bluuebunny/crossref_metadata_2025 huggingface dataset:
Quantum Operator Ordering and the Feynman Formulation
Authors: Testa F. J.
Published: February 2004

A functional integral representation for the quantum Hamiltonian propagator is obtained from the Feynman formulation. It is shown that operator ordering arbitrariness in the quantum Hamiltonian is directly related to arbitrariness in the algorithmic definition of the functional integral. Examples are cited which demonstrate this fact.
Formal Equivalence of the Hydrogen Atom and Harmonic Oscillator and Factorization of the Bethe-Salpeter Equations
Authors: Basu Debabrata
Published: February 2004

We investigate the possible factorizations of the confluent hypergeometric equation and show that this leads to a formal equivalence of the usual hydrogen atom problem with that of a set of multidimensional harmonic oscillators of appropriate classical frequency in a space of varying (even) dimensionality ranging from 4l + 4 to 2. We next use this method to investigate the solutions of some relativistic bound-state equations. As specific examples we consider Goldstein's eigenvalue problem and the Wick-Cutkosky scalar meson equation. A formal similarity also exists between the Goldstein problem and the scalar meson equation in the zero binding limit. The factorization of either of these equations leads to an infinite ladder of nonsquare integrable solutions. On the other hand, for arbitrary nonvanishing binding energies a complete solution of the scalar meson problem has been obtained by investigating the zero-energy factorization of the equation.
Linear Spin Chain with Nearest and Next-Nearest Neighbor Interactions
Authors: Niemeijer Th.
Published: February 2004

We study the properties of a linear chain of spins governed by the Hamiltonian H=J1 ∑ j=1NSj·Sj+1+J2 ∑ j=1NSj·Sj+2and derive equations for an upper bound of the free energy by means of a temperature dependent Hartree-Fock approximation. These equations can be solved at zero temperature, yielding an approximate wavefunction for the ground state, of which the energy is an upper bound for the exact ground state energy. The upper bounds obtained are improvements of the results of Majumdar and Ghosh. There are several different cases to be considered, depending on the relative values of J1 and J2. In none of these is there a gap between the ground state and the first excited state in the thermodynamic limit. Finally, correlation functions are shortly discussed in connection with spiral structures in classical spin systems.
Specific Heat and Entropy Bounds for Ising Spin Systems
Authors: Falk H.
Published: February 2004

For quite general Ising spin systems of arbitrary dimensionality and with ferromagnetic interactions of arbitrary range, an entropy lower bound is obtained from Griffiths' inequalities and convexity relations. The bound is valid for nonnegative magnetic fields which may vary from site to site. The specific heat computed from the bound is shown to be an upper bound for the exact specific heat. If the magnetic field is taken to be zero, the entropy bound is shown to be tighter than that obtained previously by truncating a cumulantlike entropy expansion at second order. The present lower bound achieves equality with the exact entropy of the nearest-neighbor, N-spin, Ising ring as N → ∞ for zero field and positive temperatures. An interpretation of the entropy bound is that if in the truncated expansion only binary terms arising from primary correlation are retained, the result is, nevertheless, an overestimate of the order.
Motion of a Particle in a Random Field
Authors: Papanicolaou George C.
Published: February 2004

The motion of a particle in a random force field is investigated using the diffusion approximation.
Theorem on the Convergence Rate of Generalized Fourier Series
Authors: Schneider Thomas R.
Published: February 2004

We prove a theorem on the convergence rate of generalized Fourier expansions. Our result is not restricted to any particular basis.
Group-Theoretic Derivation of Crossing Sum Rules
Authors: Cooper C. S. , Pennington M. R.
Published: February 2004

Crossing relations between amplitudes with definite isospin for ππ scattering are expressed in terms of the symmetric group S3. The sum rules, involving s-channel partial wave amplitudes, are then derived without reference to the Balachandran and Nuyts expansion and are shown to be a direct consequence of the group-theoretic orthogonality relations. This results in closed expressions for all possible sum rules.
Evaluation of Certain Statistical Averages in the Hamiltonian Form
Authors: Howgate David W.
Published: February 2004

A compact method is presented for the evaluation of certain statistical averages involving a quadratic Hamiltonian generator.
Space-Time of the de Broglie Wave Field
Authors: Kulhánek J.
Published: February 2004

A geometrical characterization is given of the space-time with a metric satisfying the equations of the de Broglie wave field. To do this, we exploit a formal analogy with a ``perfect fluid'' whose energy and pressure depend on the components of the metric field and its derivatives. To determine the properties of the space-time, we use the Ricci principal directions.
Thermodynamical Theory of Directed Curves
Authors: DeSilva C. N. , Whitman A. B.
Published: February 2004

A nonlinear thermodynamical theory of directed curves is obtained by postulating an energy balance, an entropy production inequality, and invariance requirements under superposed rigid body motions. Constitutive equations for a class of simple materials without memory are presented.
Regge Trajectories at High Energies for a Class of Analytic Potentials
Authors: Johnson Porter W.
Published: February 2004

