bluuebunny/crossref_metadata_2025 huggingface dataset:
Canonical transforms. II. Complex radial transforms
Authors: Wolf Kurt Bernardo
Published: February 2004

Continuing the line of development of Paper I [J. Math. Phys. 15, 1295 (1974)], we enlarge the concept of canonical transformations in quantum mechanics in two directions: first, by allowing the definition of a canonical transformation to be made through the preservation of an so(2,1) algebra, rather than the usual Heisenberg algebra, and providing the bridge between the classical and quantum mechanical descriptions, and, second, through the complexification of the transformation group. In this paper we study specifically the transformations which can be interpreted as the radial part of n-dimensional complex linear transformations in Paper I. We show that we can build Hilbert spaces of analytic functions with a scalar product defined through integration over half the complex plane of a variable which has the meaning of a complex radius. A unitary mapping to the ordinary Hilbert space Lrn−12(0,∞) is provided with a kernel involving a Bessel function. Special cases of this are shown to be the Barut-Girardello, one-dimensional Bargmann and Hankel transforms. The transform kernels provide a series of representations of a subsemigroup of SL(2,C) and allow the construction of coherent states for the harmonic oscillator with an extra centrifugal force. We present a hyperdifferential operator realization of these transforms which yields new Baker-Campbell-Hausdorff and special function relations.
Green's function for Laplace's equation in an infinite cylindrical cell
Authors: Peskoff A.
Published: February 2004

The Green's function for Laplace's equation in an infinite-length cylinder with a homogeneous mixed boundary condition is considered. Its eigenfunction expansion converges slowly when the axial separation between the source and observation points is small compared to the cylinder radius, and diverges when the axial separation is zero. Applying a modified form of a contour integral method of Watson to an integral representation of the Green's function, a more general expansion of the Green's function is derived. Watson's original method had previously been applied to the case when the source and observation points were both on the axis of the cylinder. The expansion contains a free parameter which may be adjusted to give rapid convergence for any axial separation. It fails, however, when the source and observation points are both near the surface of the cylinder. For two special values of the parameter, the general expansion reduces to the eigenfunction expansion or to the integral representation. The derivation is somewhat obscure, but the resulting formula has a simple interpretation as the superposition of the potential of two related boundary value problems in finite-length cylinders. Some numerical results are given in the spatial region which previously could not be calculated, for a boundary condition approaching a homogeneous Neumann condition, and for a homogeneous Dirichlet condition.
Effects of long range interactions in harmonically coupled systems. I. Equilibrium fluctuations and diffusion
Authors: Phillipson Paul E.
Published: February 2004

Systems of harmonically coupled identical particles at thermal equilibrium provide dynamical models for studies of diffusion due to equilibrium fluctuations. The velocity autocorrelation function and mean square displacement of a particle selected from a given system are investigated for various models which have the common feature that the particle is directly coupled to L > 1 neighbors, reflecting the influence of long range interactions. Theorems are developed which indicate how the time course of diffusion is dictated by analytic properties of the vibrational frequency distribution as well as by quantum fluctuations whose presence is betrayed by the increasingly important role at progressively lower temperatures of τq = ℏ/πk T, the quantum transient time. The formalism is first applied to a system for which the long range couplings are so parametrized by a range parameter z that when z=0 the frequency distribution is identical to that for nearest neighbor coupling only (L=1), while as z approaches unity (L→∞) the frequency distribution becomes identifiable with that of Ford, Kac, and Mazur which served as the starting point for their dynamical theory of Brownian motion. Consequences of this model are: (1) when z <0.5, the classical velocity autocorrelation functions exhibit similar qualitative features to those computed for molecular diffusion in simple liquids; (2) as z approaches unity, the classical velocity autocorrelation function approaches the e-λτ Gaussian Markoffian form, and the mean square displacement in the same limit is identical to that predicted by the Langevin equation; (3) at low temperatures such that λτq>1, quantum fluctuations tend to dominate thermal fluctuations, resulting in severe departures from Gaussian Markoffian behavior. The low temperature effects are analyzed in some detail, and it is suggested that the predicted departure of the mean square displacement from its classical behavior might be displayed by a particle of macroscopic size suspended in a superfluid. Other models are developed which yield mean square displacements which depart even at high temperature from the linear dependence upon time characteristic of classical diffusion. The reasons and possible physical implications of these behaviors are discussed, together with a brief consideration of Poincaré cycles, whose neglect is implicit in any dynamical theory of irreversible processes.
A remark on the Green's function for the face-centered cubic lattices
Authors: Mano Koichi
Published: February 2004

