bluuebunny/crossref_metadata_2025 huggingface dataset:
Note on the Kerr Spinning-Particle Metric
Authors: Newman E. T. , Janis A. I.
Published: January 2005

It is shown that by means of a complex coordinate transformation performed on the monopole or Schwarzschild metric one obtains a new metric (first discovered by Kerr). It has been suggested that this metric be interpreted as that arising from a spinning particle. We wish to suggest a more complicated interpretation, namely that the metric has certain characteristics that correspond to a ring of mass that is rotating about its axis of symmetry. The argument for this interpretation comes from three separate places: (1) the metric appears to have the appropriate multipole structure when analyzed in the manner discussed in the previous paper, (2) in a covariantly defined flat space associated with the metric, the Riemann tensor has a circular singularity, (3) there exists a closely analogous solution of Maxwell's equations that has characteristics of a field due to a rotating ring of charge.
Metric of a Rotating, Charged Mass
Authors: Newman E. T. , Couch E. , Chinnapared K. , Exton A. , Prakash A. , Torrence R.
Published: January 2005

A new solution of the Einstein-Maxwell equations is presented. This solution has certain characteristics that correspond to a rotating ring of mass and charge.
Integrals of the Second-Order Linear Differential Equation
Authors: Kane J. , Surynarayan E. R.
Published: January 2005

In this study we describe procedures for the numerical solution of the second-order linear differential equation which have either continuous or discontinuous coefficients. Our motivation is a well-known technique in the theory of inhomogeneous transmission lines: the treatment of a continuously varying line by considering it to be comprised of various sections of uniform lines. Although this procedure is very suggestive physically, there are difficulties with its applications to second-order equations which do not describe wave propagation. First, the language of the circuit engineer is such that a pair of first-order equations describing some analogs of the complex quantities voltage and current seem to be required. Whereas these equations appear naturally in transmission line theory, we show that it is an unnecessary burden to find their counterparts when the problem is but to solve a second-order equation. The second objection to this approach is that it is not apparent that a piecewise constant partition of the coefficients in a differential equation will yield the rigorous solution if the subdivision is carried out to an arbitrary degree. Indeed, we show that the limit of the quantization scheme can not yield the rigorous solution. On the other hand, we are led to a well-defined technique which generates the solution by a method suggested by the procedures used in the discrete case. This enables the second-order equation to be solved rigorously by iteration with no complications, and in a form ideally suited for computer programs.
On the Quantum Field Theories Leading to the Corben Equations
Authors: Norton Richard E.
Published: January 2005

Formulations are presented for the second quantized versions of the field theories which lead to Corben's equations of motion. It is demonstrated that an indefinite metric is required to guarantee positive energies for all the particles, but that otherwise the theories are physically unambiguous. The number and properties of the resulting particles are studied and compared with the conclusions from previous work. Alternative formulations are also discussed.
Magnetic Properties of Charged Ideal Quantum Gases in n Dimensions
Authors: May Robert M.
Published: January 2005

We consider the mathematical model of an ideal gas of charged bosons or fermions in an n-dimensional space, treating n as a continuous variable. The investigation shows the extent to which the magnetic behavior depends on the dimensionality of the system. In particular, the charged Bose gas in a homogeneous magnetic field does not condense unless n > 4, in contrast to the field-free gas which condenses for n > 2: however so long as n > 2 and T < Tc this system completely expels homogeneous magnetic fields weaker than a certain critical field, Hc. (Tc is the field free transition temperature.) This field expulsion comes explicitly from the condensed ground-state bosons for n > 4; but it is still present, and Hc has the same form, for 4 > n > 2 where there is no condensation.
A Proof of Nakanishi's Inequality
Authors: Boyling J. B.
Published: January 2005

Nakanishi's conjectured inequality for the coefficients of the external masses and invariants in the Feynman denominators for scattering processes is proved by a determinantal method suggested by the analogy between Feynman diagrams and electrical networks.
A Covariant Theory of Relativistic Brownian Motion I. Local Equilibrium
Authors: Hakim Rémi
Published: January 2005

This paper is devoted to the study of some relativistic methods in statistical mechanics and their applications to the construction of a covariant theory of Brownian movement. In this work we deal only with times which are long compared with the relaxation time β−1. As a consequence of this covariant theory we derive relativistic Wiener integrals.
On the Solution of the BBGKY Equations for a Dense Classical Gas
Authors: Andrews Frank C.
Published: January 2005

Formal solutions of the BBGKY equations of classical statistical mechanics are obtained in the form of integral equations. This form makes it particularly straightforward to obtain the density corrections to the functional equation for f2 and to the evolution equation for f1. The physical implications of the derivation, in particular the validity of Bogoliubov's functional hypothesis, are discussed in detail.
Hydromagnetic Switch-on Shocks
Authors: Sarason Leonard
Published: January 2005

