bluuebunny/crossref_metadata_2025 huggingface dataset:
Algebraic Derivation of the Partition Function of a Two-Dimensional Ising Model
Authors: Thompson Colin J.
Published: January 2005

In the algebraic formulation of the Ising model, the partition function is expressed as the trace of a power VM of the transfer operator V, or equivalently, as the sum of Mth powers of the eigenvalues of V. In the derivations of Kaufman, Onsager, and more recently of Schultz, Mattis, and Lieb (SML), the transfer operator is first reduced to a more amenable form for computation and then, in principle at least, diagonalized. For the infinite lattice, only the largest eigenvalue of V is needed, and this is all Onsager and SML compute. Kaufman finds all the eigenvalues and is thus able to write down the partition function for the finite lattice. In the present work we give an alternative derivation of the SML form for V, and show how the Kaufman result can be obtained from this form without actual diagonalization. Instead of diagonalizing V, the evaluation of the trace is done directly after assigning a simple representation to V.
On the Proof and Uniqueness of Wulff's Construction of the Shape of Minimum Surface Free Energy
Authors: Johnson Charles A. , Chakerian G. D.
Published: January 2005

The existing proof of Wulff's theorem shows that, among all convex bodies of fixed volume, the shape given by Wulff's construction has the least surface free energy. Here it is pointed out that the restriction to convexity is unnecessary: among all bodies of fixed volume, the shape given by Wulff's construction has (uniquely) the least surface free energy. Obvious generalizations are noted.
Theorem on Nonradiative Electromagnetic and Gravitational Fields
Authors: Papapetrou A.
Published: January 2005

A vacuum electromagnetic field is considered which is (a) stationary below a hypersurface Σ intersecting all parametric lines of the time coordinate t and (b) nonradiative above Σ. It is proved that such a field is stationary also above Σ. The same theorem is proved to be valid for the pure gravitational field in general relativity and for the combined gravitational and electromagnetic field in the Einstein—Maxwell theory.
Reduced Density Matrices of Quantum Gases. III. Hard-Core Potentials
Authors: Ginibre Jean
Published: January 2005

In two previous papers, the reduced density matrices of quantum gases, in the grand canonical formalism and for suitably restricted interaction potentials, have been shown to be analytic vector-valued functions of the activity in a neighborhood of the origin, to tend in some sense to well-defined limits as the volume of the system becomes infinite, and to satisfy a cluster decomposition property. The same results are extended here by the same methods to a wider class of potentials, including hard-core, and allowing attractive interactions, which were excluded previously.
On a Quantum Field Theory with Degenerate Vacuum and a Special Type of Symmetry
Authors: Lopuszanski Jan , Reeh Helmut
Published: January 2005

We investigate a frame of a model of quantum field theory with a degenerate vacuum. At least one vacuum is cyclic. The field is covariant under a ``gauge'' transformation. We show the existence of non-gauge-invariant vacuum states. We define ``observables'' as gauge-invariant operators; the algebra of these does not coincide with the algebra of the field operator; the reduction of the former algebra reflects a superselection rule.
Some Exact Solutions of the Field Equations of General Relativity
Authors: Misra M.
Published: January 2005

A method for generating nonstatic solutions of the Einstein-Maxwell field equations in vacuo from nonstatic solutions of the empty space-time field equations is given. It is shown that under certain conditions one of the metrics under investigation admits algebraically degenerate vacuum solutions. The necessary and sufficient condition in order that the vacuum solutions for this metric be of type null is obtained. Some exact solutions are listed.
Lehmann-Symanzik-Zimmermann Formalism in a Model Field Theory
Authors: Scarfone Leonard M.
Published: January 2005

The Lehmann-Symanzik-Zimmermann (LSZ) formalism is used as a calculational method to obtain an equation for the determination of the V + N potential energy in a slightly modified Lee model. This approach to the problem is compared with the standard eigenvalue technique and the dispersion theory treatment. It is found that an exact solution to the VN − 2N θ sector can be obtained with one algebraic equation and this evidence gives additional support to the desirability of the LSZ method as a calculational tool for the model.
Space-Time Theory of Elementary Particles. II. Complex Minkowski Space Formalism
Authors: Shin Ernest E. H.
Published: January 2005

The space-time formalism of elementary particles presented previously is generalized to a complex ``internal'' Minkowski space described by (zμ, ωμ) and (zμ*, ωμ*). In this way, we are able to accommodate the dual signatures of the ``superselection'' operator and the odd-half spins in a natural manner. The full dynamic symmetry group of the 16-dimensional phase space is a 136-parameter group G̃ of which the reciprocity-invariant content is a 64-parameter group isomorphic with the 64-parameter Lie group. The complete ℒ-invariant subgroup of G̃ is a 10-parameter group which is identified as the five-dimensional real ``Lorentz'' group and which is the ``unitary spin'' subgroup of 𝒢̃. Discussions on the various reduced or subgroup structures of 𝒢̃ are given. In particular, the physical nature of the ℒ-invariant generators and possible forms of mass formula are discussed.
Distribution of Zeros of the Grand Partition Function
Authors: Hemmer P. C. , Hauge E. Hiis , Aasen J. O.
Published: January 2005