The lattice Green's function G(2p,0,0) for the face-centered cubic lattices, which was obtained by Inoue as a linear combination of the F4 function of Appell, is shown to be expressible as the product of the pth derivatives of two complete elliptic integrals of the first kind.
Proof of the charge superselection rule in local relativistic quantum field theory
Authors: Strocchi F. , Wightman A. S.
Published: February 2004

The paper interprets and proves the charge superselection rule within the framework of local relativistic field theory as the statement that the charge operator commutes with all quasilocal observables. Once the basic formalism expressing the property of locality of the observables has been accepted, the proof is an elementary application of Gauss law relating the electric charge in a region to the flux of electric field through the boundary of the region. Most of the paper is devoted to the evidence that the indefinite metric formalism and its accompanying definitions of gauge, gauge transformation, and gauge invariance are internally coherent and consistent with the evidence from free field theory and the renormalized perturbation theory of coupled fields. The paper closes with speculations on analogous explanations of the baryon and lepton superselection rules within the framework of gauge models of strong and weak interactions.
Perturbation theory of a nonideal Bose gas. II
Authors: RamaRao I. , Mohling Franz
Published: February 2004

With the pair Hamiltonian model as the starting point, perturbation theory calculations are performed for the radial distribution function and the structure factor through second order in the two-body interaction potential for a many-boson system below the Bose-Einstein transition temperature. For the special case of a dilute hard-sphere Bose gas at T=0° K, the structure factor is calculated in the low-momentum limit keeping terms through second order in the hard-sphere gas parameter (n a3)1/2, where n is the gas density and a is the hard-sphere diameter. The resulting expression for the structure factor is shown to satisfy the Feynman-Bijl relation explicitly.
Physical axiomatics
Authors: Marlow A. R.
Published: February 2004

An axiomatic mathematical structure is presented in terms of which arbitrary mathematical models of a physical system can be rigorously formulated and studied. Physical systems, observables, and states all arise in a natural way from the primitive notion of a physical operation. In particular, the structure is independent of the special mathematical completion defined by the quantum mechanical model, since no lattice theoretical or Hilbert space assumptions are used. The precise relationship between the present structure and the usual quantum mechanical model is investigated in a succeeding paper.
Twistors and the conformal group
Authors: Klotz Frederick S.
Published: February 2004

The connected symmetry group SU(2, 2) of twistor space (T), a four-dimensional complex manifold with metric dsT2≡dX0 dX2¯+dX2 dX0¯+dX1 dX3¯+dX3 dX1¯,and the connected symmetry group O0(2, 4) of conformal space (C), a six-dimensional real manifold with metric dsC2≡(dX0)2−(dX1)2−(dX2)2−(dX3)2−(dX4)2+(dX5)2,are 4:1 and 2:1 homomorphic, respectively, to the restricted conformal group in compactified Minkowski space M. We obtain explicit realizations for these homomorphisms and explore the invariant geometrical relationships they imply between T, C, and M. As an application of the twistor formalism, we show that every continuous conformal transformation has a unique decomposition as the product of a Lorentz transformation, a translation, an acceleration, a dilation, and one of four special conformal transformations.
Multiple time scales and the φ4 model of quantum field theory
Authors: Varga B. B. , Aks S. O/.
Published: February 2004

Multiple time scales perturbation theory is applied to the weakly nonlinear φ4 quantum field theory model. The multiple time scales perturbation equations are solved to lowest order, leading to the removal of secular and quasisecular terms from the standard perturbative solution. This removal occurs in a manner similar to that developed in a previous quasisecular perturbative approach which focused on small energy denominators. The multiple time scales approach provides a better rationale for the quasisecular perturbation theory, as well as providing a systematic method which can be extended to higher orders in the coupling constant. It leads to the natural introduction of a first-order renormalized Hamiltonian, which is a well-defined self-adjoint operator on a certain Hilbert space of physical states. This renormalized Hamiltonian is a direct sum of Schrödinger Hamiltonians on N-particle subspaces, which describe the interactions of pairs of particles via a nonlocal potential.
Reduction on the Lorentz subgroup of UIR's of the Poincaré group induced by a semisimple little group
Authors: Angelopoulos E.
Published: February 2004