We consider scattering by nonsingular, energy-independent, central potentials V(r) which are analytic in r in a sector of half-angle θ about the real positive axis. Simple considerations show that at high energies all Regge trajectories leave the sector of the angular momentum plane given by |arg l| ≤ θ. One finds in general, however, that Regge trajectories remain in the right half l plane at sufficiently high energies for potentials of the above type. The Wood-Saxon potential is analyzed numerically. It is found that Regge trajectories which represent bound states remain in the right half l plane at high energies.
Relativistic Wave Equations: Proper Lorentz Invariance and Invariance under Discrete Transformations
Authors: Seetharaman M. , Jayaraman J. , Mathews P. M.
Published: February 2004

Considering the standard form i∂ψ/∂t=Hψ [with ψ transforming according to D(0,s)⊕D(s,0)] of wave equations for free particles of arbitrary spin, we determined in a recent paper the admissible forms of H consistent with invariance of the equation under the Poincaré group and under T, C, and P. Here we show that even if T and C invariance is not imposed, the admissible Hamiltonians are the same (apart from one extra possibility H = E). Expressed differently, except for the trivial case H = E, invariance of free-particle equations under the connected Poincaré group and P implies T and C also.
Analytic Solutions of the Reference Spectrum Equation
Authors: Grypeos M. E.
Published: February 2004

Analytic solutions of the fundamental equation of the reference spectrum method for nuclear matter are obtained in the cases of the square well and exponential potentials with hard cores. In the former case analytic wavefunctions are obtained for every partial wave L. These wavefunctions are expressed in terms of spherical Bessel and Hankel functions or in terms of spherical Bessel, Hankel, and Newmann functions of order L. In the latter case an analytic expression is obtained for the s wavefunction only. This is given in terms of the transcendental functions G±v(r) and M±v(r) which are defined as series of well-known functions. Finally an application is made of our results to the calculation of the well depth of a Λ particle in its ground state in nuclear matter.
Quantum Potentials on Lattices
Authors: Greenberg William
Published: February 2004

The existence and analyticity of thermodynamic states of v-dimensional lattices is proved for non-number-conserving potentials at all values of fugacity for sufficiently high temperatures.
Linear Canonical Transformations and Their Unitary Representations
Authors: Moshinsky M. , Quesne C.
Published: February 2004

We show that the group of linear canonical transformations in a 2N-dimensional phase space is the real symplectic group Sp(2N), and discuss its unitary representation in quantum mechanics when the N coordinates are diagonal. We show that this Sp(2N) group is the well-known dynamical group of the N-dimensional harmonic oscillator. Finally, we study the case of n particles in a q-dimensional oscillator potential, for which N = nq, and discuss the chain of groups Sp(2nq)⊃Sp(2n)×O(q). An application to the calculation of matrix elements is given in a following paper.
Formulation of the Many-Body Problem for Composite Particles. III. The Projected Hamiltonian
Authors: Girardeau M. D.
Published: February 2004

A previously developed representation for many-atom problems is extended by incorporation of all effects of interatomic exchange of electrons and nuclei into a ``projected Hamiltonian.'' An expression for the projected Hamiltonian is derived which is exact on the two-atom subspace, and hence incorporates those exchange effects which are important at low densities. By the use of the center-of-mass separation of atomic wavefunctions, this expression for the projected Hamiltonian is transformed into a representation in terms of atomic field operators ψν(r) and ψν†(r), where r is the center-of-mass position of an atom and v stands for all of its internal quantum numbers.
L-Wave Inverse Scattering Problem
Authors: Corbella Oscar D.
Published: February 2004

The inverse scattering problem for the Schrödinger equation is considered. Under certain restrictions on some of the odd derivatives of the potential, we obtain expressions for the values of the potential and its derivatives at the origin, as functions of the phase shift and bound state data for any fixed partial wave. Closed expressions for the first coefficients of the expansion of the potential are obtained.
The Jahn-Teller Theorem
Authors: Blount E. I.
Published: February 2004

A compact proof of the Jahn-Teller theorem is given. The method distinguishes between two cases: (1) If the irreducible representation Γ to which the wavefunction belongs is reducible under one of the subgroups Gs which leave one atom invariant; the proof is trivial and would apply in space of any number of dimensions. (2) If Γ remains irreducible under all Gs, more detailed attention is necessary. In two or three dimensions, however, it is straightforward to establish the theorem for this case. It is further shown that in composite-dimensional spaces, some violations of the theorem would be found under (2).
Structure of Neutral Mesonic Atoms Formed in Liquid Helium. III. More Accurate Treatment of the Electron Wavefunction
Authors: Chen L. C. , Guo J. , Russell J. E.
Published: February 2004