The distribution of zeros of the grand partition function is calculated in the thermodynamic limit for a class of one-dimensional gas models in two ways: (1) from the equation of state and (2) directly from the partition function. In this way one obtains (for these cases) a verification of the assumptions we had to make in order to associate a unique distribution of zeros with a given equation of state. In the Appendix we present some numerical evidence for the validity of these assumptions also in the case of the van der Waals gas.
Physical Region Decoupling Procedure for Coupled Channel Scattering Amplitudes
Authors: Fleming Gordon N.
Published: January 2005

A method for expressing unitary, coupled channel, scattering amplitudes in terms of amplitudes satisfying ``uncoupled'' or ``elastic'' unitarity equations is presented. The method is given a physical interpretation by relating the equations to equations of the Heitler type. It is shown how continuous channels may be incorporated into the formalism, in some circumstances, without requiring the solution of integral equations. The influence of inelastic channels on pure elastic scattering is mentioned briefly and a pseudoelastic form of the exact unitarity equation is discussed. No applications of the method are undertaken here.
Asymptotic Behavior of Phase Shift in λ for Strongly Singular Potentials
Authors: Jakšić B. , Limić N.
Published: January 2005

The asymptotic form of the phase shift is derived for strongly singular potentials for large complex λ, |arg λ| < ½π, and real k. This result is valid also for usual (regular) potentials. It is shown also that the S-matrix for strongly singular potentials must have an infinite number of poles in λ-plane accumulating asymptotically in a narrow region along the imaginary axis in the first and third quadrants.
Construction of Vanishing Cycles for Integrals over Hyperspheres
Authors: Boyling J. B.
Published: January 2005

The homological methods of Fotiadi et al. are applied to the study of the analytic properties of an integral over a l-sphere Γ of a closed meromorphic l-form on the complex quadric of which Γ is the real section. Vanishing cycles are explicitly constructed at points of a certain standard type, and the relevant Kronecker indices are evaluated. The Picard-Lefschetz theorem and the decomposition theorem are then applied to obtain linear relations between the discontinuities round various singularities. The results have a direct physical interpretation in the cases l = 4 and l = 2 in terms of the Riemann sheet structure of single-loop Feynman diagrams with four, five, or six vertices. They give linear relations between the various discontinuity functions, which generalize the results obtained by Fotiadi and Pham for the two-particle discontinuity of the five-point loop and for the complete Feynman amplitude of the four-point loop.
On an Algebraic Method for the Decomposition of Direct Products of Representations of the Groups A2(SU(3)) and B2(SO(5))
Authors: Gruber B.
Published: January 2005

A prescription for the decomposition of the direct product of two irreducible representations of A2 and B2 is given, which is completely general and direct, i.e., it does not make use of any auxiliary means like Young tableau or Cartan-Stiefel diagrams although it is based on the latter. The addition of weights alone under the observation of certain rules gives the desired result. This method can in principle be generalized to the semisimple groups of arbitrary rank provided an algebraic expression for the multiplicities of the weights contained in an irreducible representation can be found.
Bipolar Expansion of Screened Coulomb Potentials, Helmholtz' Solid Harmonics, and their Addition Theorems
Authors: Nozawa Reikichi
Published: January 2005

Helmholtz' solid harmonics (spherical Bessel functions × spherical surface harmonics) are generated from fundamental spherical waves through a ladder procedure using raising and lowering operators. The addition theorem for them and the bipolar expansion formula of a screened Coulomb potential are derived. A method for evaluating two-center integrals with a general potential is given in the last section. This is new and useful in practical calculations. A key function Jlnm(x)=12 ∫ −11 dμ eiμxPlm(μ)Pnm(μ),which appears in all the essential results, is studied in detail.
Invariance and Conservation Laws in Classical Mechanics. II
Authors: Denman Harry H.
Published: January 2005

In this paper, the invariances of the equation of motion of a classical particle, to coordinate and time translations, to scale transformations and inversions, and to Galilean transformations, are considered individually. Resultant conditions on the equation of motion are given, and, for invariance to the one-parameter continuous transformations, it is shown that the equation of motion can be reduced from second to first order. Associated with each such reduction is a conservation law. The implications of the invariance of the system Lagrangian to these transformations are indicated, and the conservation laws, if any, associated with them. Some requirements on the Lagrangian for invariant equations of motion are also presented, and it is shown that the invariance of an equation of motion derived from a Lagrangian does not imply the invariance of that Lagrangian to the transformation. It is also shown that time-translation invariance of the equation of motion does not always require conservation of the Hamiltonian.
Complex Temperatures and Phase Transitions
Authors: Jones Gerald L.
Published: January 2005

The thermodynamic limit is considered for complex temperatures, and a picture of a phase transition, similar to the Yang-Lee picture, is proposed. For certain cases a representation of the partition function as an infinite product is obtained. Some simple models are considered.
Bi-Orthogonality Relations for Solving Half-Space Transport Problems
Authors: McCormick N. J. , Kuščer I.
Published: January 2005

The method of singular eigenfunction expansions is applied to time-independent, one-speed, half-space transport problems with anisotropic scattering. Adjoint eigenfunctions are constructed such that a set of half-range bi-orthogonality relations is valid. These relations lead to the expansion coefficients in a direct manner. The adjoint eigenfunctions are also used to express the half-space albedo operator which relates the emerging angular density to the ingoing one.
Nonexistence of Localized Periodic Solutions to Nonlinear Field Theories
Authors: Rosen Gerald
Published: January 2005