All UIR's of the Poincaré group corresponding to nonzero mass are reduced on a Lorentz subgroup by means of a unique formalism. The maximal differential domain of each UIR is proved to be a nuclear space. The completeness relations (generalized matrix elements) are established between the energy-orbital angular momentum-total angular momentum and one of its components-basis, and the relativistic-orbital-total angular momentum and one of the components of t.a.m. basis.
A note on lattice sums in two dimensions
Authors: Zucker I. J.
Published: February 2004

A slight simplification of Glasser's approach for obtaining lattice sums in two dimensions is suggested. The result for the triangular lattice is given.
Exact formulas for 2 × n arrays of dumbbells
Authors: Grimson R. C.
Published: February 2004

Several exact results are given for the problem of enumerating arrangements of q indistinguishable dumbbells on a 2 × n array of compartments.
Physical applications of multiplicative stochastic processes. II. Derivation of the Bloch equations for magnetic relaxation
Authors: Fox Ronald Forrest
Published: February 2004

The multiplicative stochastic process treatment of the time development of the density matrix for a subsystem in contact with a heat reservoir is applied to the specific problem of the relaxation of a nuclear magnetic moment which is interacting with a fluctuating magnetic environment. A model for the fluctuating interaction Hamiltonian, appropriate for the magnetic moment case, is presented, and the Bloch equations for nuclear magnetic relaxation are constructed as a consequence. Agreement with empirical observations is noted.
On normalization problems of the path integral method
Authors: Um Gregory S.
Published: February 2004

Ambiguities of the path and of normalization in Feynman's path integral method are discussed. The investigation shows that the Feynman path integral method possesses inherent ambiguities, which can be resolved by a prescription which agrees completely with the Schrödinger equation.
On the conditions that a vector field vanish outside a given radius
Authors: Bosco B. , Sacchi M. T.
Published: February 2004

The constraints that the curl and divergence of a vector field must satisfy in order that the field be identically zero outside a given radius are investigated. These result in two equations which connect the multipoles of the components of the curl and the multipoles of the divergence of the field for each given l. In an alternative proof of this constraint it is shown that the same relations still hold for the full space provided that the radial functions, which are the coefficients of the expansion of the field in vector spherical harmonics, satisfy certain conditions at infinity.
Analytic vectors for the Poincaré group in quantum field theory
Authors: Nagel Bengt , Snellman Håkan
Published: February 2004

We give a new proof of the theorem stating that in a quantum field theory with tempered field operators the dense domain of the polynomial algebra of these field operators applied to the vacuum state contains a dense invariant set of analytic vectors for the representation of the Poincaré group.
Regge trajectory structure of the Amati-Bertocchi-Fubini-Stanghellini-Tonin multiperipheral model
Authors: Balakrishnan V.
Published: February 2004

The Regge pole spectrum of the ABFST multiperipheral model with a resonance kernel is studied, using both the forward and nonforward partial-wave integral equations. Insight into the complicated pattern of the trajectory spectrum is provided by an analysis of the singularity structure of the basic kernel using appropriate representations for it, and by an elucidation of the process of generation of trajectories in the weak-coupling limit. This also establishes a framework for understanding the characteristics of the approximate solutions to the problem that are taken up subsequently. The trace approximations for both the nonforward and forward equations are worked out in detail. The traces involved are evaluated in convenient closed forms from which all the necessary information can be extracted easily. It is found that the approximation preserves, to a fair degree of accuracy, the trajectory-generating singularity structures of the relevant kernels, and that good `effective' trajectory positions for the leading and secondary poles are obtained in both the forward and nonforward cases. It is also shown that, in this approximation, other phenomena such as complex Regge poles, the threshold behavior of the trajectories, and the intercept and slope of the leading trajectory can be investigated in a close simulation of the actual situation. Recent factorizable approximations are then examined from the point of view of the pole spectra they lead to, and it is concluded that, by and large, they oversimplify the problem and that their shortcomings are thus more extensive than those of the trace approximation.
Spinor calculus in five-dimensional relativity
Authors: Leibowitz Elhanan
Published: February 2004

A consistent spinor calculus is developed within the framework of five-dimensional relativity. The formalism is manifestly five-covariant, and in special coordinate systems and special spin frames it reduces to a familiar spinor formalism in curved space-time. The five-dimensional formulation is free of the difficulties involving the coupling of the electromagnetic field, which characterize the four-dimensional approach to spinor calculus. Some theorems and useful identities in the five-dimensional spinor calculus are proved.
A one-dimensional fermion model exhibiting an anomalous type of phase transition
Authors: Moscheo R. , Moya R. P.
Published: February 2004