The ground-state energy of a spinless nonrelativistic electron in the field of two fixed spinless nuclei with charges +2 and −1 is computed exactly for a large number of values of the internuclear separation. The calculation is performed using a method devised many years ago by Baber and Hassé. The results of this calculation are then used to estimate values, for a few highly excited states of απ−e− and αK−e− atoms, of a correction to a previous calculation of the binding energy. This energy correction increases, by one unit, a previous estimate of the multipolarity of the most favored Auger transition from a circular orbit of the αK−e− atom with n = 29; a similar increase is found to be most likely for circular orbits of the απ−e− atom with n = 20 and circular orbits of the αp̄e− atom with n = 32, 35, and 37. For αK−e− atoms with n = 27 and 29, the energy corrections cause the calculated energy difference between a circular and a nearly circular orbit with the same principal quantum number to be between 15 and 30% smaller than had been estimated previously. Two other corrections are estimated and are found to be probably negligible. One of these corrections is the inaccuracy in the calculated binding energy of a heliumlike mesonic atom, as obtained using the Born-Oppenheimer approximation, which is associated with the angular correlation between the positions of the electron and the meson. The other correction is the change in the computed value of the mean meson orbital radius which occurs when the interactions responsible for the electron-meson angular correlation are taken into account.
Scattering from a Periodic Corrugated Structure: Thin Comb with Soft Boundaries
Authors: DeSanto John A.
Published: February 2004

An incident plane wave is scattered from a surface, corrugated in one dimension, and given by an infinite number of periodic, finite-depth, infinitesimally thin parallel plates (thin comb) having soft boundary conditions. The solutions of the Helmholtz equation are assumed to be upgoing plane waves above the plates and standing waves in the plate wells. Both have unknown amplitude coefficients. Continuity of the solutions and their derivatives across the common boundary yields a doubly infinite set of linear equations for the unknown amplitudes. The equations are solved using the modified residue calculus technique due to Mittra. The amplitudes are expressed as values or residues of a certain meromorphic function. The residue calculus and Wiener-Hopf techniques are related; thus, an example of a solvable finite-range Wiener-Hopf-type problem is presented. Numerical evaluations of reflection coefficients are presented as a function of frequency, depth, and incident angle. The Wood P anomaly and the Brewsterangle anomaly are demonstrated. Results for backscatter at near-grazing incidence are also presented, and correspondences between the reflection coefficients and amplitude phases, as a function of depth, are indicated.
Markov Approach to Density Fluctuations Due to Transport and Scattering. I. Mathematical Formalism
Authors: van Vliet K. M.
Published: February 2004

A kinetic approach to fluctuations and correlations of stochastic processes depending on a continuous set of parameters y is presented. In particular, we consider particle densities np(y, t) which may refer to macroscopic densities in position space, or to microscopic quantities such as distributions in phase space, or occupancies of quantum states of which the labeling is continuous (as with Bloch states in solids). In a Markovian sense such processes are infinite dimensional. We describe the fluctuating particle densities in a Hilbert space: the analog of de Groot's a-space for non-spatial-dependent variables. Mainly, we employ a Langevin description; i.e., we start from presumed phenomenological equations, amended with source densities ξp(y, t). A theorem is derived for the density-density or two-point covariance function (Λ theorem). In its general form, the theorem applies to the nonequilibrium steady state. It closely resembles the generalized g-r theorem for finite-dimensional processes. However, the solutions may involve extra parts stemming from stochastic boundary conditions and constraints. Simplifications for the thermal equilibrium case and the connection with generalized Onsager's relations are discussed. A variety of expressions for the spectral intensities Σpq(y, y′, ω) are derived. In order to justify the Langevin procedure as well as to calculate the source terms and generalized Fokker-Planck moments, we consider the master-rate functional Wγγ′ for transitions γ→γ′ of the over-all state. Expressions are given for transitions involving change of species and scattering due to one- or two-body collisions. These determine uniquely the quantities entering into the Λ theorem. The statistical-mechanical basis for our formalism is discussed in some detail.
The Jost Function of a Momentum-Dependent Potential
Authors: Warke Chindhu S.
Published: February 2004

It is proved that the Jost function of a central, momentum-dependent, S-state interaction is equal to the ratio of the Fredholm determinant of the kernel of the integral equation for the outgoing scattering solution in the momentum space representation to that of the regular solution in the same representation. This proof of the expected result is more general than that given by Warke and Bhaduri for a non-local interaction.
General Structure of the Distribution Functions for the Heisenberg Model and the Ising Model
Authors: Morita Tohru
Published: February 2004

The general structure for the distribution functions (reduced density matrices) for systems composed of a number of elements is given by taking the variation with respect to the distribution functions in the formalism of the cluster variation method. The parameters or the Lagrange multipliers occurring in the distribution functions must be determined by the reducibility condition of the distribution functions or by the stationariness condition of the free energy.
Example Related to the Foundations of Quantum Theory
Authors: Davies E.B.
Published: February 2004

We construct a very simple example of a statistical system which satisfies almost all of the axioms used by various authors in the quantum logic approach to the foundations of quantum mechanics. Since the example is not quantum mechanical, it is seen that present arguments are a long way from characterising quantum mechanics in terms of a set of physically meaningful axioms.
Kramers-Kronig Relations and Sum Rules
Authors: Kubo Ryogo , Ichimura Munetake
Published: February 2004