A simple proof is given which precludes the existence of any spatially localized and temporally periodic singularity-free solution to the c-number field equation for a physically interesting Lorentz-covariant self-interacting scalar theory.
Some Observations on Enveloping Algebras of Noncompact Groups
Authors: Rosen Joe , Roman Paul
Published: January 2005

In order to provide the particle physicist with useful mathematical tools (and a large number of interesting identities), the enveloping algebras of the noncompact homogeneous O(p, q), U(p, q), and inhomogeneous IO(p, q), IU(p, q) groups are discussed in some detail. The construction of the generators of O(p, q + 1) and O(p + 1, q) from the enveloping algebra of IO(p, q) and the analog result for the corresponding pseudo-unitary groups are also presented.
Radiative Transfer. II
Authors: Siewert C. E. , Zweifel P. F.
Published: January 2005

This paper presents an exact solution to the equations of radiative transfer for a generalization of the Uniform-Picket-Fence model discussed in a previous work. Here the absorption coefficient is allowed to take N different values over the frequency spectrum. Case's method is used to construct the normal mode solutions to the set of N coupled integral equations. Then half-range completeness and orthogonality theorems are proved that enable one to solve typical half-space problems. Explicitly, the asymptotic solution to the Milne problem is developed, including the extrapolated end point, while implicitly the complete solution is available.
Singular Integral Equations
Authors: Case K. M.
Published: January 2005

The integral equation P ∫ cK(ζ′,ζ)ζ′−ζφ(ζ′) dζ′=h(ζ)φ(ζ)+f(ζ)is shown to have simple solutions obtained by standard and elementary methods if h and K have appropriate analytic properties.
Global and Democratic Methods for Classifying N-Particle States
Authors: Lévy-Leblond Jean-Marc
Published: January 2005

The ``global method'' for describing N-particle systems (which relies on the existence of a large invariance group of the total Hamiltonian for N noninteracting particles, the ``great group'', whose Lie algebra is generated by the ``grand angular momentum tensor''), is adapted to describe systems of identical particles by means of basis states with simple symmetry properties (with respect to permutations of the particles). We are led to define and study the concept of ``democracy'' among the particles, from which we obtain the ``democratic'' subgroups of the great group. The eigenvectors of a complete set of commuting observables, consisting essentially of Casimir operators of democratic subgroups, may furnish the desired basis. Unfortunately the scheme is seen to be sufficient only in the 3- and 4-particle cases, which, however, are most important. The Appendix contains a discussion of the possible relativistic generalizations of the global method.
Factorization Theorems
Authors: Chester G. V. , Sykes J.
Published: January 2005

A precise set of conditions is given for which the momentum correlation functions of quantum mechanical, weakly interacting, many-particle systems can be factorized.
Relationship between Linear Response Theory and the Boltzmann Equation for a Weakly Interacting System of Electrons and Phonons
Authors: Chester G. V. , Sykes J.
Published: January 2005

Van Hove's weak coupling master equation and the factorization theorem of Kac are used to show that the transport coefficients derived from linear response theory are equivalent to those derived from the Boltzmann equation for a weakly interacting system of electrons and phonons.
Minimal Potentials for Schrödinger Equation with Fixed Eigenvalue
Authors: Majumdar C. K. , Zittartz J.
Published: January 2005

It is shown that the potential V(x)=−nEn−1sech2[(−E)12xn−1]solves the problem of minimizing ∫−∞∞ Vn (x)dx (n>1), where V is such that the Schrödinger equation has an eigenvalue E, specified in advance, with a square-integrable eigenfunction.
Applications of the Gel'fand-Moshinsky Bases in Unitary Symmetry and its Breaking
Authors: Alcarás J. A. Castilho , Navarro V. C. Aguilera , Ferreira P. Leal
Published: January 2005

The Gel'fand-Moshinsky bases for the unitary irreducible representations of the SU3 group are applied to the unitary scheme for the classification of elementary particles and resonances. A unified method is given for the derivation of the matrix elements of the octet tensor operators in a way which makes transparent its application for other irreducible tensors. The results are given in a remarkably simple form. The systematic use of the basis provides a methodological alternative to the current tensorial methods.
The Stability of Many-Particle Systems
Authors: Fisher Michael E. , Ruelle David
Published: January 2005

It is shown that a quantal or classical system of N particles of distinct species α,β = 1, 2, … μ interacting through pair potentials φαβ(r) are stable, in the sense that the total energy is always bounded below by −NB, provided φαβ(r) exceeds some φαβ(2)(r) whose Fourier transform φ̂αβ(p) corresponds to a positive semidefinite μ × μ matrix for all p.

