bluuebunny/crossref_metadata_2025 huggingface dataset:
Connection between Spin, Statistics, and Kinks
Authors: Finkelstein David , Rubinstein Julio
Published: February 2004

Sufficiently nonlinear classical fields admit modes called kinks, whose number is strictly conserved in virtue of boundary conditions and continuity of the field as a function of space and time. In a quantum theory of such fields, with canonical commutation (not anticommutation) relations, kinks and their conservation still persist, and even if the intrinsic angular momentum is an integer, a rotating kink can have half-odd angular momentum, if double-valued state functionals are admitted. We formulate a natural concept of exchange appropriate for kinks. The principal result is that for fields with integer-valued intrinsic angular momentum, the observed relation between spin and (exchange) statistics follows from continuity alone, parastatistics being excluded. It is likely that in the theories with even (odd) exchange statistics, suitable creation operators will commute (anticommute). We show that, while the rotational spectrum of a kink will in general possess both integer and half-odd spin states, in fields with integer-valued intrinsic angular momentum only one of these two possibilities will ever be observed for each kind of kink, and that there is a nonzero ``particle number'' (strictly conserved, additive, scalar quantum number) attached to half-odd-spin kinks of each kind. It then follows that a boson and a fermion kink will always differ in at least one particle number, as well as in spin, and that, in particular, every fermion kink will have some nonzero particle number. These results are consistent with the hypothesis that the spinor fields usually employed to describe half-odd-spin quanta are not fundamental, but are useful ``point-limit'' approximations to operators creating or annihilating excitations in a nonlinear field of particular kinds of kinks in particular internal states.
Principle of Compensation of Dangerous Diagrams for Boson Systems. II. Minimum Quasiparticle Number
Authors: Kobe Donald H.
Published: February 2004

The principle of compensation of dangerous diagrams (PCDD) postulated by Bogoliubov to determine the coefficients in his canonical transformation in boson systems is obtained from four criteria: (1) the number of quasiparticles in the true ground state is a minimum; (2) the ``best'' approximation to the true density matrix and pair amplitude is made; (3) the expectation value of an arbitrary operator is diagonalized up to terms cubic in the quasiparticle operators; (4) the most convenient starting point for dressing the quasiparticles is used. Quasiparticle Green's functions are introduced to obtain a diagrammatic expansion of the PCDD. The reducibility of the diagrams is also discussed.
Variational Approach to Multiple Scattering
Authors: Levine A. D. , Hayes C. F.
Published: February 2004

Using a variation technique, two coupled equations are derived whose transition matrix is shown to describe multiple scattering. The resulting index-of-refraction equation differs from that obtained in previous theories by our inclusion of the effect of the scatterer on the target and certain constants of approximation.
Cell Model of a Fluid. I. Evaluation of the Partition Function and Series Expansions
Authors: Tross Ralph G. , Lund Louis H.
Published: February 2004

The partition function of a one-dimensional system of particles with all interactions active is formulated in terms of Ising ferromagnetic spin states. It is shown how the partition function for two- and three-dimensional systems can be obtained from the one-dimensional one by restricting the number of bonds per particle. After writing the partition function in matrix form, the operator of interest is diagonalized and its trace expressed in the form of a convenient infinite series. The series is shown to be absolutely convergent and its analytic properties are briefly investigated. It is then applied to one-, two-, and three-dimensional systems with nearest-neighbor interactions. The validity of the model is established by summing the one-dimensional series and comparing it with the known solution obtainable by other methods. Two- and three-dimensional series are determined by algebraic techniques identical to the one-dimensional series. These are seen to agree with the low-temperature expansions obtained by other authors. The method of this article is seen to have the advantage of simplicity and uniformity regardless of the dimension of the system. A subsequent article is devoted to the thermodynamics of the model.
Reduction of Reducible Representations of the Poincaré Group to Standard Helicity Representations
Authors: Moses Harry E.
Published: February 2004

In this paper we introduce realizations of the generators of the Poincaré group for real and imaginary masses which are close in form to the Lomont-Moses realizations for zero mass. These realizations (which we call ``standard helicity realizations or representations'') are characterized by the way that the infinitesimal generators are given in terms of the helicity operator. We also give the global form of the realizations and discuss in detail the realizations for the case that they are unitary and irreducible. We then show how any reducible representation of the Poincaré group for which the infinitesimal generators of the translation and rotation subgroups are Hermitian and integrable and for which the space-time generators are integrable (but not necessarily Hermitian) can be reduced to the standard helicity realizations. In the case that the reducible representation is unitary, this process enables one to reduce the reducible representation to irreducible unitary standard helicity representations. Finally, we show how the Foldy-Shirokov realizations for real mass are related to the standard helicity representation.
Majorana Representations of the Lorentz Group and Infinite-Component Fields
Authors: Stoyanov D. Tz. , Todorov I. T.
Published: February 2004