The concept of moments, which are integrals of positive or negative integral powers ωn weighted by real or imaginary parts of admittance functions, is here generalized so as to be applied to a wide category of admittance functions, including Lorentzian functions. The generalized moments are related to the derivatives or integrals of sum rules in a general sense. This analysis is based on differentiation and integration-mapping of admittance functions and the associated Kramers-Kronig relations. Some model calculations are also shown.
Steady-State Solutions in the Two-Group Theory of Neutron Diffusion
Authors: Burniston E. E. , Mullikin T. W. , Siewert C. E.
Published: February 2004

Functional analysis arguments are used to prove the existence of a unique solution to the integral form of the two-group neutron-transport equation for subcritical half-spaces. The analytic properties of the solutions are discussed and used to prove that the partial indices of canonical solutions of the matrix Riemann problem, basic to H-matrix or half-range completeness considerations, are nonnegative.
A Perturbation Method for Two Synchronously Tuned, Coupled, Autonomous, Nonlinear Oscillators
Authors: Streifer William , Paxton K. Bradley
Published: February 2004

A perturbation procedure is developed for two synchronously tuned, coupled, autonomous, nonlinear oscillators. The procedure results in ordinary nonlinear differential equations for the slowly varying amplitude envelopes and the slowly varying phase difference of the two oscillators. A method of obtaining initial values is included as are two examples for coupled van der Pol and linear oscillators.
Neumann Series Solution for the Atom-Rigid Rotor Collision
Authors: O'Brien T. J. , Holloway T. T.
Published: February 2004

The solutions of the coupled differential equations arising in the quantum mechanical discussion of the collision of an atom with a rigid, rotating diatom are written as Neumann series, i.e., expanded in terms of spherical Bessel functions. The coefficients of these series are generated by a set of coupled recursion relations. The formalism is limited to potentials less singular than r−2 at the origin.
On the Connection between Levinson's Theorem and Singular Integral Equations
Authors: Becchi C. M. , Collina R.
Published: February 2004

Levinson's theorem is deduced from a general property of singular integral equations in the case in which both the unperturbed and the total Hamiltonian have a finite number of discrete eigenvalues. We also discuss the conditions of validity of the theorem.
Linear Inequalities for Density Matrices. II
Authors: McRae Walter B. , Davidson Ernest R.
Published: February 2004

A general method is described for finding linear inequalities relating physical properties of an ensemble which can exist only in a finite number of states. This algorithm is used to solve a few examples of the fixed-N and variable-N Slater hull problem and the fixed-N Boson hull problem. Interpretations of the results are made in terms of boundary conditions for fermion and boson reduced density matrices, pair distributions of lattice vacancies, and pair distributions of spins in an Ising model.
On the Convergence of the Born Series for All Energies
Authors: Bushell P. J.
Published: February 2004

Formal solution of the Schrödinger equation for nonrelativistic scattering by a spherically symmetric static potential −μV(r) leads to a power series in the real parameter μ for the scattering amplitude (the Born series). It is shown that if ∫0∞ r|V(r)|dr<∞, ∫0∞ r2|V(r)|dr<∞ and if −μ|V(r)| is too weak to support a bound state, then the Born series converges at all energies. The method gives a lower bound for the radius of convergence of the Born series which is exact if V ⩾ 0.
Nonmetrical Specification of Space-Time Sources
Authors: Pereira C. Martin
Published: February 2004

The role played by the energy-momentum conservation law in general relativity is examined. It is noted that this law can be interpreted in two ways. It may be thought of as a condition determining the evolution of the energy-momentum tensor density in time, or it may be thought of as a condition determining the metric. In the present paper, the second of these ways of thinking about the energy-momentum conservation law is explored. Einstein's nonvacuum gravitational field equations (which imply the conservation law) are examined. It is shown that given any analytic symmetric contravariant energy-momentum tensor density as a function of the space-time coordinates, a solution to the gravitational field equations always exists. Furthermore, this solution is such that the law of conservation of energy-momentum is satisfied. The proof uses a coordinate transformation method to exploit the covariance of the energy-momentum conservation law. Riquier's existence theorem enters as an important part of the proof, and a general discussion of Riquier's existence theorem from a physical point of view is given. Both the geodesic nature of the trajectories of free particles and the unit magnitude of the velocity 4-vector are discussed. An interpretation of the above-described results is given.
The λφ24 Quantum Field Theory without Cutoffs. IV. Perturbations of the Hamiltonian
Authors: Glimm James , Jaffe Arthur
Published: February 2004

We introduce an inductive method to estimate the shift δE in the vacuum energy, caused by a perturbation δH of the P(φ)2 Hamiltonian H. We prove that if δH equals the field bilinear form φ(x,t), then δE is finite. We show that the vacuum expectation values of products of fields (Wightman functions) exist and are tempered distributions. They determine, via the reconstruction theorem, essentially self-adjoint field operators φ(f), for real test functions f∈S(R2). We also bound the perturbation of the P(φ)2 Hamiltonian by a polynomial (P1(φ))(h)=δH. so long as P+P1 is formally positive. In that case, and with ‖h‖∞≤ 1, δE is bounded by const(1 + diam supp h).
Reduction of the Poincaré Group with Respect to the Lorentz Group
Authors: MacDowell W. W. , Roskies Ralph
Published: February 2004