In one-dimensional hydromagnetic flow, switch-on shocks have been shown to be nonevolutionary, e.g., by Syrovatskii. Such shocks, however, may be considered as a superposition of a switch-on shock and an Alfvén shock, and in this paper some results of such an assumption are examined. If the two shocks remain superimposed, the shock pair is, in fact, evolutionary. If the pair splits under the influence of incoming waves, a first-order nonlinear analysis indicates that highly unstable situations can occur. But there is a non-uniqueness implicit in the ansätz, and the author has not been able to exclude the possibility that a solution always exists which is stable except between shocks.
Inequalities for the Solutions of Linear Integral Equations
Authors: Balachandran A. P.
Published: January 2005

Inequalities are derived for the solutions of linear integral equations of a certain class in terms of their inhomogeneous terms and kernels. The construction of these inequalities appears to be very simple in practice as it involves only quadratures. The results presented here are, therefore, expected to be useful in the investigation of physical problems.
S-Matrix Theory and Double Scattering
Authors: Iagolnitzer Daniel
Published: January 2005

In the double scattering case, we show that the introduction of a pole in the S-matrix elements, is consistent with a description in terms of successive interactions.

We then show that among Olive's class of possible ``propagators'' c(k2 - m2 + iε)−1 - (1 - c) ·(k2 - m2 - iε)−1, only the usual value c = 1 gives a consistent result.
Time-Dependent Perturbation Theory
Authors: Hammer C. L. , Weber T. A.
Published: January 2005

A time-dependent perturbation theory which is based upon the U-matrix approach is presented using the interaction e-αt(1 + e-βt)−1V(x) with β real, α complex and β > Re α > 0. Thus the adiabatic or time-independent approximation (β → 0) and the sudden approximation (β → ∞) can be obtained using just one formalism. The usual series for the U matrix is derived and shown to converge for a semi infinite range if the interaction is of the form |t|-δ, δ > 1, for large times t. Two interesting results are (1) The derivation of the ``golden rule'' from the discrete-state time-dependent perturbation theory presented in most text books of quantum mechanics leads to erroneous physical interpretations because the energy-level shift is ignored. (2) When considering scattering between states in the continuum, it is found that a characteristic feature of time-dependent interactions is a discrete momentum spectrum of final states which, in the relativistic case, leads to a mass spectrum. These spectra cannot be obtained using the S matrix.
Crossing Symmetric Regge Representation for the Invariant Scattering Amplitude
Authors: Rothe Heinz J.
Published: January 2005

A crossing symmetric Regge representation for the invariant scattering amplitude is constructed which simultaneously exhibits all Regge poles in the three channels. It is assumed that the amplitude satisfies the Mandelstam representation, and that the usual Mandelstam-Sommerfeld-Watson transform exists. To achieve explicit crossing symmetry it is found necessary to work with the Legendre function of the second kind. Except for neglecting the influence of possible angular momentum cuts, the representation is exact for all s, t, and u, with no restriction on the location of the Regge poles. As an illustration of how it might be used in practice, the Chew-Jones formula for the amplitude of definite signature is derived in the strip approximation.
Correlation Functions and the Coexistence of Phases
Authors: Fisher Michael E.
Published: January 2005

We discuss the existence, continuity and other properties of the canonical and grand canonical many-particle correlation functions ns(r1, … rs) in the thermodynamic limit of classical and quantum mechanical systems.

If the pressure of the system for fixed T is constant in the range of specific volume va to vb, one expects physically to observe the coexistence of two separated phases. In terms of the correlation functions this is expressed by ns(v)=xa(va/v)ns(va)+xb(vb/v)ns(vb),where x and xb are the mole fractions of the phases so that v = xava + xbvb. With the aid of various lemmas on convex functions we prove that such a ``separation of the phases'' follows rigorously from statistical mechanics provided the correlation functions are ``well defined'' in an appropriate sense.
Higher-Dimensional Periodic Systems
Authors: Chambers Charles M.
Published: January 2005

This short note describes a technique which is useful for solving higher-dimensional periodic systems in which a large amount of homogeneity and symmetry is absent.
Rotationally-Symmetric Model Field Theories
Authors: Klauder John R.
Published: January 2005

A class of highly symmetric ,nonrelativistic, Euclidean invariant, model scalar field theories are examined assuming the existence of field and momentum operators that satisfy the canonical commutation relations (CCR). The high degree of symmetry that we assume permits explicit determination of every relevant CCR representation. These consist of a two-parameter family of unitarily inequivalent representations, some of which are irreducible while the others are reducible. It is demonstrated that only those models that are analogs of the free field can be encompassed within the irreducible representations. Hence every model with interaction—including an analog of the relativistic λφ4 theory—requires a reducible CCR representation. For the reducible representations, we determine every relevant Hamiltonian operator possessing the required high degree of symmetry. These Hamiltonians, as well as the generators of space translations, cannot be expressed (solely) as functions of the field and momentum operators, which is characteristic of any system with a unique ground state and reducible CCR representation. Nevertheless, it is demonstrated that these Hamiltonians, as well as the generators of space translations, fulfill the ``weak correspondence principle,'' in which the expectation value of a quantum generator, such as the Hamiltonian operator, in a suitably labeled overcomplete family of states is identified with the associated classical generator, such as the classical Hamiltonian. Our principal results depend on the existence and make extensive use of the countably infinite number of degrees of freedom existing in a field theory. Entirely analogous results apply to related models defined in a finite spacial volume since they still have an infinite number of degrees of freedom.
Contributions to the Quantization Problem in General Relativity
Authors: Boardman John
Published: January 2005