This result is applied to discuss ``charged'' systems and stability is proved for Coulomb interactions if the charges are somewhat smeared rather than concentrated at points. For a large class of potentials it is shown that classical instability implies quantum instability in the case of bosons and, in three or more dimensions, also of fermions. Quantum systems with Coulomb interactions (point charges) are discussed and it is shown in particular that their stability cannot depend on the ratios between the masses of the particles.
Monomer Pair Correlations
Authors: Hartwig Robert E.
Published: January 2005

In this paper we evaluate the monomer pair correlation along the diagonals (p, p + 1) and (p + 1, p) of a square lattice otherwise packed with dimers. Using the perturbed Pfaffian technique the correlation can be expressed as a Toeplitz determinant ip |bi−j+1|/2x generated by the function B(θ)= ∑ −∞∞ bkeikθ=iτeiθ[sgn (sin θ)+iτeiθ1+iθeiθ]+ ∑ k=0∞(iτ)ke−ikθ,where τ = x/y and x and y are the activities of x and y dimers. We will calculate the determinant exactly and prove that the correlation decays with increasing monomer separation as B/4r½; where B is simply related to the decay constant of the diagonal spin correlation at the critical point of a square ferromagnetic Ising lattice. The exact value is found to be B = 0.989487291.
Gauge Approximations in Mesodynamics
Authors: Rivers R. J.
Published: January 2005

In a nonperturbative theory for vector and scalar mesodynamics of the kind proposed by Salam, it is found that the ``gauge approximations'' introduced in this approach are the most sensible of a set of approximation schemes that preserve the scalar gauge properties of the amplitudes of the theory. The Green's functions used are those suggested by the functional derivative approach of the paper. The generalized identities of the Ward-Takahashi kind that these Green's functions satisfy are exhibited, as well as the decomposition of the general n-point function in terms of these Green's functions.
A Method of Solution for Resonant Nonlinear Coupled Oscillator Systems
Authors: Waters John , Ford Joseph
Published: January 2005

A method of solution for coupled oscillator systems having commensurable frequencies ωk = kω and suitable nonlinear couplings is presented. The method is that of perturbation expansions about periodic solutions. For simplicity, a three-oscillator system is discussed, but larger systems may be treated in the same way. The method provides results which are considerably better than those obtainable by any other currently available method, such as the perturbation method of Wigner-Brillouin. As presented, the method is rather unrefined, but it demonstrates that nonlinear oscillator systems of this resonant type are susceptible to analysis.
Model of Interacting Radiation and Matter. III. Multimode Gas Lasers
Authors: Willis Charles R.
Published: January 2005

We extend the investigation of the long-time behavior of a model consisting of N two-level atoms interacting with a single electromagnetic cavity mode to include interaction with many cavity modes. We show that, as a consequence of the coupling between radiation modes produced by spatial density variations of the population inversion, there is no strictly stationary state possible for multimode behavior. However we obtain a stationary state by neglecting the rapidly oscillating terms. The steady-state population inversion is then a solution of an eigenvalue problem. The eigenvalue determinate is a function of the number of modes and the coupling between modes in addition to the usual dependence on frequencies and relaxation times. We explicitly solve for the unique eigenvalue in special cases. The corresponding eigenvector gives the steady-state mode intensity ratios. The absolute values of the steady-state intensities are determined by the energy conservation equation generalized to include pumping and dissipation. We also calculate the steady-state frequency shifts for each mode. The mode frequency shifts are practically independent of each other and have the same functional form as the single-mode frequency shifts.
A New Method in the Theory of Potential Scattering
Authors: Gilbert R. P. , Shieh S. Y.
Published: January 2005

A new method is given for investigating the position, number, and type of singularities the scattering amplitude may have as a function of complex momentum transfer. The advantage of this method over ones relying on the Watson transform is that one needs only to know the partial amplitudes for physical values of the angular momentum.
On the Coupling and Recoupling of Relativistic States
Authors: Goldberg Haim
Published: January 2005

Systems containing more than two relativistic particles are analyzed from the point of view of irreducible representations of the Poincaré group. Corresponding Clebsch—Gordan coefficients are calculated for three-particle systems, and recoupling functions (which are the analog of the Racah coefficients) are defined.
A General Theory of First-Passage Distributions in Transport and Multiplicative Processes
Authors: Moyal J. E.
Published: January 2005

The ``Milne problem,'' expressed in probabilistic terms, is solved for general transport and multiplicative processes. If a particle initially in a given state at a given position inside a surface τ is multiply scattered while traveling through a fixed medium, then given the scattering cross sections and, if required, the probability distribution for a change of state between collisions (e.f., by diffusion or ionization), the problem is to obtain the probability that the particle eventually effects a first passage through a specified position on the surface τ and in a specified state. In the case of a multiplicative process, the problem is, given in addition the rates of creation and annihilation of particles (considering the nature of the particle as a state variable), to obtain the probability that eventually n particles will emerge for the first time through specified positions on τ and in specified states (with n = 0, 1, 2, …). A general solution is given in the form of a convergent series whose terms are obtained by iteration; this solution is unique if and only if the probability θ∞ of an infinity of atomic events before a first passage (which is the limit of a certain nonincreasing sequence) is identically zero; in the multiplicative case θ∞ ≢ 0 may be taken to mean that the process is ``supercritical.'' The mathematical theory which leads to this solution is a generalization of the corresponding theory for time-dependent Markov processes in which the time variable is replaced by a set of surfaces ordered by inclusion of their ``insides'' and is valid for Euclidean space of any number of dimensions. Applying it to the 4-dimensional space of special relativity with ordered sets of spacelike surfaces, one obtains a Lorentz-invariant formulation of the theory of physical Markov processes. A few examples are given.
Model of an Oscillating Cosmos which Rejuvenates during Contraction
Authors: Schmidt Helmut
Published: January 2005