A self-contained exposition is given of the theory of infinite-component fields with special emphasis on fields transforming under the Majorana representations of the Lorentz group, for which the scalar vertex function is written down explicitly for particles with arbitrary momenta and spins. The problem of spin and statistics for such fields is analyzed. A class of coupled representations of SL(2, C) is studied, containing unitary as well as nonunitary representations (including the Dirac 4-component spinors), for which invariant first-order equations can be written down for the free field. Most of the results are known (either from old or from recent publications), but are presented here in a unified way, their derivation sometimes being simplified. Among the few new points we mention: (1) The location of singularities of the matrix elements of some infinite-dimensional representations of SL(2, C) for complex values of the group parameters. (2) The construction of an infinite-component local Fermi field transforming under a unitary representation of SL(2, C). (3) the discussion of the quantization of Majorana fields with a proper account of the Fourier components with spacelike momenta.
2V Sector of the Lee Model
Authors: Scarfone Leonard M.
Published: February 2004

The Lehmann-Symanzik-Zimmermann (LSZ) formalism is further used to analyze the 2V sector of the Lee model with boson sources at zero separation. Unlike previous LSZ investigations of the model, it is found that the solutions to two singular integral equations solve the entire sector. Two scattering amplitudes, a production amplitude, and an equation for the determination of the 2V potential energy are obtained. Similarities and differences between this sector and the V + θ subspace are pointed out.
Einstein Tensor and Spherical Symmetry
Authors: Plebanski Jerzy , Stachel John
Published: February 2004

The classification of symmetric second-rank tensors in Minkowski space and its application to the Einstein tensor is reviewed. It is shown that, for spherically symmetric metrics, the Einstein tensor always has a spacelike double eigenvector; and the possible types of Einstein tensor that this degeneracy allows are discussed. A complete classification of all spherically symmetric metrics with two double eigenvalues is given. A study of the timelike eigencongruence, in the case when one timelike and two spacelike eigenvectors exist, is carried out. Canonical forms for the metric, the Einstein tensor, and the Weyl tensor (which is always of type D) are given for each of the various possible types.
Unitarity of Dynamical Propagators of Perturbed Klein-Gordon Equations
Authors: Chadam John M.
Published: February 2004

After discussing the basic notions of quantizations as representations of the Weyl relations, a criterion is established for a symplectic transformation on a classical linear system to be unitarily implementable in the free (zero-interaction) representation. The result is applied to the temporal propagators of □φ=m2φ+Kφ to obtain a condition which is sufficient to ensure that they are unitarily implementable in the free representation of the quantized Klein-Gordon field of mass m. Necessary conditions are also obtained when K commutes with m2I − Δ. Several examples are discussed, the most interesting of which is that of a mass jump (i.e., K = m′2I), where the results given are fairly complete.
Tail of a Gravitational Wave
Authors: Couch W. E. , Torrence R. J. , Janis A. I. , Newman E. T.
Published: February 2004

A first-order quadrupole sandwich wave of gravitational radiation exploding from a first-order Schwarzschild mass is examined to second order. If the second-order field preceding the sandwich wave vanishes, it is shown that the region of space-time following the sandwich wave contains a second-order, imploding quadrupole wave. The rest of the second-order field in the space-time region following the sandwich wave is also given, and it is seen to consist of monopole, quadrupole, and 16-pole nonradiative motions.
Dyadic Analysis of Spatially Homogeneous World Models
Authors: Estabrook F. B. , Wahlquist H. D. , Behr C. G.
Published: February 2004

The dyadic formalism is applied to cosmological models, and leads to a convenient set of first-order ordinary differential equations. The Bianchi-Behr type of any model is shown to be constant in time, regardless of the state of the matter content. The case of perfect fluid matter content is formulated. Type V models and Type VIII and IX models with incoherent matter are discussed, and some consistent subtypes delineated. The Gödel Hamiltonian for symmetric Type IX models is derived and generalized.
Alpha-Function Technique for Two-Center Integrals
Authors: Sharma R. R.
Published: February 2004

A closed form has been derived for the function αl(NML | a,r) introduced by Löwdin for two-center integrals in molecules and solid states. This expression is general and applied to all values of l, L, and M.
Some Properties of the Contact between Theory and Experiment
Authors: Benioff Paul A.
Published: February 2004

This paper uses the sample probability-space description to review, under general conditions, the measurement process whereby an empirical expectation value is obtained for comparison either with other values or with values calculated from a theory. The emphasis here is on some of the conditions which must be satisfied by general sequences of single measurements, about which an observer may have relatively little knowledge, in order that such sequences yield suitable expectation values. In particular, sequences are considered for which the requirements that the single measurements of the sequence be independent and made of the same physical quantity on ensembles of identically prepared systems are not necessarily satisfied. The differences between sequences which satisfy these requirements and those which do not are discussed in terms of the implications or meaning of the resultant expectation value as a point of contact between theory and experiment.
Current Formalism. I. Ordering Theorems for Currents
Authors: Wray J. G.
Published: February 2004