The representations of the Poincaré Group for spinless particles, reduced with respect to the Lorentz subgroup, are investigated. They involve the principal series of representations of SL(2, C) and use is made of a basis, introduced by Gel'fand in which the states are labeled by a complex number z. The transformation matrices relating to the Wigner basis are derived. The matrix elements of the momentum operators are obtained. The general form of the S matrix in the new basis is discussed. This basis may be relevant for a field theoretical description of the Veneziano model.
Some Theorems on Atomicity in Axiomatic Quantum Mechanics
Authors: Jenč F.
Published: February 2004

Given a complete orthocomplemented lattice L and a set S of nonnegative real functions on L, sufficient conditions are established that S should fulfill in order that L be atomic. The conditions are investigated under which L may be represented by the lattice of all closed subspaces of a separable Hilbert space. (As is well known, the atomicity of L plays an important role here.) Some unsolved problems are pointed out. In axiomatic quantum mechanics, the lattice L may represent the set of propositions whereas the set of functions S represents the set of physical states. The conditions imposed on the pair (L,S) then have a simple and plausible physical interpretation; an important condition imposed on (L,S) is the existence of the ``maximal'' (i.e., maximally determined) states which appear in the theory as limit constructions.
Approximate Functional Integral Methods in Statistical Mechanics. I. Moment Expansions
Authors: Siegel Armand , Burke Terence
Published: February 2004

In this paper, four distinct ideas are combined, which under a wide range of circumstances can give very rapidly converging series expansions for functional integrals. (1) Expansion of the functional being integrated in functional Taylor series. In the familiar case arising in quantum statistical mechanics, that of the Wiener integral of exp[−∫V(x(t))dt],V(x) being the perturbing potential, this is equivalent to expanding the characteristic functional of the probability functional of V(x(t)) in central moments of V(x(t)). The lowest-order term of the series is the approximation obtained by Feynman and Hibbs through a variational method. (2) Transfer of the harmonic term of the potential, when the functional integral is the quantum-statistical density matrix (Green's function of the Bloch equation), to the weighting function. This transforms the functional integral from a Wiener to an Uhlenbeck-Ornstein integral. The formal expressions for the terms of the expansion are somewhat more complicated, but they can be worked out, and the result is a great improvement in the speed of convergence of the series with decreasing temperature and/or decreasing relative magnitude of the anharmonic part of the potential. (3) ``Reservation of variables'' in the integration. This amounts to breaking the averaging process down into an average over subsets of the distributed random function (conditional average), followed by an averaging of these averages. Any step of this kind (it may be repeated within the subsets, etc.) gives an improvement of accuracy. (4) When the quantity being evaluated through functional integration is the partition function, the device introduced by Feynman and Hibbs, of interchanging the functional integration with the integration of the Green's function over the equated initial and final configuration-space points, may be combined with the above techniques. This eliminates one integration in the terms of the expansion and seems to improve accuracy at the same time. The general series obtained is correlated with more conventional operator techniques of quantum-mechanical perturbation theory, in order to answer the perennial question, does the path-integral method bring with it anything that could not be derived by other methods? It is in some sense a Feynman-Dyson expansion of the Green's function, but one that is further modified mathematically in a way characteristic only of the path-integral point of view, and which, moreover, improves its accuracy. It thus appears unlikely that the result is merely one of standard type disguised as a functional integral result. Sample numerical calculations are given to assay the accuracy of the methods, which are shown to compare very favorably with the traditional approximation of finite subdivision of the time interval.
All Stationary Vacuum Metrics with Shearing Geodesic Eigenrays
Authors: Kóta J. , Perjés Z.
Published: February 2004

The general solution of the field equations of stationary vacuum gravitational fields possessing geodesic eigenrays with nonvanishing shear is obtained. Nontrivial solutions exist only if the eigenrays do not rotate. The resulting metrics fall into two classes: either there is a functional dependence among the field quantities (this class belongs to the Papapetrou solutions), or the quantity γ0, which in the shear-free case has been interpreted as the central mass, is uniquely determined. This latter class consists of two space-times. The curvature invariants vanish in the r→∞ limit for both solutions; however, the metrics exhibit singular behavior in this limit.
Null Plane Restrictions of Current Commutators
Authors: Brandt Richard A. , Otterson Paul
Published: February 2004

We consider some mathematical aspects of the problems of defining restrictions of quantum fields and commutators of such fields to null planes. We give precise meanings to these restrictions and discuss how these lead to unambiguous derivations of the usual formal results. We discuss and relate various definitions of null plane charges and derive some of their properties such as vacuum annihilation. We define and exhibit finite null plane restrictions for causal solutions of the Klein-Gordon equation. Commutator functions defined by integral representations with various spectral functions are then considered. Light cone operator product expansions are used to calculate some null plane current commutators. In this way we can give precise derivations of Fubini sum rules and electroproduction structure function asymptotic behavior.
Absence of Long-Range Order in Thin Films
Authors: Garrison John C. , Wong Jack , Morrison Harry L.
Published: February 2004