We construct a one-dimensional fermion model (rigorously reducible to a mean field theory). We show that this model exhibits a second order phase transition associated with a spontaneous breakdown of continuous space translational symmetry in favor of a periodic symmetry. However, Landau and Lifshitz conjectured that a phase transition in which there is a spontaneous breakdown of Euclidean symmetry in favor of a crystallographic symmetry must be a transition of the first order. Thus we obtain a counterexample to this conjecture in the case of one dimension.
Conformal Killing vector fields on timelike two-surfaces
Authors: du Plessis J. C.
Published: February 2004

A topological description of Killing vector fields as well as conformal Killing vector fields on a 2-space-time is given, and the block diagram extension technique is generalized.
Renormalized number operators
Authors: Fabrey James D.
Published: February 2004

A number operator for a Weyl system is called renormalized essentially if it is obtained from the total number operator by subtraction of a (possibly infinite) constant (in exponentiated form). Necessary and sufficient conditions for the existence of a renormalized number operator are obtained.
On algebraically irreducible representations of the Lie algebra sl(2)
Authors: Arnal D. , Pinczon G.
Published: February 2004

An algebraic study of the irreducible representations of the complex Lie algebra sl(2) is presented in this article. This study generalizes a former series of works of W. Miller. Though the list is not complete, it gives hints as to the construction of a very vast family of representations.
On some mathematical aspects of deterministic classical electrodynamics
Authors: Stuck B. W.
Published: February 2004

A new commutative diagram summarizing some of the mathematical structure of deterministic classical electrodynamics is presented. The diagram clearly delineates the fundamentally different roles played by the space-time differentiable manifold (vis à vis exterior calculus) and by matter of vacuum (vis à vis the constitutive relations for dielectric permittivity and magnetic permeability) in electrodynamics. Two different elliptic operators, called here the Laplace-Beltrami and Laplace-Poisson operators, arise naturally from this formulation. Some properties of eigenfunctions of elliptic operators with compact support are briefly reviewed with regard to potential application in numerical analysis of practical problems in electrodynamics. The action of the so-called inhomogeneous Lorentz group on electrodynamical functions is described. Several scalar inner products which remain invariant under the action of this group are seen to arise naturally from the mathematical structure discussed here. By using some of these invariant quantities, a new variational approach to deterministic classical electrodynamics is then developed. First, a new Lagrangian function is presented and used to derive the Euler-Lagrange equations for electrodynamics. Second, a series of new Hamiltonian functions are presented and used to derive the Hamiltonian equations for electrodynamics. All results are illustrated by a detailed examination of the electrodynamical structure of a model for an inhomogeneous nonisotropic medium.
Wavepackets for particles of indefinite mass
Authors: Greenberger Daniel M.
Published: February 2004

Using a formalism that includes particles with indefinite and variable masses, we can create a much richer set of states than in conventional quantum mechanics. For example, in a gravitational field the equivalence principle implies that the motion of a particle is independent of the mass. Thus it is possible to create physical states with large Δm but very small Δν and Δx, so that the trajectory of a particle is well determined, while the Δp · Δx uncertainty relation is satisfied. We also provide a quantitative description of wavepackets with arbitrary distributions in momentum and mass (or alternatively velocity and mass) and discuss a simple diffraction slit experiment as an example of their physical propagation. The Schrödinger equation is solved for a decaying particle at rest. It is also shown that Galilean invariance plays a natural and cohesive role within the variable mass formalism, unlike the case in conventional quantum mechanics where the existence of multiple mass states would violate Galilean invariance.
Mayer's theory analysis of repulsive and weak, long range potentials
Authors: Liebman Alan J. , Parlange Jean-Yves
Published: February 2004

The irreducible integrals defined in the Mayer theory of real gases are derived for one-dimensional systems having hard rod, weak long range, Curie-Weiss and van der Waals potential functions. In two cases, independent knowledge of the exact equation of state of the gas permits the derivation of general star graph degeneracy relationships. These, in turn, are useful for the study of new potential functions; a penetrable repulsive force is shown to produce attractive force behavior in the gas state equation.
The Kerr congruence
Authors: Newman Ezra T. , Winicour Jeffrey
Published: February 2004