The basic assumptions of the theory are strong unitarity, Bogoliubov causality, completeness of the in (out) fields on a unique vacuum, and Poincaré invariance. The algebra of II functions, which are integral operators in the form of tempered distributions, is the main technical tool developed here. These II functions can be regarded as generalized step functions where the combination law is such that products with δ functions and their derivatives are well defined. An application of this algebra of II functions in the context of the above assumptions leads to the current-formalism representations of nth-order functional derivatives of the current and Sop. These are alternatively called the RP and P product representations, respectively, the counterparts to the R and Φ product representations of the nth-order derivative of the field and Sop in the field formalism. In a subsequent paper these relations are used to derive the integro-differential equations of Pugh [R. E. Pugh, Ann. Phys. (N.Y.) 23, 335 (1961)] in a form amenable to a diagrammatic analysis. The perturbation series is then shown to be unique and finite with no cutoffs and a number of parameters that is independent of (increases with) the order of expansion for renormalizable (nonrenormalizable) interactions.
Modified Born Approximation and Elastic Scattering by Weak Central Potentials
Authors: Dutta S. K. , Wilson W. A. , Green A. E. S.
Published: February 2004

When only a few partial waves are substantially phase shifted and yet many partial waves are slightly phase shifted, it is possible to use the direct Born approximation, provided that one projects out the inaccurate lower partial waves and replaces them by accurate theoretical or phenomenological phase shifts. We test this technique for central potentials with two different well strengths, i.e., one which will fail to bind the 1S wave, and one which can bind the 1S state. We compare numerically generated angular distributions and total cross sections with those obtained from a modified form of the direct Born approximation. The technique would be useful for weak forces, e.g., the nucleon-nucleon and electron-atom interactions, but inapplicable for strong forces, e.g., atom-atom interaction.
Analytic Properties of a Class of Nonlocal Interactions. I
Authors: Gutkowski D. , Scalia A.
Published: February 2004

The analytic properties of the functions Sl(k) for a class of nonlocal interactions are studied in the complex k (wavenumber) plane, for physical angular momenta. The results are compared with those of the local interactions. Two specific examples are discussed.
Perturbation Expansion for Real-Time Green's Functions
Authors: Craig R. A.
Published: February 2004

The development of the time-translation operators in a matrix element of an arbitrary operator is examined. It is noted that we may interpret time as evolving from some remotely early time (t0) to a time in the far future (t∝) and then back to (t0). Using this interpretation, a perturbation expansion is developed for Green's functions defined along this path and a separation of the two-particle interaction terms into self-energy parts and single-particle Green's function terms is justified for quantities on this path. A connection is established between the real-time Green's functions and the Green's function defined along the path, thereby yielding a perturbation expansion for the real-time functions and a justification of the separation of the interaction terms in the equations of motion for the real-time quantities. The transport equations of Kadanoff and Baym are derived without resorting to an analytic continuation from imaginary times and without the correction terms of Fujita.
Note on the Geometric Theory of Neutrinos
Authors: Collinson C. D.
Published: February 2004

The geometric theory of neutrinos proposed by Penney is investigated. It is shown, from the conditions imposed, that the space-time is conformally flat. All solutions of the field equations are found and attention is paid to the limiting process described by Penney.
Irreducible Representations of the Semidirect-Product Group Kn = An : Sn and the Harmonic-Oscillator Shell Model
Authors: Kramer Peter
Published: February 2004

If An denotes the Abelian group of n × n unitary diagonal matrices and Sn the symmetric group represented by n × n permutation matrices, the set of elements ap with a∈An and p∈Sn form a group Kn which is the semidirect product of An and Sn. Irreducible representations of Kn and the chains Kn⊃Sn and Un⊃Kn, with Un being the unitary group in n dimensions, are discussed with applications in the harmonic-oscillator shell model.
Error Bounds in Equilibrium Statistical Mechanics
Authors: Gordon Roy G.
Published: February 2004

A new method is presented for the calculation of thermodynamic properties from equilibrium statistical mechanics. Starting from the high-temperature expansion coefficients for the canonical partition function, error bounds are obtained, which are both rigorous and optimal.
Quantum-Mechanical Description of a Brownian Particle
Authors: de la Peña-Auerbach L. , Braun E. , Colín L. S. García
Published: February 2004

It is shown that the motion of a Brownian particle in the Smoluchowski approximation may be described by a Schrödinger-like equation defining a complex probability amplitude whose norm is the same as the stochastic probability density. Furthermore, the quantum dynamical operators have a physical meaning which arises in a natural way, from the stochastic nature of the process. These operators satisfy the usual commutation relations and thus the uncertainty principle. Here the constant ℏ is replaced by a parameter depending on the characteristics of the system. In particular, the potential-energy operator for a Brownian particle subject to no external forces can be interpreted as a Rayleigh dissipative function.
Some Properties of Ladder Operators
Authors: Komy S. , O'Raifeartaigh L.
Published: February 2004

The commutation relations [H, P ± iQ] = ± (P ± iQ) for the symmetric operators H, P, Q are considered without assuming (a priori) any other relationship between H, P, Q, in particular without making any assumption concerning the commutator [P, Q]. It is shown that under certain mild restrictions the spectrum of H is integer spaced, and that in the two particular cases [P, Q] = iεH, ε = 0, ±1 and H = ½(P2 + Q2) + iσ[P, Q], corresponding to Lie groups and parastatistics, respectively, it is simple. For these two cases the explicit representations of P, Q, and H are found in a simple manner. The question of the existence of a common analytic domain for P, Q, and H is investigated, and some sufficient conditions for this are found.
Nonexistence of Finite-Energy Stationary Quantum States in Nonlinear Field Theories
Authors: Rosen Gerald
Published: February 2004