It is possible to quantize most classical field theories by identifying the group of canonical transformations which maintain the covariance properties with a group of unitary transformation in Hilbert space which has the same commutator algebra. The commutators among the canonical field variables are equal to the Dirac delta function times a factor which may be zero. But in the general theory of relativity the classical group of the canonical transformations which maintain the covariance properties of the theory has an invariance subgroup. The ambiguities thus introduced by the usual process of quantization can be avoided by the use of the Dirac quantization procedure for theories with constraints. We establish an analogy between classical Dirac brackets and commutators, and fix an intrinsic coordinate system. This choice of local intrinsic coordinate conditions leads to commutators among the canonical field variables of the general theory of relativity which depend upon the Dirac delta function and its first seven derivatives.
On the Complete Unitarity Equations for Pion-Pion Scattering
Authors: Broido Michael M.
Published: January 2005

The off-the-mass-shell equations for pion-pion scattering in the lowest approximation of the complete unitarity formalism of Taylor are discussed. It is shown that if the vertex-function renormalization constant is taken to be zero, the equations have no (nonzero) solution. These equations are equivalent to certain bootstrap equations, which thus also have no solution. Both systems are discussed in the case where the renormalization constant is not put equal to zero.
Perturbation Expansion for Lattice Thermal Conductivity
Authors: Hardy Robert J. , Swenson Robert J. , Schieve William C.
Published: January 2005

A method is given for obtaining a perturbation expansion for the correlation function formula for thermal conductivity. The problem is reduced to the determination of the matrix elements of the products of resolvent operators Xll′ and Yll′ to different orders in the perturbation λH′. The coefficients in the general equations for Xll′ and Yll′ derived by Van Hove, Janner, and Swenson are iterated, and the resulting approximate equations are used to deduce the formulas for the contributions to the lattice thermal conductivity proportional to λ−2 (lowest order) and to λ−1.
Solution of an Integral Equation in V — θ Scattering
Authors: Kazes E.
Published: January 2005

The Muskhelishvili method is used to obtain the off-the-mass- shell V — θ scattering amplitude.
Observations on the Spherical Model of a Ferromagnet
Authors: Yan C. C. , Wannier G. H.
Published: January 2005

A discrepancy between the methods of the grand and the canonical ensemble which arose in the study of the spherical model of a ferromagnet even for properties of individual spins is traced to an incorrect order of taking limits. The spin system must be considered for a small but not vanishing field first, and the limit of zero field must only be taken after the limit of an infinite number of particles has been taken. For this case no discrepancy between the two ensembles arises. A calculation proceeding entirely at zero field cannot be considered as logically admissible; discrepancies arising in this case are thus of no physical consequence.
Wave Scattering and the Geometry of a Strip
Authors: Myers John M.
Published: January 2005

A new method is introduced to find properties of wave and other fields. The relationship between the geometry of the strip and the symmetry of the Helmholtz equation is shown and leads to previously undiscovered properties of the field. The field pattern of the strip is shown to have a particularly simple form and, moreover, to be completely determined by symmetry-like principles.
A Relation between the Hydrogen Atom and Multidimensional Harmonic Oscillators
Authors: Bergmann D. , Frishman Y.
Published: January 2005

A simple connection between the radial Schrödinger equation for the bound states of a hydrogen atom with angular momentum l and that of an isotropic harmonic oscillator of even dimension from 2 to 4l + 4 is noted. The case of highest dimensionality 4l + 4 is shown to lead in a very simple way to the energy levels and degeneracies of the hydrogen atom, once the energy levels of a one-dimensional harmonic oscillator are known.
Cartesian Tensors in Spaces with an Indefinite Metric with Applications to Relativity
Authors: Foldy Leslie L.
Published: January 2005

A new formalism for dealing with Cartesian tensor analysis in flat spaces with an indefinite metric with the same ease as in Euclidean spaces is introduced. It avoids the necessity of distinguishing covariant and contravariant indices and the consequent use of the metric tensor in raising and lowering indices; neither does it require the introduction of imaginary coordinates and components of tensors. It is based on the use of a modified Einstein summation convention combined with a modified differentiation with respect to tensor components in such a way that all formal manipulations are essentially identical with those employed in Cartesian tensor analysis in Euclidean spaces. The further introduction of a modified matrix multiplication and a modified definition of a determinant serves to round out the formal analogy with the Euclidean space. The convenience, simplicity, and typographical economy of the new formalism is illustrated by examples drawn from special relativity. The formalism can be trivially generalized to complex linear vector spaces with an indefinite metric.
Thermodynamic Evolution Equation for a Quantum Statistical Gas
Authors: Fujita S.
Published: January 2005