We present the special relativistic Kerr congruence from two new points of view. The importance of the Kerr congruence stems from its role in the general relativistic rotating body problem. In the special relativistic limit, it is the simplest twisting generalization of the ordinary light cone. We first show that the Kerr congruence can be obtained from the light cone of complex Minkowski space, which induces a family of oblate spheroids in real Minkowski space. We then show that the rigid rotation of one of these spheroids with constant angular velocity also generates the Kerr congruence by shining comoving flashlights normal to the surface. In fact, the oblate spheroid is the unique surface which generates a shear-free twisting null congruence in this manner. This result has direct generalization to the full Kerr geometry.
On the problem of diffraction
Authors: Bailey Paul B.
Published: February 2004

It is shown how the methods of Hadamard, developed for the Cauchy problem in free space, can be extended to include the presence of simple obstacles. The modifications necessary are illustrated by treating the problem of diffraction by a conducting half-plane in two and three dimensions.
Note on gauge invariance and conservation laws for a class of nonlinear partial differential equations
Authors: Watanabe Yoiti
Published: February 2004

Relations between gauge invariance and the conservation laws are discussed relative to the Korteweg-deVries and related equations. The technique used here is conventional in field theory-the canonical formalism related to the invariant variational problem. The function of constants of motion, when represented in terms of canonical variables, is to generate infinitesimal partial gauge transformations of any order, under which the variational problem is invariant. From this point of view, one example is presented together with the general theory.
Applications of the concept of strength of a system of partial differential equations
Authors: Mariwalla K. H.
Published: February 2004

The concept of ``strength'' of a system of field equations was introduced by Einstein, and is of such generality that one can compare vastly different systems of field equations. We review here this concept in arbitrary number of dimensions and apply it to some of the well-known equations of physics. We calculate the strength, in arbitrary dimensions, of massless Klein-Gordon equations, Maxwell equations (in both potential and field formulation), and Einstein equations. We also determine the strength of massless Dirac equation and Weyl's neutrino equation for the case of four dimensions. It turns out that the strength for all these equations is identical for space-time dimensionality of four. Other possible applications of this concept are indicated.
Energy transfer in radiation chemistry. I. Dynamics of the electron-oscillators system
Authors: Kutz Henry Douglas , Kozak John J.
Published: February 2004

Single-mode excitation events in radiation chemistry are investigated by considering a simple model: an electron (characterized by mass m and momentum ℏk) in interaction with a collection of harmonic oscillators. The Hamiltonian corresponding to this model is identified, and then used within the framework of a master equation constructed from the time-dependent Schrödinger equation. The usual long-wavelength approximation is employed, which, in the infinite-system limit, necessitates an upper bound on the frequency spectrum of the oscillator bath. Once these constraints have been imposed, however, the time evolution of the system is determined exactly (i.e., no ``weak-coupling'' approximation) in two limiting regimes-the case of a low-energy incident electron and that of a high-energy incident electron. Our results are compared with those obtained using a weak-coupling approximation, first within the framework of the master equation cited above and then in conjunction with the Prigogine-Résibois master equation, and it is pointed out that for the system under study, the use of a weak-coupling approximation in both equations leads to unphysical results. Our results are also compared with those obtained earlier by Van Hove and co-workers on the electron-random scatterers model, and an attempt is made to understand the role of the approximations introduced in both models. Finally, suggestions for future work are given; in particular, we discuss the generalization of our approach to deal with multiple-mode excitation events in radiation chemistry.
Spectral properties of phase operators
Authors: Dombrowski J.
Published: February 2004

This paper studies the spectral properties of phase operators associated with the phase of the harmonic oscillator. It is shown that all such phase operators have an absolutely continuous part and that those of a certain subclass are absolutely continuous.
Brownian motion in assemblies of coupled harmonic oscillators
Authors: Kim Sungwoon
Published: February 2004

The generalized Langevin equation is derived for a particle of arbitrary mass in an assembly of harmonic oscillators with general interaction matrix and with an external force acting on the particle. The reduction of the equation to the ordinary Langevin equation is studied in various limits. The reduction to the Langevin equation is achieved apart from the distribution of the bath particles, and the results thus obtained are valid whether the bath is in equilibrium or not. It is found that if the Ford-Kac-Mazur interaction is assumed, the particle achieves Brownian motion regardless of its mass ratio to the bath particle. The weak coupling limit is effected by scaling the equation with the mass ratio. In the weak coupling limit, the explicit formula for the friction coefficient is obtained assuming a general interaction matrix. It is demonstrated that the generalized Langevin equation is a very convenient starting point for the study of Brownian motion.
New wave-operator identity applied to the study of persistent currents in 1D
Authors: Mattis Daniel C.
Published: February 2004