A simple proof is given which precludes the existence of any finite-energy stationary quantum-state solution to the Schrödinger equation for a physically interesting Lorentz-covariant self-interacting scalar theory.
New Derivation of the Integro-Differential Equations for Chandrasekhar's X and Y Functions
Authors: Bellman R. , Kagiwada H. , Kalaba R. , Ueno S.
Published: February 2004

The X and Y functions of radiative transfer satisfy a system of integro-differential equations which form the basis of an effective numerical treatment. These integro-differential equations are derived from the integral equation for the source function and the differential equation for the resolvent.
Nonequilibrium Statistical Mechanics of Open Systems
Authors: Emch Gerard G. , Sewell Geoffrey L.
Published: February 2004

A theoretical framework for the nonequilibrium statistical mechanics of open systems is constructed. This is concerned with a formulation of a generalized master equation governing the evolution of an arbitrary system S in interaction with a ``large'' reservoir R. The dynamics of S are analyzed on the basis of a precise quantum-mechanical treatment of the microscopic equations of motion for the combined system S + R. On proceeding to the thermodynamical limit for R we obtain a generalized master equation for S, subject to specified conditions on the many-particle structure of R, its initial state, and its coupling to S. This master equation corresponds to a self-contained law of motion for S, in which the R variables appear only in the forms of certain thermal averages, taken over the initial state. This dynamical law is a generalization of the quantum-mechanical Liouville equation to a form appropriate to open systems.
Variational Bounds for the Potential in Terms of the S-Wave Phase Shift
Authors: Calogero F. , Corbella O. D. , Degasperis A. , De Stefano M. B.
Published: February 2004

We establish a variational expression involving the S-wave phase shift and bound-state parameters and the potential, which appears particularly suited to evince from the S-wave-scattering data information (i.e., bounds or variational approximations) on the potential. An application of this approach to solvable potentials yields a number of inequalities involving special functions.
Model for Converging Detonations in Solid Explosives
Authors: Conger Robert L.
Published: February 2004

The fluid-dynamic equations which describe converging detonation fronts in high explosives are solved over a coordinate system that changes from circular to a pleated pattern as the detonation converges. There are three reasons for introducing such a coordinate system rather than making the usual assumption that when a spherical or cylindrical explosive charge is initiated simultaneously on its curved surface the detonation front maintains its symmetry as the detonation converges to the center: (1) Calculations made elsewhere show that a converging circular shock wave is unstable. (2) Calculations in this paper show that if spherical or cylindrical symmetry is maintained, density and velocity become infinite, but if the detonation front folds these quantities remain finite except at a few points which can be removed by cuts. The average fluid velocity remains almost constant over 99% of the detonation front. (3) Experiments indicate that a cylindrical detonation front becomes rather symmetrically deformed.
Type-Null Vacuum Solutions in General Relativity
Authors: Misra M.
Published: February 2004

It is shown that the necessary and sufficient conditions for the vacuum solutions of a certain metric to be of type null according to the Pirani-Petrov classification are that a certain other metric be conformally flat. The general solution is obtained.
Error Bounds in Spectroscopy and Nonequilibrium Statistical Mechanics
Authors: Gordon R. G.
Published: February 2004

Upper and lower bounds are derived for the response of a system initially in equilibrium to a weak damped-harmonic perturbation. The only information required in the construction of these error bounds are equilibrium properties of the unperturbed system, in particular, the equilibrium moments of the spectral density corresponding to the perturbation are used. The error bounds are shown to be the most precise possible, given only this equilibrium information. As an example, error bounds are obtained for the shape of a nuclear-resonance spectrum due to dipolar broadening in solids, and good agreement is obtained with nuclear-magnetic resonance experiments on CaF2. The error bounds are applicable to many other areas of spectroscopy and nonequilibrium statistical mechanics.
Nearest-Neighbor Spacing Distribution for an Ensemble of Random Matrices with a Nonrandom Bias
Authors: McDonald J. F. , Favro L. D.
Published: February 2004

The nearest-neighbor spacing distribution for the biased Gaussian distribution exp [−γ Tr (H − H0)2] is calculated in the limits of large and small γ. The results for the small-γ limit are found to approach those for an unbiased Gaussian distribution (i.e., H0 proportional to the unit matrix). To order γ2 the mth-order spacing distribution is expressed in terms of the mth-order spacing distribution for the unbiased Gaussian ensemble. The results for the large-γ limit are found to depend strongly on H0. That is, the nearest-neighbor spacing distribution reflects the structure of H0. Thus, a biased distribution offers a possible description for the experimental deviations from the Wigner surmise and apparent multiple-peak structure exhibited by some nuclear-spacing data.
Remarks on the Burgers Equation
Authors: Rosenblatt M.
Published: February 2004