Thin films are described as idealized systems having finite extent in one direction but infinite extent in the other two. For systems of particles interacting through smooth potentials (e.g., no hard cores), it is shown that an equilibrium state for a homogeneous thin film is necessarily invariant under any continuous internal symmetry group generated by a conserved density. For short-range interactions it is also shown that equilibrium states are necessarily translation invariant. The absence of long-range order follows from its relation to broken symmetry. The only properties of the state required for the proof are local normality, spatial translation invariance, and the Kubo-Martin-Schwinger boundary condition. The argument employs the Bogoliubov inequality and the techniques of the algebraic approach to statistical mechanics. For inhomogeneous systems, the same argument shows that all order parameters defined by anomalous averages must vanish. Identical results can be obtained for systems with infinite extent in one direction only.
Some Asymptotic Expressions for Prolate Spheroidal Functions and for the Eigenvalues of Differential and Integral Equations of Which They Are Solutions
Authors: Cloizeaux J. des , Mehta M. L.
Published: February 2004

The asymptotic behavior of the prolate spheroidal functions of order zero fn(x, c), where n is the number of zeros of the function in the interval − 1 ≤ x ≤ 1, is studied for large values of the parameter c and all values of n. The method used involves solving the differential equation which defines the functions by using a classical approximation. The corresponding eigenvalues χn are given by an implicit equation and the norm of the functions is calculated. The functions fn(x, c) are also solutions of an integral equation and associated with eigenvalues λn(c). Asymptotic expressions of [1 − λn(c)] are derived by using the values obtained for the norm of fn(x, c). All these results generalize and interpolate partial results obtained by Slepian and others in two special cases, namely, n finite and n ≃ c.
Generalized Semidirect Product in Group Extensions
Authors: Šijački Dj. , Vujičić M. , Herbut F.
Published: February 2004

The case when there exists a homomorphism σ of a group G into Aut(K) of a non-Abelian group K[σ having at most one image in every coset of Aut(K) with respect to I(K)] is investigated. It is shown that any extension E ∈ extσ(G, K) can be obtained as a generalized semidirect product (GSP):E=(K̂τH)/C′, where H belongs to extσ(G, C) (the group C being the center of K), the semidirect product of K and H is based on τ which equals σ∘n (n being the homomorphism of H onto G), and C′ is the antidiagonal of C⊗C. The GSP is a natural generalization of the central extensions, it is applicable to most groups in theoretical physics, and it has a suitable form for the derivation of the irreducible representations of E.
Note on Nonlinear Representations
Authors: Raghavacharyulu I. V. V.
Published: February 2004

In the theory of non-linear representations of a continuous group G with respect to a closed subgroup H, the peculiar transformation behavior of the reduction matrix Lφ is found to be identical with the transformation behavior of a set of coset representative elements of G with respect to H. The limitations of the extended definition of the boost by Salam and Strathdee are discussed.
Relativistic Continua with Directors
Authors: Maugin Gérard A. , Eringen A. Cemal
Published: February 2004

In this article, we give an axiomatic introduction of directors in the space-time continuum of Minkowski. A variational principle is presented that leads to the complete set of field equations, boundary conditions, and jump relations of the Kafadar-Eringen theory of relativistic polar media. The constitutive equations follows from the variational formulation.
Spin-½ Lattice System: Group Structure and Duality Relation
Authors: Merlini D. , Gruber C.
Published: February 2004

Properties of general lattice systems are investigated using the group properties of such systems. The duality transformation is generalized and is expressed in terms of exact short sequence between the groups associated with one lattice and the groups associated with the dual lattice. A general method is given for constructing explicitly a dual lattice for any lattice system and is illustrated with some two- and three-dimensional models. In particular it is shown that the two-dimensional triangular lattice with three-body forces is self-dual.
Relativistic Excitation of Cavity Modes
Authors: Liboff Richard L.
Published: February 2004

Fields and energies due to a charged particle and other planar charged configurations, which move with relativistic speed along the axis of finite and infinite cylinders with perfectly conducting walls, are obtained. Explicit criteria are derived for modes of zero and maximum energy deposited in a finite closed can by a point particle. Infinities of wake fields are discussed vis a vis field energies of particles at rest, enclosed in cavities. The wake energy deposited in a semi-infinite can with forward target wall is found to include an infinite self-energy term modulated by the causality factor γ−1.
Structure of the Bondi-Metzner-Sachs Group
Authors: McCarthy Patrick J.
Published: February 2004

A simple example of an aymptotic symmetry group in two dimensions is described. The structure of the corresponding group for asymptotically flat (four-dimensional) space-times, the BMS group, is given explicitly. The recent result that all induced representations of the BMS group have discrete spins is explained in terms of the relationship between this group and the Poincaré group. In fact, it is shown that the BMS group is, in a sense, the smallest generalization of the Poincaré group which eliminates the (physically embarrassing) continuous spin representations of the Poincaré group.
Coordinate systems associated with asymptotically shear-free null congruences
Authors: Aronson B. , Newman E.T.
Published: February 2004