It is shown by a perturbation diagram method that partial Green's functions satisfy closed evolution equations exact in the thermodynamic limit except for the neglect of the contribution of initial particle correlations. This contribution is negligible for a system at a time t ≫ τc (average collision duration) when the main interaction processes are localized in space and time. In particular this makes unnecessary the often imposed assumption of the absence of initial particle correlations for the derivation of the usual Boltzmann equation or its generalizations.
An Exactly Soluble Model Showing Ferromagnetism
Authors: Katsura Shigetoshi , Inawashiro Sakari
Published: January 2005

A Hamiltonian of a one-dimensional Heisenberg model with ferromagnetic interaction is expressed in terms of fermion operators, and renormalized linked cluster expansion has been carried out. It is shown that the approximation leads to ferromagnetic behaviors similar to the molecular field approximation. A model for which the second- and higher-order terms vanish is presented and regarded as an example of quantum-mechanical systems that shows ferromagnetism rigorously. It is also noted that the model is very much like the Husimi-Temperley model or the van der Waals gas with respect to a long-range character of interaction and the vanishing of higher-order terms.
On Expanding the Exponential
Authors: Kumar Kailash
Published: January 2005

Systematic methods for generating various expansions of the function exp (a + λb)t, of noncommuting operators a and b, are presented. The usual perturbation expansion in powers of λ, and several other formulas found in the earlier literature occur as special cases. Brief remarks about relative merits and physical applications are made.
Generalized Solutions for Massless Free Fields and Consequent Generalized Conservation Laws
Authors: O'Connell R. F. , Tompkins D. R.
Published: January 2005

Generalized solutions to the equations for a massless free field with arbitrary spin are written down. It is shown that they lead immediately to generalizations of all the usual conservation laws.
Critical Störmer Conditions in Quadrupole and Double Ring-Current Fields
Authors: Urban Eugene W.
Published: January 2005

A theoretical study has been made of the behavior of the critical Störmer pass points for general axially symmetric magnetic configurations. A topological method has been derived to predict the occurrence of the critical Störmer conditions for charged-particle exclusion. This analytic technique, when applied to geomagnetically interesting fields, should be a useful aid to the understanding of experimental data. The method is applied here to three magnetic geometries: double ring currents with parallel dipole moments and with antiparallel dipole moments, and the axial magnetic quadrupole. The topology of the regions representing allowed motion is treated systematically and the behavior of the critical pass points is illustrated in typical Störmer plots. For the quadrupole and the antiparallel ring system critical pass points are found to occur only out of the equatorial plane. For the parallel ring system, critical points can occur in or out of the equatorial plane. For certain special conditions as many as three simultaneous critical pass points are found, and two simultaneous points occur for a wide range of parameters.
Cluster-Star Inversion by Means of Generating Functionals
Authors: Stell G.
Published: January 2005

The cluster-star equations are inverted. These equations, Eq. (2.1), define a set of cluster functions Um in terms of star functions Vn for 2 ≤ n ≤ m. The inversion, Eq. (2.2) gives the Vn in terms of the Um; 2 ≤ m ≤ n.

The cluster-star inversion yields the coefficients βn that appear in the number-density expansion of the logarithm of the grand partition function Ξ of a statistical mechanical system in terms of the coefficients bn that appear in its fugacity expansion, even when the system is in the presence of an external field.

In the course of obtaining the inversion, an expression for the work necessary to bring a particle from infinity to a point r inside a classical system at equilibrium is obtained in terms of the Vm and the one-particle distribution function ρ(r), and also in terms of the Um and ρ. The expression in terms of the Vm and ρ has been previously derived by others with restrictions on the form of the potential energy; the alternative expression in terms of the Um seems to be new.

Operators with essentially the same algebraic structure as the Vm appear in a recently considered asymptotic expansion of the distribution functions of a nonequilibrium system. The cluster-star inversion facilitates the determination of these operators in terms of the solution operators of the n-body Liouville equation, n ≥ 2.
Trace Formalism for Quantum Mechanical Expectation Values
Authors: Langerholc John
Published: January 2005

The trace of a positive bounded operator in a Hilbert space is defined and shown to be independent of the basis used in the definition. The trace of the product WA is defined for bounded A and positive bounded W with unit trace and is also shown to be basis-invariant. An integral representation is derived and used to define Tr(WA) for unbounded A. Linearity, isotony, and continuity with respect to uniform covergence are proved for Tr(WA) as a function of (bounded) A. Several formulas used in statistical mechanics are derived, and it is proved that if A and B are commuting positive operators, then Tr(W(A + B)) = Tr(WA) + Tr(WB). A counter example is given which shows that the commonly used definition of Tr(WA) in terms of an orthonormal basis is not invariant under permutation of the basis vectors even in the case of a very simple unbounded operator A.