Periodic and aperiodic solutions of the Burgers equation ut + uux = μuxx, μ > 0, are studied in this paper. A harmonic analysis of the solutions is carried out and the form of the spectrum is estimated for large time. Corresponding estimates of energy decay are also made. In Burgers' work on this equation, the case in which μ ↓ 0 with t fixed, and one then lets t → ∞, is studied. In our investigation, a fixed value of μ > 0 is taken and then one lets t → ∞. A similar analysis is also carried out for an irrotational solution of a similar 3-dimensional system of equations. For large time and moderate wavenumbers there is, to the first order, a drift of spectral mass from low wavenumbers to higher wavenumbers. Comments are also made on the asymptotic distribution of a class of random solutions.
Analyticity Properties of the Scattering Amplitude for Singular Potentials
Authors: Dombey Norman , Jones R. H.
Published: February 2004

A modified Sommerfeld-Watson transformation is established for the singular potential V(r) = g2r−4. The positions of the Regge poles and their residues are obtained for a general class of singular potentials and the analyticity properties of the scattering amplitude f(k, cos θ) are discussed.
Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation
Authors: Miura Robert M.
Published: February 2004

An explicit nonlinear transformation relating solutions of the Korteweg-de Vries equation and a similar nonlinear equation is presented. This transformation is generalized to solutions of a one-parameter family of similar nonlinear equations. A transformation is given which relates solutions of a ``forced'' Korteweg-de Vries equation to those of the Korteweg-de Vries equation.
Approach to Scattering Problems through Interpolation Formulas and Application to Spin-Orbit Potentials
Authors: Sabatier Pierre C.
Published: February 2004

In many problems of potential scattering, and particularly in the inverse-scattering problem, two equations prove to be of essential interest: the Gel'fand-Levitan equation and the Regge-Newton equation. These and their generalizations apply, respectively, to energy-independent and to λ-independent potentials. In this paper, a method is devised for obtaining equations applying to more general cases. The requirement is the existence of analytic properties of the wavefunctions corresponding to special classes of potentials, enabling one to construct interpolation formulas of the Lagrange form. From these formulas, it is possible to derive integral equations which may then be generalizable to much larger classes of potentials. This method is fully developed in the case of potentials depending linearly on λ. Interpolation formulas and analytic properties of the wavefunctions in the λ plane are exhibited. Integral equations are given and proved to apply to very large classes of potentials. Existence, uniqueness, and analytic properties of their solutions are thoroughly studied. An example is given for which all the wavefunctions are calculated exactly. Application of the method to the inverse scattering problem in the presence of a spin-orbit potential will be the object of a forthcoming paper.
Extended Energy-Integral Technique for Linear Differential Equations
Authors: Kadish Abraham
Published: February 2004

An extended energy-integral technique for boundary-value problems is presented for a class of differential equations which are prevalent in mathematical physics. The extended technique provides a method for answering questions in wave propagation and stability which could not be treated by the familiar method of energy integrals.
Quasibinomial Representations of Clebsch-Gordan Coefficients. II. ``Negative'' Representations
Authors: Ansari S. M. Razaullah
Published: February 2004

New quasibinomial forms are derived from the quasibinomial forms given previously by making use of both positive and negative generalized powers. They turn out to be a new representation of the Wigner-type unsymmetrical formulas of Clebsch-Gordan coefficients for angular momenta. Consequently, formulas of Racah, Majumdar, and Shimpuku are deduced as special cases. Rules to construct a square symbol are given from which all these ``negative'' quasibinomial representations or, more precisely, expansions can be read off directly. Thus, a unified treatment of both symmetrical and unsymmetrical formulas of Clebsch-Gordan coefficients is thereby accomplished.
Interaction of Particlelike Solutions in a Classical Nonlinear Model Field Theory
Authors: Pinski G.
Published: February 2004

The Lagrangian for the interaction of two particles is evaluated in a model nonlinear scalar field theory. A trial function suggested by a Rayleigh-Ritz procedure is used and an exact calculation is performed. The terms in the interaction are expressed as complete elliptic integrals.
Asymptotic Behavior of Stieltjes Transforms. II
Authors: Woolcock W. S.
Published: February 2004

The results of a previous paper concerning the asymptotic behavior of Stieltjes transforms for large |z| are extended to prove theorems which hold uniformly for all directions in the complex plane. Special additional assumptions, which hold for all sufficiently large values of the argument of the function whose transform is taken, are required to obtain these extended results.
Irreducible Corepresentations of Groups Having a Compact Simple Lie Group as a Subgroup of Index 2
Authors: Mehta M. L. , Srivastava P. K.
Published: February 2004

For all possible extensions G of the compact simple Lie groups G, such that G be a subgroup of G of index 2, we determine those corepresentations of G in which unitary operators correspond to the elements of the subgroup G, antiunitary operators to its coset. We find that any irreducible unitary representation of G can be extended to an irreducible corepresentation of G in various ways summarized in Table IV.
Invariants of Nearly Periodic Hamiltonian Systems. II
Authors: Whiteman K. J. , McNamara B.
Published: February 2004