For an oscillating cosmos we assume time-symmetric initial conditions, invariant under t→ —t and t→ T + t, where t = 0, ±T, … are the times of maximal cosmos contraction. In particular we specify the same value U0 for the cosmos' ``internal energy'' U at all these times. The expectation value of an Heisenberg operator becomes now 〈Q(t)〉 = Tr {Q(t) D}, with D=[A(T),A(0)]+/2 Tr {A(T)A(0)}. Here A(0) is the projector into the space of the eigenvectors of U with eigenvalue U0, and A(t) has the time dependence of an Heisenberg operator.

The time symmetry implies that the cosmos' oscillations are periodic and that expansions and contractions occur (except for local statistical fluctuations) time-symmetrically to each other: If the entropy increases during expansion then it must decrease during contraction.

The general theory is applied to a highly simplified cosmos model in which no star condensation occurs. Assuming here that the initial state contains equal numbers of particles and antiparticles, the theory predicts a slightly inhomogeneous distribution of these particles such that during the cosmos' expansion not all particles annihilate, but a realistic density of particles and antiparticles (in different space regions) survives the expansion.
Overlap Integrals between Atomic Orbitals
Authors: Ruedenberg Klaus , O-Ohata Kiyosi , Wilson D. G.
Published: January 2005

General formulas are developed for overlap integrals between Slater-type atomic orbitals of arbitrary integer quantum numbers (nlm) and parameter values ρ=12R(ζ+ζ′),τ=(ζ−ζ′)/(ζ+ζ′). The overlap integrals are expressed as finite trilinear forms of powers of ρ and certain auxiliary functions Iαβ(τρ),Jμνλ(τ). The auxiliary functions are related to confluent hypergeometric functions and Jacobi polynomials, respectively, and stable recurrence procedures for their evaluation are given. The method is practical for use with an electronic computer and, even for high orbital quantum numbers, the loss in significant figures is found to be small for all parameter values. The overlap integral between two atomic orbitals (Anlm) and (Bn′l′m′) is shown to be proportional to RAB|l−l′|.
Indefinite Metric Resulting from Regularization in the Infrared Region
Authors: Dubin Daniel A. , Tarski Jan
Published: January 2005

We consider the free scalar massless field in two dimensions, defined with the help of Wightman's regularization at p = 0. The one-particle sector of this field is completed, and is shown to be a space of type Π1, studied by Iohvidov and Krein. (Alternately, one can also obtain a direct sum of two such spaces.)
Point Transformations and the Hard-Sphere Bose Gas
Authors: Eger F. M. , Gross E. P.
Published: January 2005

The method of point transformations is used to provide a Hamiltonian for strongly interacting particles that is equivalent to the usual Hamiltonian. The new Hamiltonian is Hermitian, Fourier analyzable, velocity dependent, and free of the difficulties of pseudopotentials. The present work is restricted to the case that two-body encounters are dominant. The theory is expressed in the quantized wave formalism so that number-violating approximations can be applied. The well known results for the spectrum and ground-state energy of the dilute hard-sphere gas are then derived as an elementary application.
Leading Landau Curves of a Class of Feynman Diagrams
Authors: Islam Jamal N.
Published: January 2005

In a previous paper it was shown that the leading Landau curves of some Feynman diagrams do not give singularities on the physical sheet if some of the internal and external masses satisfy certain simple inequalities. In the present paper it is shown that a similar property is satisfied by a class of Feynman diagrams. The inequalities involve a fixed number of masses for the whole class.
Solution of Schrödinger Equation Involving Time
Authors: Sasakawa Tatuya
Published: January 2005

The general solution of the Schrödinger equation involving the time-dependent perturbation is presented in a compact and manageable form both for periodic and aperiodic perturbations. The method includes as a special case the solution of the Schrödinger equation involving the time-independent perturbation. Formulas ready for practical uses are explicitly described. The essential part of the procedure is the determinantal method in the Laplace-transformed space. The solution is applicable to strong perturbations as well as weak perturbations.
Quantum-Mechanical Extension of the Lebowitz-Penrose Theorem on the Van Der Waals Theory
Authors: Lieb Elliott
Published: January 2005

Recently Lebowitz and Penrose gave a rigorous derivation of the van der Waals-Maxwell theory of the liquid-vapor transition, and showed how the Maxwell equal area-rule could be obtained from a proper statistical mechanical calculation. Their results are quite general—being valid in any number of dimensions and for a broad class of pair potentials—but they were proved only for classical mechanics. In the present work we extend the proof to quantum systems with any statistics—Boltzmann, Bose, or Fermi. One corollary of this extended theorem is a model of a Bose gas with a first-order phase transition.
On Alternate Commutation Relations
Authors: Parks W. F.
Published: January 2005