An expectation-value function M which associates the expectation value M(A) to the operator A is assumed given and subject to certain restrictions. For bounded operators, these include positivity, normalization, additivity, and a condition which may be considered as a requirement of regularity for the probability function induced by M. Modifications of these requirements are imposed for unbounded operators, and von Neumann's statistical formula is proved: there is a unique bounded positive operator W with unit trace for which M(A) = Tr(WA). The requirements placed on M are weaker than those of von Neumann, and are in fact satisfied by Tr(WA) as a function of A.
Can the Position Variable be a Canonical Coordinate in a Relativistic Many-Particle Theory?
Authors: Kerner Edward H.
Published: January 2005

The time-symmetrical interaction of charges (Wheeler-Feynman electrodynamics) is shown in principle to yield second-order Newtonian-type equations of motion under the restriction that the motions be analytic extensions of free-particle motions. The means for explicitly generating the electrodynamic equations of motion describing invariant world-lines are given. These physically relevant equations do not fit into Dirac's (1949) formulation of Hamiltonian relativistic particle dynamics, where either world-line invariance is given up, or only trivially straight world lines can be described (``zero-interaction theorem'' of Currie, Jordan, Sudarshan, 1963). The misfit is due to the requirement in Dirac's scheme that position x be canonical. Under the Lie-Königs theorem, however, Hamiltonian statements of dynamics with invariant world lines remain possible when suitable Q(x, ẋ) are introduced instead of x as canonical position variables. A group of necessary conditions on the structure of any dynamics that permits x to be canonical are worked out to indicate how stringent is this permission in general.
Scattering of Surface Waves by a Submerged Circular Cylinder
Authors: Levine Harold
Published: January 2005

The effect of a rigid circular cylinder, wholly immersed within and lying parallel to the free surface of an incompressible and inviscid fluid, on straight-crested surface waves passing overhead is investigated. A mode of analysis is developed, on the hypotheses of small amplitude and time-periodic fluid motions, that encompasses all directions of incidence of the primary wave; and is used to extend results previously obtained in the case of normal incidence. It is shown, in particular, that the absence of surface-wave reflection at normal incidence gives way to a partial reflection for other primary directions, which in turn verges on completeness as the direction of the incoming wave becomes more closely aligned with that of the cylinder axis.
Homogeneous Solutions of the Einstein-Maxwell Equations
Authors: Ozsváth István
Published: January 2005

In this paper the solutions of the Einstein-Maxwell equations are investigated under the assumption that the metric of the space-time and the electromagnetic field are invariant under the transformations of a four-parametric, simply transitive group.

The results can be summarized as follows: In the case of null electromagnetic fields there are two different possibilities; If Λ = 0, all the solutions are Robinson waves; if Λ ≠ 0, there exists only one solution, first given here by (6.26). There exist no other solutions for null electromagnetic fields. In the case of nonnull electromagnetic fields two solutions are found. One metric is known having been first given by Robinson; we give a new solution of type I. The question as to whether there are solutions different from these remains open.
Particlelike Solutions to Nonlinear Scalar Wave Theories
Authors: Rosen Gerald
Published: January 2005

According to a recent theorem proved by Derrick, no absolutely stable time-independent particle-like solution of finite energy is obtainable from a large class of Lorentz-covariant scalar wave theories. We study a solvable nonlinear scalar wave theory and derive a rigorous metastable particlelike solution of finite energy, a quasistatic solution having a rate of dissolution which is free to be arbitrarily small relative to the associated particle rest mass. Derrick's theorem notwithstanding, the specific example presented here suggests that particlelike quasistatic solutions to a nonlinear scalar wave theory may still be of some relevancy to meson field physics, where no absolutely stable but instead metastable elementary particles are present.
Studies in Perturbation Theory. IX. Connection Between Various Approaches in the Recent Development—Evaluation of Upper Bounds to Energy Eigenvalues in Schrödinger's Perturbation Theory
Authors: Löwdin Per-Olov
Published: January 2005

The treatment of Schrödinger's perturbation theory based on the use of a series of inhomogeneous differential equations of iterative character is briefly surveyed. As an illustration, the method is used to derive the general expression for the expectation value of the Hamiltonian to any order which provides an upper bound for the ground-state energy. It is indicated how the well-known theory for inhomogeneous equations may be utilized also in this special case.

The solution of the Schrödinger equation by means of the partitioning technique and the concept of reduced resolvents is then treated. It is shown that the expressions obtained are most conveniently interpreted in terms of inhomogeneous differential equations. A study of the connection with the first approach reveals that the two methods are essentially equivalent, but also that the use of reduced resolvents and inverse operators may give an alternative insight in the mathematical structure of perturbation theory, particularly with respect to the ``bracketing theorem'' and the use of power series expansions with a remainder. In conclusion, it is emphasized that the combined use of the two methods provides a simpler and more powerful tool than any one of them taken separately.
On the Possibility of Relating Internal Symmetries and Lorentz Invariance
Authors: Itzykson Claude
Published: January 2005