We show that a large class of backward-scattering matrix elements involving Δk ∼ ± 2kF vanish for fermions interacting with two-body attractive forces in one dimension. (These same matrix elements are finite for noninteracting particles and infinite for particles interacting with two-body repulsive forces.) Our results demonstrate the possibility of persistent currents in one dimension at T = 0, and are a strong indication of a metal-to-insulator transition at T = 0 for repulsive forces. They are obtained by use of a convenient representation of the wave operator in terms of density-fluctuation operators.
On the application of quasi-Lagrangian coordinates to random shear flows
Authors: Thiebaux M. L.
Published: February 2004

An ensemble of homogeneous random shear flows with steady linear mean velocity profiles is considered from a purely kinematical point of view. Quasi-Lagrangian coordinates (advected by the mean flow) are used so that a proper orthogonal decomposition of the fluctuation velocity field is possible and periodic boundary conditions can be imposed. The conditions of stationarity in time and incompressibility take on special forms when applied to wave-vector moments. A simple application of the methodology is presented in the construction of a two-dimensional random shear flow.
Smoothing operators for field domains
Authors: Hegerfeldt Gerhard C.
Published: February 2004

We consider sharp-time fields and write down, in terms of the fields, simple and explicit expressions for operators with very strong smoothing properties. When applied to any vector in Hilbert space, the resulting vector is in the domain of any power of the space-smeared fields, and it even is entire for the fields. It is shown that in this way one obtains a common dense domain of definition on which the field operators are essentially self-adjoint. Attention is focused on the space S of rapidly decreasing C∞ functions as smearing functions for the fields; here the smoothing operators are simply products of exponentials of the field smeared with Hermite functions.
High-frequency backscattering from an elliptic metal plate
Authors: Uslenghi P. L. E. , Lee S. W.
Published: February 2004

The high-frequency backscattered field produced by a plane, linearly polarized electromagnetic wave obliquely incident on a perfectly conducting disk of elliptical shape, is considered. The leading term of the asymptotic expansion is obtained by means of the geometrical theory of diffraction, and it is matched to the physical optics result for normal incidence via Bessel functions. The formula thus obtained is uniformly valid for all directions of incidence and polarization; it reduces to the known result for a circular disk in the case of zero eccentricity. Numerical results are presented for direct- and cross-polarized monostatic cross sections. The difficulties encountered in obtaining higher-order terms of the asymptotic expansion are discussed in detail.
Quantum conservation laws for charged particle systems in magnetic fields
Authors: Petru Zygmunt K.
Published: February 2004

The conservation laws in the exact operator form are derived for the two-component system of interacting charged particles in magnetic and electric fields. These laws represent the equations of motion for the mass-, current-, and energy-density operators, where both the pressure tensor and energy-current operators are calculated exactly.
Momentum distribution in the Tomonaga model at finite temperatures
Authors: Aizenman M. , Gutfreund H.
Published: February 2004

The momentum distribution function in the one-dimensional Tomonaga model is evaluated and its properties are discussed. The effect of finite temperatures on the applicability of the model is investigated.
Thermal conductivity of an isotopically disordered harmonic crystal
Authors: Semwal B. S. , Sharma P. K.
Published: February 2004

Using the Kubo formalism, an expression is obtained for the lattice thermal conductivity of a three-dimensional harmonic Bravais crystal, containing a certain number of randomly distributed isotopic impurities, by the method of double-time thermal Green's functions. It is shown that the total thermal conductivity can be separated into two contributions, namely, diagonal and nondiagonal contributions; the former in the case of small half-width of the phonons reduces to the expression obtained from the Boltzmann transport equation. An approximate expression for the dominant nondiagonal contribution to the conductivity is obtained.
Deformation of the SO(2, C) subgroup of the Lorentz group
Authors: Huszár M.
Published: February 2004