An alternate quantization procedure for Bose fields is proposed. This procedure leads to a field algebra which is related to that of angular momentum rather than momentum. With this algebra is associated a maximum (n0) to the number of particles allowed in a given momentum state. It is indicated by the investigation of models that physical observables converge for large n0 to those obtained using the canonical commutation relations.
An Axiomatic Approach to the Formalism of Quantum Mechanics. II.
Authors: Prugovečki Eduard
Published: January 2005

Another axiom has to be introduced to make the formalism given in Part I physically equivalent to the conventional Hilbert-space formalism. Then it is shown that, given a certain fundamental set of observables, a B*-algebra A can be built into which the set 𝒪b of all bounded observables can be mapped injectively. The closure of the algebra generated by the image of 𝒪b into A is A itself. A Hilbert space ℋ exists into which the set 𝒪0 of all pure physical states can be mapped injectively. The closure of the subset of ℋ which is the image of this mapping is ℋ itself. The algebra A can be mapped in such a fashion into the C*-algebra B(ℋ) of all bounded observables that these mappings provide, essentially, just a translation of the original formalism in a Hilbert-space formalism.
The Dirac Bra and Ket Formalism
Authors: Roberts J. E.
Published: January 2005

The place of the Dirac formalism in quantum theory is investigated using rigged Hilbert spaces. Emphasis is laid on the representation of observables by continuous linear operators and on the existence of sufficient eigenkets. Using the concept of labeled observables, a canonical procedure is given for constructing a rigged Hilbert space and the bra and ket spaces are constructed for nonrelativistic quantum systems of n interacting particles. Spectral theory is investigated in this framework and the results are compared with the Dirac formalism.
Polynominal Bases and Isoscalar Factors for SU(3)
Authors: Sharp R. T. , Von Baeyer Hans
Published: January 2005

The generators of SU(3) are represented by differential operators which act on states represented by functions of six independent variables. Orthonormal bases for irreducible representations are presented in the form of polynomials. These are used to construct bases for product representations, to derive the Clebsch-Gordan series, and to find explicit expressions for certain special isoscalar factors. The general isoscalar factors are then expressed as sums over products of these special ones. Also, two types of recursion relation are derived for the general isoscalar factors; we illustrate our method of deriving these by deriving recursion relations for SU(2) which have been obtained recently by other means.
Covariant Conservation Laws for General Relativistic Exploding Matter
Authors: Droz-Vincent Philippe H.
Published: January 2005

In this paper we attempt a general relativistic extension of some simple notions, e.g., total angular momentum, so far correctly defined only in the frame of special relativity. The mathematical aspect of the problem leads us to ask, given a tensor of vanishing divergence, how to construct an integral object, conserved in time and covariant.

A formalism based upon bitensors ensures the covariance, while the assumption of an exploding (or imploding) schema of matter seems to be the only available means to preserve conservation when the space-time is curved. This can be formulated in a general theorem then applied to different physical situations. The total linear momentum occurs as a vector fixed at the point of explosion (or implosion). Its length turns out (at least when a pure matter schema is concerned) to be superior to the total mass of the fluid. The excess appears as the energy carried by the explosion. The case of a so called ``uncompressible'' holonomic fluid gives a quite analogous result. In order to find a nontrivial angular momentum we also consider, in the last section, the case of a fluid possessing an intrinsic spin density. Both linear and angular momenta are conserved and covariantly defined. Moreover, they reduce to the conventional ones when the curvature vanishes.
Electromagnetic Fields of Moving Dipoles and Multipoles
Authors: Ellis J. R.
Published: January 2005

A method of invariant Green's functions which is frequently used to find the fields of a moving charge is applied to evaluate the fields of dipoles and multipoles. Concise expressions are obtained from the integrals by successively integrating by parts. Two well-known methods for finding the radiation field on the world line of a charge are repeated for a dipole. It is found that a nonrotating (Fermi-Walker propagated) electric dipole has vanishing radiation field on the world line when it moves hyperbolically, as in the corresponding case for a charge. Radiation on the world lines of multipoles is also discussed (with particular reference to quadrupoles and octupoles), and the problem of evaluating the radiation reaction for a dipole is described within the context of the methods here given. It is further shown that a classical description of mass renormalization is possible to within the approximation of first-order terms, but not beyond.
Kinks
Authors: Finkelstein David
Published: January 2005

In sufficiently nonlinear field theories there are extended objects whose number is strictly conserved because of continuity of the underlying field as a function of space. We call these kinks. Kinks provide a covariant description of extended but indestructible particles. We give the properties the field theory must possess in order for kinks to exist, and the circumstances under which kinks can have spin ½.
Solution of very Singular N/D Equations—An Approach to Nonrenormalizable Field Theory
Authors: Halpern Martin B.
Published: January 2005

In this paper, we find closed form solutions to unsubtracted and once-subtracted N/D equations, both nonrelativistic and relativistic, with pathological left-hand absorptive parts that increase at large ν like α(−ν) ∼ −λνm, m not necessarily integral. The solutions allow dispersive, unitary and regulator-free calculation in nonrenormalizable field theory. For example, N/D equations with exchange of a higher spin particle (spin 32 etc.) can be solved. In general, the technique allows the use of a large class of divergent graphs as input, that is, those whose left-hand absorptive parts are finite, although asymptotically ill behaved. For example, in the W theory of leptonic weak interactions, one of the possible inputs is any number of ladder graphs cut so that all the bosons are on the mass shell. Many nonplanar graphs can be included as well. In much the same way, we can also calculate in the Fermi theory, (multiple exchanges in) theories of higher spin in general, and theories with derivative coupling.