In this note we investigate the possibility that the inhomogeneous Lorentz group is only a subgroup of a larger Lie group G of symmetries for strong interaction physics. The discussion is restricted to the Lie algebra ℒ of G. We make the assumption that the remaining generators Ai of G commute with the generators of translations Pλ which build the ideal ℐ in ℒ. It is then shown that the Ai generate an ideal in ℒ modulo ℐ. If this ideal is semi-simple then ℒ breaks up in a direct sum ℒ = 𝒫 ⊕ 𝒶, where 𝒫 is isomorphic with the Lie algebra of the inhomogeneous Lorentz group and 𝒶 is semisimple.
Backward Superconducting Switching
Authors: Cohen Hirsh , Odeh Farouk
Published: January 2005

A discussion is given of the initial speeds at which superconducting material changes state according to the London electrody namics. These transitions are taken to occur in the form of phase boundary motions. Phase changes from the normal to the superconducting state and vice versa are considered for the cases in which the external magnetic field is radiated to the boundary of the superconducting material. A distinct difference is found in transition rates depending on whether the transition is from the superconducting or from the normal state. In another case considered, the transition from normal to super is studied when the superconducting material is bounded by a good conductor. In all cases, constant critical field is taken as the switching criterion. The mathematical treatment involves the approximate solution of free boundary problems and mixed hyperbolic—parabolic boundary value problems.
Interacting Fermions in One Dimension. II. Attractive Potential
Authors: McGuire J. B.
Published: January 2005

The exact energies and wavefunctions for a system of (N − 1) one-dimensional fermions all of the same spin and one fermion of the opposite spin are calculated in the large volume, finite density limit, when the particles interact via an attractive delta function potential. It is found that the attractive potential gives rise to a bound state, but, in spite of the presence of this bound state, all of the physical properties which are calculated (ground-state energy, effective mass of a certain class of excitations, etc.) are analytic continuations in the coupling constant of the corresponding results in the repulsive case. In addition, it is possible to have eigenstates which do not have the bound state present. These excited states are also discussed and are found to exhibit a negative effective mass and to modify the particle density at very large distances from the different particle.
Complex Space-Time and Geometrization of Electromagnetism. III
Authors: Das A.
Published: January 2005

It is shown here that if we demand the covariance under general circular transformations (rotations in complex planes), the electromagnetic potentials can be geometrized as the affine connections necessary for such covariance. The geodesic hypothesis yields the Lorentz equation of motion with an interesting correction term.
Variation of Green's Functions
Authors: Devooght J.
Published: January 2005

The variation of the Green's function of a linear differential operator is computed as the variation of an n-tuple integral with variable boundary. This generalization of Hadamard formula is shown to lead naturally to the method of ``invariant imbedding'' of R. Bellman. Three applications of the general formalism are given: the Dirichlet problem, the neutron or photon transport in a plane parallel anisotropically scattering slab, and scattering in a central field where three identities used in potential scattering are shown to be a consequence of the invariance of the asymptotic Green's function.
On the Dimer Solution of Planar Ising Models
Authors: Fisher Michael E.
Published: January 2005

Derivations of the partition function of the Ising model on a general planar lattice L, which proceed via an associated dimer problem and use Pfaffians, are simplified by constructing a lattice LΔ (the ``terminal lattice'' derived from an ``expanded lattice'' of L) for which (A) the allowed dimer configurations are in one-one correspondence with allowed Ising polygon configurations on L, and which (B) is planar if L is planar so that Kasteleyn's theorem may be used directly to construct the appropriate Pfaffian. This is in contrast to previous use of nonplanar associated dimer lattices for which the correspondence is not one-one, so that is has been necessary to prove a somewhat obscure ``cancellation theorem.''
High-Energy Behavior of Feynman Integrals with Spin. I
Authors: Greenman J. V.
Published: January 2005

A method of determining the leading behavior of planar graphs for two-body processes in a spin-½-spin-1 conserved vector current theory is outlined. The leading behavior can be found by inspection. Coefficients of lower-order terms can be found explicitly. In a later paper we hope to use our methods together with analysis of nonplanar graphs to justify the Reggeization hypothesis in nth order.
Scattering Cross Section for a Beam of Wave Packets
Authors: Katz Amnon
Published: January 2005

The scattering cross section is evaluated for a beam of wave packets of almost arbitrary form. It is found that this cross section is the superposition of the cross sections of various plane waves, which make up the wave packet without interference. For wave packets of well-defined momentum, the usual rule that the scattering cross section is the absolute square of the scattering amplitude is regained.
Classification of Irreducible Unitary Representations of Compact Simple Lie Groups. I
Authors: Mehta M. L.
Published: January 2005

An irreducible unitary representation of any group belongs to one of the three Wigner classes, potentially real, pseudo-real, or complex. The irreducible unitary representations of all the compact simple Lie groups except those of the type E are hereby classified. The similar classification for the simple groups E6, E7, and E8 is completed in the next paper.
Discrete Degenerate Representations of Noncompact Rotation Groups. I
Authors: Raczka R. , Limić N. , Niederle J.
Published: January 2005