In a previous paper the first few terms of the adiabatic invariant of a particular class of dynamical systems were found by solving Liouville's equation. The system considered was a periodic motion to which small perturbations were applied. The period of the unperturbed orbits was a constant and the perturbations were time-independent. In this paper similar methods are used to find the invariant for the more general system, in which the period of the unperturbed orbits is a function of the coordinates and in which the perturbation varies slowly with time. The results are applied to a simple example, the Lorentz pendulum.
Asymptotic Estimates of Feynman Integrals
Authors: Fink James P.
Published: February 2004

In this paper, we consider the problem of determining logarithmic, as well as polynomial, asymptotic estimates for certain convergent integrals containing parameters. We state and prove an asymptotic theorem which gives the logarithmic asymptotic behavior of a convergent integral where any subset of the parameters becomes large while the remaining parameters remain bounded. This theorem is then applied to the photon and electron self-energy graphs of quantum electrodynamics.
Iterative Solutions by Means of Trial Operators
Authors: Goldstein Rubin
Published: February 2004

The problem of finding a weighted average of an unknown solution to an inhomogeneous equation is examined. An analytic approximation technique is developed in terms of an iterative series involving a trial operator. By choosing the operator so that successive terms in the series vanish, one obtains a solution which has characteristics similar to variational solutions to the problem. The iterative approach has the added features of giving error estimates, the sign of the error, a testing ground for the quality of classes of trial operators or functions, and a possible means of determining upper and lower bounds to the exact result. Several examples are given for both self-adjoint and non-self-adjoint systems. It is shown that the trial operator approach can give useful analytic approximations, with results which may be superior to variational calculations.
Coherent Superposition of Local States
Authors: Licht A. L.
Published: February 2004

The notion of coherent superposition is generalized so as to apply to local states.
Problem of Two Spin Deviations in a Linear Chain with Next-Nearest-Neighbor Interactions
Authors: Majumdar Chanchal K.
Published: February 2004

The problem of two spin deviations from the fully aligned state is studied in a linear chain for the Hamiltonian [J(i,j) > 0]: H=−½ ∑ (nn)J(i,j)Si·Sj−½α ∑ (nnn)J(i,j)Si·Sj,where (nn) and (nnn) mean nearest- and next-nearest-neighbor interactions, respectively. The behavior of the bound state, which is found to exist for α ≥ 0 only, is discussed.
Combinatorial Structure of State Vectors in Un. I. Hook Patterns for Maximal and Semimaximal States in Un
Authors: Ciftan Mikael , Biedenharn L. C.
Published: February 2004

It is shown that, in the boson-operator realization, the state vectors of the unitary groups Un—in the canonical chain Un⊃Un−1⊃⋯⊃U1—can be obtained ab initio by a combinatorial probabilistic method. From the Weyl branching law, a general state vector in Un is uniquely specified in the canonical chain; the algebraic determination of such a general state vector is in principle known (Cartan-Main theorem) from the state vector of highest weight; the explicit procedure is a generalization of the SU(2) lowering-operator technique. The present combinatorial method gives the normalization of these state vectors in terms of a new generalization of the combinatorial entity, the Nakayama hook, which generalization arises ab initio from a probabilistic argument in a natural way in the lowering procedure. It is the advantage of our general hook concept that it recasts those known algebraic results into a most economical algorithm which clarifies the structure of the boson-operator realization of the Un representations.
Remarks on Lie-Algebra-Invariant Equations. II
Authors: Humi Mayer
Published: February 2004

We deal with a generalization of Gel'fand method which provides us with a simplified and constructive derivation of some known and new results on the construction and general properties of tensor and nth-order Lie-algebra-invariant equations.
Diffraction by a Slit or Strip
Authors: Bailey Paul B. , Barr George E.
Published: February 2004

The problem of diffraction by a slit plane (or an infinite strip) is solved exactly for the case of a two-dimensional source distribution, the Green's function being given explicitly in terms of the fundamental solution of the wave operator. Also treated are the limiting case of plane waves and the asymptotic behavior with respect to large wavenumber.
Bounds for Effective Bulk Modulus of Heterogeneous Materials
Authors: Miller Melvin N.
Published: February 2004

Bounds for the effective bulk modulus for statistically isotropic and homogeneous materials have been developed in terms of statistical information, i.e., one-point and three-point correlation function from variational principles. Aside from the one-point correlation function, i.e., the volume fraction, this statistical information is difficult or impossible to obtain for real materials. For a broad class of heterogeneous materials which we shall call cell materials, the functions of the three-point correlation function that appear in the bounds of effective bulk modulus are simply a number for each phase. Furthermore, this number has a range of values 19 to ⅓ and a simple geometric significance. The number 19 implies a cell of spherical shape, the number ⅓ a cell of plate-like shape, and all other cell shapes, no matter how irregular, have a corresponding number between. Each value of this number determines a new set of bounds which are substantially narrower and always within the best bounds for two-phase media in terms of volume fraction alone (i.e., Hashin-Shtrikman bounds). For dilute suspensions the new bounds are so narrow in most cases as to be essentially an exact solution. There is a substantial improvement over previous bounds for a finite suspension and yet greater improvement for multiphase materials where the geometric characteristics of each phase are known. The shape factor G is found to have exactly the same range of numerical values and the same geometric significance as was found in the determination of effective dielectric constant bounds. It was found further that under certain conditions the bounds on effective bulk modulus and dielectric constant become numerically identical.
Spectral Representation of the Covariant Two-Point Function and Infinite-Component Fields with Arbitrary Mass Spectrum
Authors: Todorov I. T. , Zaikov R. P.
Published: February 2004