We present here the asymptotic coordinate transformation between a coordinate system associated with null hypersurfaces and one associated with an asymptotically shear-free (but twisting) null congruence. The general asymptotically flat metric is expressed in this new coordinate system. Special cases of this are the algebraically special metrics in their ``natural'' coordinate system.
Erroneous bound state conditions from an algebraic misrepresentation of spin wave theory
Authors: Trubatch S. L.
Published: February 2004

A recently derived condition [C. J. Liu and Yutze Chow, J. Math. Phys. 12, 2144 (1971)] for the existence of bound states in the Heisenberg ferromagnet is shown to be the erroneous result of an improper construction of the Hilbert space for an algebraic representation of the spin operators.
The inverse scattering problem at fixed energy for L2-dependent potentials
Authors: Hooshyar M. A.
Published: February 2004

The problem of finding central and L2-dependent potentials, acting among spinless particles, from the knowledge of the S matrix as a function of angular momentum at a fixed energy is studied. The Newton method for central potentials is generalized to this case, and it is shown that phase shift information at fixed energy is not enough to give us both the central and the L2-dependent potential.
Elastic general relativistic systems
Authors: Glass Edward N. , Winicour Jeffrey
Published: February 2004

A theory of elastic deformations of general relativistic systems is presented. The theory is derived from a generalized Hooke's law. An important feature of this theory is that its classical limit corresponds to the classical elasticity theory of prestressed materials. A perturbation description of small deformations is developed and applied to the test body case. For the first time, the strain-curvature equation for an elastic test body interacting with a gravitational wave has been derived from a complete theory. The semi-classical work of Dyson, showing the interaction of a gravitational wave with the inhomogeneities of the shear modulus, is rederived and placed within the framework of general relativity. The theory presented is quite comprehensive in scope and applicable to fully relativistic situations such as the elastic behavior of neutron stars.
A new representation of the solution of the Ising model
Authors: Stephen M. J. , Mittag L.
Published: February 2004

It is shown that the transfer matrices for various Ising lattices in two dimensions commute with certain linear operators. The problem of finding an explicit form for the largest eigenvector is considerably simplified. The expansion coefficients appearing in the eigenvectors found as the solution of a set of nonlinear difference equations are Pfaffians. The connection between this type of solution and other solutions is clarified. This form for the eigenvector also simplifies the calculation of correlation functions. Some geometrical aspects of the Ising model are discussed.
Gauge transformations of second type and their implementation. I. Fermions
Authors: Gille J. F. , Manuceau J.
Published: February 2004

A necessary and sufficient condition for implementation of some local gauge transformations in a class of irreducible representations of the CAR algebra is proved. Some particular results on the unitary group of implementation are then given. Not all of the pure states induced by these representations are unitarily equivalent to ``quasifree'' states of the class we consider; it is shown that such a state is unitarily equivalent to a quasifree state if and only if a certain property (characterizing the ``discrete'' states) holds.
On the divergent perturbation expansion for the vacuum polarization by an external field
Authors: Graffi S. , Grecchi V.
Published: February 2004

The divergent perturbation expansion of the exactly solvable vacuum polarization by an external constant electromagnetic field is examined. It is proven that the Stieltjes method, known to be valid for the vacuum polarization by a pure electric or a pure magnetic field, fails in the general case to sum the perturbation expansion to the exact solution. This implies the non-convergence of the Padé approximants to the solution under these conditions. The validity of the Borel summation method and the convergence of the related approximation procedures are also proven.
Radiative transfer in adjacent half-spaces with specular reflection
Authors: Yener Y. , Özişik M. N.
Published: February 2004

Radiative transfer in absorbing, emitting, isotropically scattering, gray adjacent half-spaces with specular reflection at the interface is solved rigorously by the application of normal-mode expansion technique. An alternative method based on the superposition of half-space problems is also presented for the solution of the problem. Once the expansion coefficients for the solutions are evaluated from the given relations, the physical quantities such as the angular distribution of radiation intensity and the net radiative heat flux anywhere in the medium can readily be determined.
Operator Treatment of the Gel'fand-Naimark Basis for SL (2, C)
Authors: Bars Itzhak , Gürsey Feza
Published: February 2004

An operator form is developed to treat the Gel'fand-Naimark z basis for the homogeneous Lorentz group. It is shown that the operator Z with eigenvalues z is a definite operator-valued function of the generators of SL (2, C). A unified formulation of the unitary representations of the Lorentz group is obtained in a Hilbert space endowed with an affine metric operator G whose functional dependence on the generators is derived explicitly. The Dirac bra-ket formalism is extended by making a distinction between covariant and contravariant state vectors. The matrix elements of G are shown to coincide with the intertwining operator of Gel'fand and co-workers. The principal series, the supplementary series, and the two kinds of integer point representations are unified by means of a single scalar product involving the metric operator.
Approach to Stochastic Lagrangian Integrals and Their Asymptotic Evaluation for Sound Propagation in Continuous Stochastic Media
Authors: Neubert Jerome A. , Lumley John L.
Published: February 2004