The discrete most degenerate principal series of irreducible Hermitian representations of the Lie algebra of an arbitrary noncompact as well as compact rotation group SO(p, q) are derived. The properties of these representations are discussed and the explicit form of the corresponding harmonic functions is given.
The Momentum Autocorrelation Function in a Bernoulli Chain
Authors: Rubin Robert J. , Ullersma Pieter
Published: January 2005

This paper is devoted to the study of the statistical dynamics of the small amplitude coplanar vibrations of a compound pendulum consisting of N + 1 particles suspended in series by weightless strings in a gravitational field. All particles have the same mass m, except for the top particle whose mass is m(1 + 𝒬); and all strings are of equal length. The behavior of this system in the limit in which N → ∞ is of particular interest, because the maximum normal mode frequency is proportional to N½. In the limit N → ∞, asymptotic formulas with error estimates are obtained for the time dependence of the momentum autocorrelation function of: (1) the top particle when 𝒬 = 0; (2) the bottom particle when 𝒬 = 0; and (3) the top particle when N ≫ 𝒬 ≫ 1.
Relativistic Effects in Atomic Fine Structure
Authors: Armstrong Lloyd
Published: January 2005

Operators are obtained which can be evaluated with respect to nonrelativistic wavefunctions to produce the same result as obtained by evaluating the Breit equation with respect to relativistic wavefunctions. This greatly simplifies calculations involving the Breit equation by allowing the calculations to be made within the more familiar framework of nonrelativistic theory. The operators are classified according to their angular dependence; a comparison with the angular dependence of each fine-structure operator leads to the relativistic equivalents of the fine-structure interactions. The operators are expanded in a power series in (v/c)2, and the lowest nonvanishing terms are shown to be the fine-structure interactions.
Unitary and Antiunitary Ray Representations of the Product of n Commuting Parity Operators
Authors: Barut A. O. , Komy S.
Published: January 2005

The unitary and antiunitary ray representations of the group of n commuting operators Γi, i = 1, 2, …, n, satisfying Γi2 = 1, ΓiΓj = ΓjΓi, have been determined explicitly. The ray representations are shown to be homomorphic to the representations of a class of generalized Clifford algebras defined in the text. The enumeration of different algebras gives a complete classification of inequivalent ray representations. Whereas the irreducible vector representations of the group are all one-dimensional, the irreducible ray representations lead to various multiplet structure of states ranging in dimensions from 1 to 2½n (n even), or 2½(n−1) (n odd), in powers of two. The arbitrary antiunitary case can be reduced to the case with only one antiunitary Γ.
On Irreducible Representation of a Class of Algebras and Related Projective Representations
Authors: Barut A. O.
Published: January 2005

The number and the dimensions of irreducible representations of a general class of algebras occurring in the projective representations of finite groups have been determined. The Lie subalgebras have been found, and the isomorphism between the quantum-mechanical ray representations of finite groups and the fundamental representations of Lie algebras is shown.
A Manifestly Covariant Description of Arbitrary Dynamical Variables in Relativistic Quantum Mechanics
Authors: Fleming Gordon N.
Published: January 2005

The concepts of instantaneous observables and dynamical variables are analyzed and generalized to arbitrary spacelike hyperplanes. A formalism is developed which gives the basic equations of relativistic quantum mechanics for dynamical variables on arbitrary hyperplanes a manifestly covariant form. A covariant linear transformation on the Poincaré generators introduces the hyperplane generators which yield commutation relations displaying a clear separation of the kinematical and dynamical properties of dynamical variables. An axiomatic study of the center-of-mass position operator yields the uniqueness of the operator and completes the physical interpretation of the hyperplane generators. The Poincaré invariance and hyperplane independence of the scattering operator is related to asymptotic conservation laws in the hyperplane formalism, and finally, a nonlocal, hyperplane-dependent, field theory of free spinless particles is considered.
A Theorem on Peratization of Singular Potentials and Other Miscellanea
Authors: Spector Richard M.
Published: January 2005

It is proved for potentials of the form V(r) = A(r)/rn (n > 3) [with A(r) more singular at r = 0 than r(dA/dr), or apporaching zero less rapidly] that the peratized scattering length can be written down immediately in known form. The distrinction between regularization and peratization is made clear, and a common conjecture about the g (coupling constant) behavior of the peratized scattering length is disproved by a counter example. Finally, various mistakes in the literature are corrected.
Singular Solutions of Certain Integral Equations
Authors: Case K. M.
Published: January 2005

A class of integral equations arising in some idealized plasma problems is discussed. While these do not have solutions in the space of square-integrable functions, they do have such in an appropriate space of generalized functions. Explicit solutions are given in some special cases. It is then shown how these solutions can be used to approximate those for more general problems.
The Time-Dependent Green's Function for Electromagnetic Waves in Moving Simple Media
Authors: Compton R. T.
Published: January 2005