The general form of a Lorentz covariant two-point function is written down in momentum space as an expansion in terms of the total spin eigenfunctions. It leads naturally to a local expression for finite-component fields, but incorporates nonlocal infinite-component fields. Explicit examples of such fields with increasing mass spectrum are constructed. The two-point function is shown to fall exponentially for large spacelike separations provided that the lowest mass in the theory is positive.
Matrices of Finite Lorentz Transformations in a Noncompact Basis. I. Discrete Series of O(2, 1)
Authors: Mukunda N.
Published: February 2004

We consider the problem of obtaining the matrices that represent finite group elements in unitary irreducible representations of the group O(2, 1), in a basis in which the ``noncompact'' generator of an O(1, 1) subgroup is diagonal. The discrete series of representations is treated and expressions obtained for the matrix elements of group elements belonging both to the O(2) subgroup and the other O(1, 1) subgroup.
Matrices of Finite Lorentz Transformations in a Noncompact Basis. II. Continuous Series of O(2, 1)
Authors: Mukunda N.
Published: February 2004

The representation matrices in a noncompact basis for finite elements of the group O(2, 1) are determined in the continuous classes of unitary irreducible representations. Integral as well as half-integral, and exceptional as well as nonexceptional, representations are treated.
Further Note on Two Binomial Coefficient Identities of Rosenbaum
Authors: Chiang David
Published: February 2004

This note gives additional condition to the finding of Gould on two binomial coefficient identities of Rosenbaum.
Theory of Observables
Authors: Deliyannis Platon C.
Published: February 2004

An alternative formulation of a general theory of observables is presented, which contains as special cases the systems proposed by Segal and Mackey. The basic properties are developed, and the exact relations to the aforementioned systems are deduced.
Character Analysis of U(N) and SU(N)
Authors: Blaha Stephen
Published: February 2004

A symmetric group analysis of the characters of U(N) and SU(N) representations yields formulas for (i) the multiplicities of weights in irreducible and tensor product representations, (ii) the coefficients occurring in the Clebsch-Gordan series decomposition of Kronecker products with an arbitrary number of factors, (iii) the content of irreducible and tensor product representations of U(Σi Ni) with respect to representations of its direct product subgroup, U(N1)⊗U(N2)⊗…≡⊗i U(Ni), and (iv) the content of irreducible representations of U(NM) with respect to irreducible representations of U(N)⊗U(M). In particular, we exhibit formulas for (i), (ii), and (iii) containing only irreducible characters and Frobenius compound characters of the symmetric group. Under the application of an operator of the subgroup, ⊗i U(Ni) with Σi Ni < N, a vector in a representation of U(N) transforms as a linear combination of vectors in irreducible representations of the subgroup. We give formulas for determining the vectors occurring in such a linear combination. They are derived in a similar fashion to the formulas for (i), (ii), and (iii). In terms of weight diagrams, the formulas give the number of times a weight diagram of the subgroup's algebra occurs in the hyperplane generated by the application of the algebra to the weight of the U(N) vector in question.
Substitution Group and the Stretched Isoscalar Factors for the Group R5
Authors: Ališauskas S. J. , Jucys A. P.
Published: February 2004

The phase relations for basis functions and Clebsch-Gordan coefficients of the representations of the group R5 under the elements of the substitution group are given. The stretched isoscalar factors as well as the semistretched factors of the first kind are expressed in terms of the quantities of the theory of representations of SU2.
Relationships among Generalized Phase-Space Distributions
Authors: Summerfield G. C. , Zweifel P. F.
Published: February 2004

The generalized phase-space distributions, including the Wigner distribution, are presented in terms of expected values of generating operators. A generalization of the Weyl correspondence is obtained to provide expressions for generalized Wigner equivalents. Finally, rather simple relationships are obtained connecting the generalized phase-space distributions to the Wigner distribution; and similar relationships are obtained for the generalized Wigner equivalents. In particular, it appears that, among the class considered, there is no reason to use any distribution other than the Wigner for performing any calculations.
Symmetry of the Ground Level of a Hamiltonian
Authors: Kleiner W. H. , Kaplan T. A.
Published: February 2004

