the application of EBC to lossy surfaces. New analytical expressions for the perturbation solutions are given.
Completely integrable relativistic Hamiltonian systems and separation of variables in Hermitian hyperbolic spaces
Authors: Boyer C. P. , Kalnins E. G. , Winternitz P.
Published: March 2003

The Hamilton–Jacobi and Laplace–Beltrami equations on the Hermitian hyperbolic space HH(2) are shown to allow the separation of variables in precisely 12 classes of coordinate systems. The isometry group of this two-complex-dimensional Riemannian space, SU(2,1), has four mutually nonconjugate maximal abelian subgroups. These subgroups are used to construct the separable coordinates explicitly. All of these subgroups are two-dimensional, and this leads to the fact that in each separable coordinate system two of the four variables are ignorable ones. The symmetry reduction of the free HH(2) Hamiltonian by a maximal abelian subgroup of SU(2,1) reduces this Hamiltonian to one defined on an O(2,1) hyperboloid and involving a nontrivial singular potential. Separation of variables on HH(2) and more generally on HH(n) thus provides a new method of generating nontrivial completely integrable relativistic Hamiltonian systems.
Connection between the existence of bisolitons for quadratic nonlinearities and a factorization of the associate linear operator
Authors: Cornille H. , Gervois A.
Published: March 2003

In a first part we investigate the exponential type bisolitons of the class of equations (ε+Lq)K =(ε+∑i+ j=1i+ j=q aij  ∂xitji+ j)K =(λ+μ∂x)K2 (ε≠0, λ≠0 or ε=λ=0), which are rational solutions and we assume that their denominators have no coupling between the solitons. We have found that their existence requires a factorization property of either the operator ε+Lq for ε≠0, λ≠0, q≤3 or Lq for ε=λ=0, q≤3 with the exception of the Burgers equation. We find three kinds of nontrivial bisolitons: either those associated with the mixed nonlinearity (λ+μ∂x)K2 alone, or those common to the mixed nonlinearity and KKx or those belonging to KKx alone. In the second part we look at the two last types of bisolitons for q>3 and give a constructive method leading both to factorized linear operators and to the explicit determination of the bisolitons. We consider mainly lq−2(t)  (a∂t +b∂x +c∂xx)G =(∂xG)2, K=Gx, with the linear operator factorizing the linear part of the Burgers equation, lq−2 (t) is a differential operator in variable t only. The general G solution is a linear combination of logΔ and Δ−i, i=1,...,q−2 with Δ=1+∑21  exp(t+γix). We determine different classes of solutions as well as the associated lq−2(t) operators.
Tetrads and arbitrary observers
Authors: Urani John R. , Kemp Marilyn H.
Published: March 2003

Recent results concerning globally isometric mappings for arbitrary observers in flat space-time are generalized to space-times admitting a time orientation. Critical to the method is the use of an orthonormal tetrad which, when it is defined globally, allows the construction of a global isometry which generalizes the pointwise boost on flat space-time. Connection coefficients are obtained, thereby defining acceleration covariant differentiation for both particle and tensor field equations. An application to orbiting observers in exterior Schwarzschild geometries is presented.
Dynamical symmetries: An approach to Jacobi fields and to constants of geodesic motion
Authors: Caviglia Giacomo
Published: March 2003

It is shown that every dynamical symmetry (DS) of the Euler–Lagrange equations derived from the Lagrangian L =(1/2)gabq̇aq̇b identifies a Jacobi field on each geodesic of the configuration manifold. Using the connections between Jacobi fields and DS’s, it is proved that DS’s always possess associated conserved quantities, whose expression is explicitly written down. An additional constant of motion concomitant with ‘‘pairs’’ of DS’s, independently of the choice of L, is also determined. Applications to general relativity are emphasized in the course of the discussion.
The rotating harmonic oscillator eigenvalue problem. I. Continued fractions and analytic continuation
Authors: Masson D.
Published: March 2003

The continued fraction approach to the solution of the rotating harmonic oscillator eigenvalue problem is examined in detail. It is shown how one may obtain eigenvalue information only from an analytic continuation of the continued fraction accomplished with the aid of modified approximants.
Symmetry and generating relations for Clebsch–Gordan coefficients arising from automorphisms
Authors: Dirl R.
Published: March 2003

A new class of symmetry and generating relations for Clebsch–Gordan coefficients is derived. It is associated with certain elements of the full automorphism group. Our approach turns out to be useful for an efficient computation of Clebsch–Gordan coefficients.
On the quaternion representation of the proper Lorentz group SO(3,1)
Authors: Rao K. N. Srinivasa , Rao A. V. Gopala , Narahari B. S.
Published: March 2003

Complex quaternions are investigated in detail, bringing out some new aspects of the relationship of the multiplicative group of unit complex quaternions (UCQ) with the proper Lorentz group SO(3,1). Constructing the proper Lorentz transformation (PLT) corresponding to a given UCQ, the quaternion parameters of a PLT are determined explicitly in terms of its element Lij, and this quaternion parametrization is then utilized to obtain an interesting geometrical interpretation of SO(3,1) as the intersection of a hyperboloid with a cone in a real eight-dimensional Euclidean space E8. The UCQ components are then related to the Lie–Cartan parameters of SO(3,1), leading to an identification of complex quantities which may be interpreted as the complex axis and angle of rotation. It is shown that any PLT admits a special type of Euler resolution which is at the same time a resolution into three Lorentz–Synge screws the two angles of which combine to form a complex Euler angle (or Euler–Brauer angle). It is also shown that on taking the rotation parameters in the formula for the D j representation of SO(3) to be complex, one obtains the D j0 representation of SO(3,1), leading at once to its D jj′ representation. Similarly, a formula for the character χ j0 of the D j0 representation, having a complete analogy to the character formula for SO(3), but in terms of a complex angle ω is obtained and this in turn yields a formula for the character χ jj′ in the Djj′ representation of SO(3,1).
Clebsch–Gordan coefficients for SU(5)⊇SU(3)×SU(2)×U(1) theories
Authors: Koh In-Gyu , Patera J. , Rousseau C.
Published: March 2003