This paper treats the problem of radiation from sources of arbitrary time dependence in a moving medium. The medium is assumed to be lossless, with permittivity ε and permeability μ, and to move with constant velocity v̄ with respect to a given inertial reference frame xyz. It is shown how the Maxwell-Minkowski equations for the electromagnetic fields in the moving medium can be integrated by means of a pair of vector and scalar potential functions analogous to those commonly used with stationary media. The wave equation associated with these potential functions is derived, and a scalar Green's function is defined to satisfy the same type of equation, with a delta-function source term δ(r − r′) δ(t − t′), and the casuality condition. The solution for the Green's function is derived in closed form, by means of a Fourier integral method. The resulting Green's function is useful not only for calculating the fields from arbitrary sources in moving media, but also for its pedagogical value. It is simpler to understand the phenomenon of Cerenkov radiation using this method than it is from the conventional approach to the Cerenkov problem.
Algebraic Aspects of Regge Recurrences
Authors: Gotsman E. , Ne'eman Y.
Published: January 2005

The algebraic structure of Regge recurrences is examined, and its relation to symmetry schemes underlying various models is established. The relationship between the Spectrum Generating Algebras (SGA) and the noncompact subalgebras of the rotational states are discussed for the Coulomb potential, the three-dimensional oscillator, the signature which appears in exchange potentials, as well as the U(6, 6) and the other suggested SGA of hadron physics.
Asymptotic Expansions of the Dirac Density Matrix
Authors: Grover Richard
Published: January 2005

Asymptotic expansions are derived for the density operator ρN(x′, x)= ∑ n=1Nψn(x′)ψn(x)for small and large values of the relative distance x′ − x with a WKB expansion for bound-state wavefunctions in a plane, one-dimensional potential. In addition to some previously obtained corrections, the particle-density expansion includes a number of steady and oscillating correction terms to the zero-order Thomas-Fermi density which are related to the more recently derived corrections of Payne and of Kohn and Sham. A convenient and accurate approximation to the density operator for all arguments is also obtained from the first two terms of the expansion for large relative distances. The expansions become inadequate in the vicinity of the classical turning point of the highest energy state, as illustrated by numerical comparisons with the exact-density operator for the quadratic potential. A novel method is described for summing a finite series of oscillating terms such as occur in the density operator.
Representations of the Homogeneous Galilei Group in a Spherical Basis and the Asymptotic Behavior of Relativistic Special Functions
Authors: Voisin Jacques
Published: January 2005

The irreducible unitary representations of the Galilei group Gh are obtained in the base |lm〉 from their expression in the base |q〉 (Mackey's representation). The faithful representations are then considered as asymptotic expressions for the representation matrices of the principal series of the Lorentz group.
Drum Shapes and Isospectral Graphs
Authors: Baker George A.
Published: January 2005

We analyze the discrete drum model of Fisher and show that the information on the shape of a smooth drum contained in its low-order spectral moments is, at best, the area, length of its boundary, and number and type of corners. We produce a counter example which proves that one cannot always hear the shape of a discrete drum.
Statistical Mechanics of Finite Systems: Asymptotic Expansions. I. Two Petit Canonical Ensembles—(N, V, T) and (N, p, T) Systems
Authors: Horwitz G.
Published: January 2005

The statistical mechanics of a finite system differs from that of an infinite system in details of calculation, possession of additional variables and modification of fundamental relations, i.e., altered thermodynamics. Results become size-dependent, and ensemble-dependent. As examples of the general situation for finite systems, two petit canonical ensembles are examined here in relation to the grand canonical ensemble. The full asymptotic expansion is obtained for a one-phase region of one-component systems for each ensemble; all terms can be calculated within a grand canonical ensemble formalism. An analysis is made of both size dependence and the modified thermodynamics resulting from various approximations. The method presented represents both an approach to the study the general problems of the statical mechanical treatment of finite systems as well as a practical device for calculation in particular problems of small systems.
A Class of Sum Rules with Application to Nondegenerate Perturbation Theory
Authors: Landsberg P. T. , Morgan D. J.
Published: January 2005

The main results of this paper are: (1) The derivation of a class of sum rules. These rules are then applied to operators H(α), which depend on a parameter α and have eigenvalues En(α). Writing An(α) ≡ H(α) − En(α), these rules give the matrix elements of ∂NAn(α)/∂αN with respect to the eigenfunctions of H(α) in terms of matrix elements of lower derivatives and the eigenvalues En(α). (2) An explicit series expression for the Nth-order eigenvalue correction, due to a perturbation, directly in terms of the unperturbed eigenfunctions and eigenvalues. This expression seems a convenient one to use, since it does not involve eigenfunction corrections. An expression is also obtained for the eigenfunction corrections, but this is in less convenient form.
Nonlinear Theory of Elastic Surfaces
Authors: Cohen H. , DeSilva C. N.
Published: January 2005

The present paper develops a nonlinear theory for the deformation of an elastic surface by assuming the existence of a strain energy function and postulating a principle of virtual work which governs its mechanical behavior. By considering the strain energy function to depend on the first- and second-order deformation gradients, the field equations and the general constitutive relations are obtained. In addition to the conventional couple stresses, there are shown to exist energetically undetermined double stresses without moment.