A general connection between nodelessness and symmetry of a function is pointed out. It is proved that a real nodeless energy eigenfunction with energy E has a nonzero part which also is an eigenfunction with energy E and which under coordinate transformations has the full symmetry of the Hamiltonian. This result can be applied to many systems of physical interest for which the ground-state energy eigenfunction is known from the nature of the Hamiltonian to be nodeless. Simple counterexamples are given however, to show that not all Hamiltonians have a nodeless ground-state energy eigenfunction.
Theory of the Propagation of the Plane-Wave Disturbances in a Distribution of Thermal Neutrons
Authors: Duderstadt James J.
Published: February 2004

The propagation of plane-wave disturbances in a neutron gas in thermal equilibrium with a moderator is studied using the linearized Boltzmann equation. The eigenvalue spectrum of the appropriate Boltzmann transport operator is investigated for both polycrystalline and noncrystalline media, and several necessary conditions for the existence of a point spectrum (and hence for the existence of plane-wave propagation) are discussed. Techniques are presented which allow the solution of various boundary-value problems using this spectral representation.
Invariants to All Orders in Classical Perturbation Theory
Authors: Coffey Timothy P.
Published: February 2004

The method of averaging is applied to systems having Hamiltonians of the form H=H0(J)+εH1(J,ψ,p,q),where H1 is periodic in each of the components of Ψ. When the system is nondegenerate it is shown that corresponding to each component of Ψ there is a quantity Ki which is invariant to all orders in ε. When the system has an m-fold degeneracy, somewhat weaker results are obtained. In this case it is shown that the Hamiltonian, when expressed in terms of the average variables, depends on the angle variables only through their m degenerate combinations. This is true to all orders in ε. Thus, if Ψ has s components there are s - m invariants provided that the average variables can be made canonical. However, the conditions under which degenerate perturbation theory can be made canonical are not known. The invariants which arise when the Hamiltonian has an adiabatic or a harmonic time dependence are also discussed. The techniques are applied to the simple case of a harmonic oscillator whose frequency varies slowly with time.
Isoperimetric Solutions Related to the Thermodynamics of Plasmas
Authors: Chen Robert L. W. , Neighbors Thomas H.
Published: February 2004

More solutions of isoperimetric problems are obtained which lead to several extensions and refinements of previous results in the thermodynamics of plasmas: (1) Energy requirement for density fluctuations in a relativistic plasma is determined. At the typical relativistic temperature of kT = mc2 it becomes ∼nkT(|Δn|¯/n)2 as compared with the previous nonrelativistic value of ∼35nkT(|Δn|¯/n)2. (2) An optimum expression for the free energy in a plasma is derived in terms of familiar thermodynamic variables. (3) For a collisional plasma, the energy requirement again assumes the same general form and is equal to 12nkT(|Δn|¯/n)2.
General Approach to Fractional Parentage Coefficients
Authors: Moshinsky M. , Devi V. Syamala
Published: February 2004

The purpose of this paper is to achieve a clearer understanding of the problems involved in the determination of a closed formula for fractional parentage coefficients (fpc). The connection between the fpc and one-block Wigner coefficients of a unitary group of dimension equal to that of the number of states is explicitly derived. Furthermore, these Wigner coefficients are decomposed into ones characterized by a canonical chain of subgroups (for which an explicit formula is given) and transformation brackets from the canonical to the physical chain. It is in the explicit and systematic determination of the states in the latter chain where the main difficulty appears. We fully analyze the case of the p shell to show that a complete nonorthonormal set of states in the physical chain U(3)⊃R(3) can be derived easily using Littlewood's procedure for the reduction of irreducible representations (IR) of SU(3) with respect to the subgroup R(3). This procedure gives a deeper understanding of the free exponent appearing in the polynomials in the creation operators defining the states in the U(3)⊃R(3) chain. As Littlewood's procedure applies to the U(n)⊃R(n) chain, and probably can be generalized to other noncanonical chains of groups, it opens the possibility of obtaining general closed formulas for the fpc in a nonorthonormal basis.
Frequency Spectrum and Momentum Autocorrelation Function for a Simple Lattice
Authors: Baroody E. M.
Published: February 2004

Calculations are made on the dynamics of a familiar lattice model: the simple cubic lattice with central and noncentral harmonic forces between nearest neighbors only. For the case of equal force constants, natural extensions are made of existing analytical approximations for the spectrum of squared frequency. The behavior of the spectrum near its singular points is described more accurately than before and expressions are derived which make it easy to obtain the density of modes at any frequency to about one part in a thousand. The new description of the spectrum is used to improve existing approximations for the classical momentum autocorrelation function for the infinite lattice ρ(τ), and for the function X3(τ′) used by Goodman in calculations on the response of surface atoms in a semi-infinite lattice. Good agreement with numerical results of Goodman for τ′ = 20, 25, and 30 is obtained. The results for the spectrum also apply to the density of states of electrons in a simple cubic lattice in the tight-binding approximation.
Projection of Exact Spin Eigenfunctions
Authors: Smith Vedene H. , Harris Frank E.
Published: February 2004

The relationships defining spin projectors are reviewed and the explicit formulations of the resulting spin-dependent (Sanibel) coefficients are shown to be consistent. Recurrence relations among Sanibel coefficients are derived. It is shown how the formal results here presented are useful in the calculation of matrix elements of spin-free and spin-dependent operators.