Previously the formal solution of the Eulerian-Lagrangian problem for sound propagation in continuous stochastic media was reframed so that the emphasis on the need for complete knowledge of the statistical nature of the Lagrangian functional of interest is shifted to the need for knowledge of the asymptotic behavior of certain stochastic Lagrangian integrals which result from the application of a central limit theorem for stochastic functionals. In this paper, the asymptotic evaluation of these Lagrangian stochastic integrals is developed and illustrated for both ensemble and subensemble expectations in a statistically isotropic medium. In addition, the relationship between this method of analysis and the comparable Wiener integral is discussed.
Contractions of the Low-Dimensional Real Lie Algebras
Authors: Conatser C. W.
Published: February 2004

A complete and detailed classification and analysis of all the Inonu-Wigner contractions of all the real Lie algebras of dimension 1, 2, and 3 is presented. Starting with a more natural classification of the algebras, many corrections and completions are made to the earlier results of Sharp. Among other things, a proper contraction is constructed between two three-dimensional Lie algebras both of which have two-dimensional derived algebras-a phenomenon previously claimed impossible.
Decomposition of the Principal Series of Unitary Irreducible Representations of SU(2, 2) Restricted to the Subgroup SU(1,1)⊗SU(2)
Authors: Cobb Donald D. , McCliment Edward R.
Published: February 2004

An explicit form is given for the unitary irreducible representations of the principal nondegenerate series of the group SU(2, 2). These representations are then restricted to the subgroup SU(1,1)⊗SU(2) and are found to be equivalent to the regular representation of SU(1,1)⊗SU(2).
Lower Bounds of the Energy Eigenvalues of Systems Containing Identical Particles
Authors: Yeh Robert H. T.
Published: February 2004

Lower bounds of the energy eigenvalues of systems containing identical particles were obtained by a generalization of the method of Calogero and Marchioro [J. Math. Phys. 10, 562 (1969)].
Upper and Lower Bounds of the Eigenvalues of a Second-Order Linear Self-Adjoint Differential Equation
Authors: Yeh Robert H. T.
Published: February 2004

Upper and lower bounds of the eigenvalues of a second-order linear self-adjoint differential equation were obtained by a generalization of the methods of Nordtvedt [J. Math. Phys. 8, 1406 (1967)].
Reduction of a Class of Nonlinear Integral Equations to a Cauchy System
Authors: Kagiwada Harriet , Kalaba Robert , Yang Chung-Chun
Published: February 2004

It is shown that a wide class of nonlinear integral equations can be transformed into a Cauchy system. Then it is shown that a solution of the Cauchy system provides a solution of the original nonlinear integral equation. Such reductions are important because modern computers can solve initial value problems with speed and accuracy. There are intended applications in the theories of multiple scattering, optimal filtering, and lateral inhibition of neural systems. This new approach makes no use of successive approximations or series expansions.
Occupation Statistics for Parallel Dumbbells on a 2 × N Lattice Space
Authors: McQuistan R. B. , Lichtman S. J. , Levine L. P.
Published: February 2004

It is shown that occupation statistics for parallel dumbbells on a 2 × N lattice obeys the central limit theorem. On the basis of this conclusion, a modification of the maximum term method is utilized to enumerate for large N the number of distinguishable arrangements arising when indistinguishable, parallel dumbbells are placed on a 2 × N array. The coverage at which the maximum number of arrangements occurs and the pseudovariance for the distribution are also determined.
On the Correlations of the Resonance Parameters for the Overlapping Resonances
Authors: Devi K. R. Sandhya , Ullah Nazakat
Published: February 2004

A statistical study of the correlations of the complex poles of the unitary collision matrix is carried out. It is shown that both for the elastic and the inelastic scattering the correlation coefficient of the two total widths is always very small. A simple relation satisfied by the correlation coefficient of the real parts of the complex poles is given. The distribution of the single width is calculated and compared with the Porter-Thomas distribution and the one obtained by a numerical calculation. Some other interesting results, like the energy correlation function for the purely elastic scattering cross section and a relation satisfied by the resonance parameters for the fluctuation calculation, are also given.
Solution of the Difference Equations of Generalized Lucas Polynomials
Authors: Raghavacharyulu I. V. V. , Tekumalla A. R.
Published: February 2004

Barakat and Baumann have introduced polynomials U(N) (a1, a2, …, aN) termed the generalized Lucas polynomials satisfying a difference equation with a set of initial conditions. We show that these polynomials can be obtained directly from the symmetric functions hn, which are of basic importance in combinatorial analysis. Moreover, we extend the definition of V(a1, a2) to V(N) (a1, a2, …, aN) and establish that these polynomials too can be obtained from the symmetric functions Sn. Further, closed expressions for the U and V are obtained.
On Projective Unitary-Antiunitary Representations of Finite Groups
Authors: Janssen T.
Published: February 2004

A generalization of Schur's treatment of projective representations is discussed for a very general class of representations occurring in physical theories: the projective representations by unitary and antiunitary operators. It is shown that for every finite group the projective unitary-antiunitary (PUA) representations can be obtained from the ordinary unitary-antiunitary representations of another finite group. The construction of such a representation group is treated. As an example we apply the theory for the determination of irreducible representations of subgroups of the Poincaré group. The classes of PUA representations for all finite crystallographic groups in spaces of dimension up to four are explicitly given.