The Clebsch–Gordan coefficients are calculated for the following tensor products of SU(5) representations: 5⊗5, 5⊗10, 5⊗1̄0̄, 15⊗5, 15⊗5̄, 10⊗10, 5⊗5̄, 10⊗1̄0̄, 5⊗24, and 10⊗24. Each case is calculated twice: once in a weight vector basis independent of any semisimple subgroup, the second time in a basis which refers to SU(3)×SU(2)×U(1)⊆SU(5).
Octonionic description of exceptional Lie superalgebras
Authors: Sudbery A.
Published: March 2003

The structures of the exceptional Lie superalgebras G(3) and F(4) are expressed in terms of octonions.
On the higher orders of hyperspherical harmonics
Authors: Arribas E. , Navarro J. , Fabre de la Ripelle M.
Published: March 2003

We suggest a procedure to evaluate matrix elements between hyperspherical harmonics of any order. The method is based on the hyperspherical expansion of a Slater determinant constructed with oscillator wavefunctions. Explicit formulas are given for all matrix elements up to order Lm+2.
Symmetries of differential equations. IV
Authors: González-Gascón F. , González-López A.
Published: March 2003

By an application of the geometrical techniques of Lie, Cohen, and Dickson it is shown that a system of differential equations of the form x(rii=Fi (where ri>1 for every i=1,...,n) cannot admit an infinite number of pointlike symmetry vectors. When ri=r for every i=1,...,n, upper bounds have been computed for the maximum number of independent symmetry vectors that these systems can possess: The upper bounds are given by 2n2+nr+2 (when r>2), and by 2n2+4n+2 (when r=2). The group of symmetries of x̄(r=0̄ (r>1) has also been computed, and the result obtained shows that when n>1 and r>2 the number of independent symmetries of these equations does not attain the upper bound 2n2+nr+2, which is a common bound for all systems of differential equations of the form x̄(r=F̄(t,x̄,...,x̄(r−1) when r>2. On the other hand, when r=2 the first upper bound obtained has been reduced to the value n2+4n+3; this number is equal to the number of independent symmetry vectors of the system ẍ̅=0̄, and is also a common bound for all systems of the form ẍ̅=F̄(t,x̄,x̣).
The rotating harmonic oscillator eigenvalue problem. II. Analytic perturbation theory
Authors: Masson D.
Published: March 2003

The theory of self-adjoint analytic families is applied to the rotating harmonic oscillator Hamiltonian in L2(0,∞) to obtain weak and strong coupling expansions of the eigenvalues. Various estimates on the radius of convergence of the weak coupling expansion are obtained. The strong coupling expansion is shown to be an asymptotic series which, with the neglect of exponentially small terms, is expressible in terms of a simple formal perturbation of the ordinary harmonic oscillator Hamiltonian in L2(−∞,∞).
Symmetries, conservation laws, and time reversibility for Hamiltonian systems with external forces
Authors: van der Schaft A. J.
Published: March 2003

A system theoretic framework is given for the description of Hamiltonian systems with external forces and partial observations of the state. It is shown how symmetries and conservation laws can be defined within this framework. A generalization of Noether’s theorem is obtained. Finally a precise definition of time reversibility is given and its consequences are explored.
Normal form and representation theory
Authors: Cushman Richard , Deprit André , Mosak Richard
Published: March 2003

Representation theory of Lie algebras is called upon to develop a procedure for normalizing a dynamical system with two degrees of freedom in the neighborhood of an equilibrium when the Hamiltonian H(x, y, X, Y) in the coordinates (x, y) and their conjugate momenta (X, Y) is of the type H=(X2+Y2)/2+V(x, y, X, Y), the potential energy V  being a sum of homogeneous polynomials in the phase variables of degree strictly greater than 2. The fact that the resulting potential V′ is a polynomial in the new coordinates (x′, y′) and the angular momentum G′=x′Y′−y′X′ implies that the normalization is a rotation in the configuration space from a fixed frame to an ideal frame. The technique is intended for normalizing an Hamiltonian in equilibrium at the origin when the Lie derivative associated with the quadratic part is not semisimple, e.g., the planar restricted problem of three bodies at the equilateral equilibrium L4 when the basic frequencies are equal (Routh’s singular case).
Transmission through a system of potential barriers. I. Transmission coefficient
Authors: Dammert Örjan
Published: March 2003

The transmission coefficient for a one-dimensional system of N potential barriers of general shapes (unequal or equal) is expressed exactly, by means of the phase-integral method of N. Fröman and P. O. Fröman, in terms of quantities characterizing the separate barriers and wells of the system. The exact formula, being of interest for further rigorous studies of transmission properties, can for evaluation readily be converted into a useful approximate formula by insertion of available phase-integral expressions (of an arbitrary order) for the characteristic quantities mentioned above. Error estimates are given. The sub- and superbarrier cases are treated in a unified way. Some key facts about the phase-integral method are given in Appendix A.
Kac–Dynkin diagrams and supertableaux
Authors: Bars I. , Morel B. , Ruegg H.
Published: March 2003

We show the relation between Kac–Dynkin diagrams and supertableaux.