There are an infinite number of solutions to these singular integral equations, each of which is characterized by a branch point at g2 = 0, and a branch point of oscillatory nature at infinite |ν|. Out of these, we pick the solution which sums the iterative expansion of the equations as most meaningful. It is seen explicitly that the unitary requirement generates its own regulation in the form of rapid oscillations at large unphysical energies, thus eliminating the need for any regulator limiting process. The oscillations are associated with an infinite number of ghosts, but these stay very far from the physical region. In addition, the solutions violate unitarity in the cross channels, so we expect the program to be useful at most in and near the physical region. As shorter range forces are systematically included, there is some indication that the program may converge rapidly for small physical energies.
Classical Field Theory and Gravitation in a de Sitter World
Authors: Roman P. , Aghassi J. J.
Published: January 2005

The algebra and the calculus pertaining to a certain class of representations of the de Sitter group is developed. This permits us to formulate covariant field equations in de Sitter space, and, in particular, to construct quantum mechanical equations of motion associated with particles of given spin. The gauge principle is invoked and a spin-two field emerges, which we identify with the gravitational field. Its coupling to sources is discussed and conservation laws are derived. The emerging nongeometric theory of gravitation is compared with both the Einstein-Riemann type and other previously proposed nongeometrical theories.
On the Chakrabarti Transformation
Authors: Sesma J.
Published: January 2005

In this note, we intend to present an appropriate Hamiltonian formulation for the extension of the Chakrabarti transformation [A. Chakrabarti, J. Math. Phys. 4, 1215 (1963)] to spin-0 and spin-1 particles. The suggested formulation is derived from that of Duffin-Kemmer and has been used previously [L. M. Garrido and P. Pascual, Nuovo Cimento 12, 181 (1959); L. M. Garrido and J. Sesma, Am. J. Phys. 30, 887 (1962); J. Sesma, J. Biel, and L. M. Garrido, Am. J. Phys. 32, 559 (1964)] to achieve a generalization of the Foldy-Wouthuysen transformation.
Doppler Measurement of Space—Time Curvature
Authors: Bertotti Bruno
Published: January 2005

In special relativity, the Doppler shift between two freely moving identical oscillators is constant if their world lines are coplanar. We show that in general relativity, instead, the rate of change of their Doppler shift is proportional to a component of the space—time curvature, averaged along the light ray. A possible application to the detection of gravitational waves is discussed.
A Two-Meson Solution of the Charged Scalar Static Model
Authors: Bronzan J. B.
Published: January 2005

Presented in this paper is a solution of the charged scalar static model, in which the scattering amplitude is crossing symmetric and has two- and three-particle intermediate states (two-meson approximation). The production and six-point amplitudes are also obtained and are shown to lead to a two- and three-particle unitary scattering matrix.
Role of Causality in Quantum Field Theory and the Dynamical Postulate
Authors: Chen T. W. , Rohrlich F. , Wilner M.
Published: January 2005

It is shown that Bogoliubov causality together with the usual assumptions of quantum field theory suffice to determine the off-mass-shell behavior of the S-operator as that resulting from the φ-product. The same assumptions lead to an equation for the current which replaces the field equation for the interpolating field. The specification of the interaction term in this equation corresponds to the specification of an interaction Hamiltonian in the usual formalism. This interaction term is an operator distribution whose support is a single point and which is otherwise severly restricted.
Anisotropic Linear Magnetic Chain
Authors: Des Cloizeaux Jacques , Gaudin Michel
Published: January 2005

The ground-state and the spin-wave states of the Hamiltonian, H= ∑ i (SixSi+1x+SiySi+1y+ρSizSi+1z),are studied for all values of ρ, and analytical expressions are given for their energies. On the other hand, by using a canonical transformation which changes H(ρ) into -H(- ρ), the states of highest energy can also be obtained. The ground state is ferromagnetic for ρ ≤ − 1 and antiferromagnetic for ρ ≥ −1. For ρ = ±1, the energy has singularities, but it remains continuous. For ρ = 1, all its derivatives are also continuous. In the range − 1 ≤ ρ ≤ 1, the spin-wave states of given momentum are degenerate but for ρ ≥ 1; this degeneracy is removed, and an energy gap G(ρ) appears.
Concise Derivation of the Formulas for Lattice Thermal Conductivity
Authors: Hardy Robert J.
Published: January 2005

A perturbation expansion for the correlation-function formula (or Kubo formula) for thermal conductivity was presented in a previous paper. The formulas obtained there for the lowest-order contribution are used here to derive the transport equations for the thermal conductivity for a lattice with imperfections and/or anharmonic forces. The result has the same form as the familiar Boltzmann equation for phonons.
Higher-Order Corrections to the Lattice Thermal Conductivity
Authors: Hardy Robert J. , Schieve William C.
Published: January 2005

In a previous paper the correlation function formula, or Kubo formula, was used to derive formulas for the lowest-order (λ−2) and first-order (λ−1) corrections to the lattice thermal conductivity (the Hamiltonian is written H = H° + λH′). The formulas obtained there are used here to derive the transport equations for the calculation of the first-order correction to the conductivity. These transport equations have the same homogeneous part as the familiar Boltzmann equation for phonons; however, their inhomogeneous parts are different and depend on the nature of the perturbation. Formulas for these inhomogeneous parts are given for both the scattering due to randomly distributed point imperfections and that due to anharmonic forces. At high temperature, the first-order correction for anharmonic scattering is independent of the temperature.
General Spherical Harmonic Tensors in the Boltzmann Equation
Authors: Johnston Tudor Wyatt
Published: January 2005

The irreducible velocity space direction cosine tensors associated with velocity magnitude spherical harmonic expansion of the distribution function are manipulated in the Boltzmann-Vlasov flow terms to yield a linked chain of equations whose general (lth) equation is given explicitly. This generalizes earlier results for l = 0, 1, 2, 3.
Lattice Statistics of Hydrogen Bonded Crystals. II. The Slater KDP Model and the Rys F-Model
Authors: Nagle J. F.
Published: January 2005

The Slater KDP model, a simple hydrogen bonded ferroelectric model, and the Rys F-model, a simple hydrogen bonded antiferroelectric model, have been treated using both high- and low-temperature series for the partition function. The high-temperature series is a modification of the residual entropy of ice series discussed in I. For each model a temperature is found at which the high-temperature series and the low-temperature series are identically equal. For the KDP model this equality gives a transition temperature and a latent heat is easily calculated, both of which are exact. It so happens that these exact results agree with previous analyses which used only mean field approximations. For the F-model the formal equality of the series gives the first evidence for a phase transition. Although the latent heat calculation throws some doubt on the existence of a transition, after further discussion of the series it is concluded that there most probably is a phase transition.
Analytic Properties of Resolvents and Completeness
Authors: Fonda L. , Ghirardi G. C. , Weber T. , Rimini A.
Published: January 2005

The main purpose of this paper is to prove, by using a simple formal procedure, the completeness of the set of eigenstates of a non-Hermitian operator whose resolvent satisfies certain physically plausible analytic properties. It is also shown how the obtained completeness relation can be related to the scattering solutions of the eigenvalue equation with extension to the multichannel case. All proofs are heuristic only.
Local States
Authors: Licht A. L.
Published: January 2005

A heuristic discussion is given of the preparation of states in finite space-time regions. Some axioms concerning such states are derived from this discussion. It is shown that states requiring for their preparation a selection of events according to the outcome of a measurement will not be ``strictly local.'' Nonselective states will, however, be ``strictly local.'' The mathematical structure of such states is investigated.
The Structure of 4-Spinors
Authors: Teitler S.
Published: January 2005

The possible underlying spinor spaces used in the description of Dirac 4-spinors are enumerated and classified within the framework of vector Clifford algebra. The relation with the usual matrix formulation is reviewed. Proper Lorentz transformation, space and time inversions are described in the Clifford algebra formalism. A representation-independent definition of charge sign conjugation is given.
Variational Principle for Eigenvalue Equations
Authors: Pomraning G. C.
Published: January 2005

A variational principle is developed to provide an estimate of an arbitrary functional of the eigen-functions of a set of eigenvalue equations. It is shown that the variational formalism is equivalent to a functional Taylor series expansion of the desired functional about the trial functions. The relationship of this work to perturbation theory is considered, and it is shown that the formalism can be used to construct higher-order variational principles, i.e., those for which first-order errors in the trial functions leads to an nth-order error in the desired functional. Finally, it is shown that the variational principle of Borowitz and Vassell for estimating off-diagonal matrix elements, as well as the usual Rayleigh quotient, are special cases of the principle presented here.
High-Energy Behavior of Feynman Integrals with Spin. II
Authors: Greenman J. V.
Published: January 2005

The analysis of a previous paper is applied to determine the leading behavior and coefficients of specific lower-order terms of planar graphs in the nucleon-meson scattering process. The results of Cheng and Wu in verifying the Reggeization hypothesis in sixth order are rederived and a method of extending the analysis to nth order is indicated.
Quasi-Classical Analysis of Coupled Oscillators
Authors: Helstrom Carl W.
Published: January 2005

A set of harmonic oscillators is coupled for a certain time, after which the coupling is removed. The initial and final states of the set are expressed as superpositions of the coherent states of the uncoupled oscillators, as in Glauber's formalism. It is shown that the expansion kernel for the final state can be obtained approximately by substituting into the kernel for the initial state the classical equations of motion of the amplitudes of the oscillators. The evolution of a density operator for the system can be similarly calculated. The approximation is the more exact, the longer the time of interaction compared with the periods of the uncoupled oscillators.
Representation Theory of Local Current Algebras
Authors: Roffman Eric H.
Published: January 2005

We prove the following theorem: Every finite-dimensional irreducible representation of the local current algebra [Fρ(k1), Fσ(k2)]=eρστFτ(k1+k2),where the {eρστ} are the structure constants of a semisimple Lie algebra L, has the form Fρ(k)→ ∑ i=1NeikxiTρi,where Tρi is a finite-dimensional representation of L, and for i ≠ j, xi; Tρi commutes with Tσj for all ρ and σ.