The two-dimensional complex sphere S12+S22+S32=S2 forms a homogeneous space under the SL(2,C) group. The little group of a point in this space is the SO(2,C) group or the horospheric group T(2), according to whether S ≠ 0 or S = 0. Deformation of the SO(2,C) group into T(2) is investigated and is demonstrated on unitary representations. This deformation is a counterpart to that of the little groups SO(3) or SO(2,1) into E(2). We conclude with a formula relating the matrix elements of unitary representations of the SL(2,C) group in SO(2) × SO(1,1) = SO(2,C) basis to those in horospheric basis.
A physical system which can be forced to execute an arbitrary unitary transformation, and its use to perform arbitrary tests
Authors: Lubkin Elihu
Published: February 2004

It is shown that a system of N spin-(1/2) magnets can be constructed so freely manipulable that an experimenter can impose any unitary transformation upon its state space, N any positive integer. This is then used with N ≥ b − 1 + 2 log2n to construct arbitrary states over an n-dimensional Hilbert space and to perform arbitrary b-tests upon these states.
Lattice Green's function for the face centered cubic lattice
Authors: Inoue Michiko
Published: February 2004

We have proved that Green's function G(l,m,n) at an arbitrary lattice site (l,m,n) in face centered cubic lattice with nearest neighbor interactions is, in general, expressed in terms of linear combinations of products of complete elliptic integrals of the first and second kinds.
Geometrodynamics regained: A Lagrangian approach
Authors: Kuchar̆ Karel
Published: February 2004

The closing relation between two super-Hamiltonians is cast into a condition on the super-Lagrangian by a functional Legendre transformation. It is shown that the ADM super-Lagrangian provides the unique representation of the ``group'' of deformations of a spacelike hypersurface embedded in a Riemannian space-time when the intrinsic geometry gij of the hypersurface is allowed as the sole configuration variable. No such uniqueness exists for the super-Lagrangians of source fields. As an illustration, the most general super-Lagrangian for a scalar field with nonderivative gravitational coupling is recovered from the closing relation.
A fluid sphere in general relativity
Authors: Adler Ronald J.
Published: February 2004

We solve the Einstein field equations for the interior of a static fluid sphere in closed analytic form. The model sphere obtained has a physically reasonable equation of state, and a maximum mass of 2/5 the fluid radius (in geometric units). As the maximum mass is approached the central density and pressure become infinite, while for masses greater than about 0.35 times the fluid radius the velocity of sound in portions of the fluid exceeds the velocity of light, indicating that the fluid is noncausal in this mass range. In the low mass limit the solution becomes identical to the Schwarzschild interior solution.
Differential inequalities and stochastic functional differential equations
Authors: Ladde G. S.
Published: February 2004

Consider the system of stochastic functional differential equations dx=f(t,xt)dt+σ(t,xt)dz(t),xt0=φ0,where σ is a n×m matrix, column vectors of σ, f are continuous, and z(t) is a normalized m-vector Wiener process with E[(z(t)−z(s))·(z(t)−z(s))T]=I|t−−s|. By developing a comparison principle, sufficient conditions are given for stability and boundedness in the mean of solutions of (S). The main technique here is the theory of functional differential inequalities and Lyapunov-like functions.
Optical equivalence theorem for unbounded observables
Authors: Klauder J. R. , Streit L.
Published: February 2004

The optical equivalence theorem relating c-number and q-number formulations of quantum optics is rigorously extended to cover various unbounded operators, and in particular those operators that directly yield counting rates.
On global embedding
Authors: Goedecke G. H.
Published: February 2004

A basis vector treatment of tensor calculus in an N -dimensional (pseudo-) Euclidean space is used to obtain new insights into the geometrical properties of curved Riemannian spaces of smaller dimension which are globally embedded in the N -space. In particular, it is shown that, in general for a globally embedded hypersurface, (i) partial derivatives of internal basis vectors with respect to internal coordinates must in general be expressed as a linear combination of external as well as internal basis vectors, (ii) there exist two different geometrical expressions, always equal in value, for the intrinsic curvature tensor, (iii) the geodesic equation contains more terms than does the usual one; the extra terms vanish for Schwarzschild metric embeddings. These points are illustrated by the example of a 2-sphere embedded in Euclidean 3-space.
Spherically symmetric static space-times which admit stationary Killing tensors of rank two
Authors: Hauser I. , Malhiot R. J.
Published: February 2004

All spherically symmetric static space-times for which a nonredundant stationary Killing tensor of rank two exists are found and discussed. The results include explicit forms for the line elements, the Killing tensors, and the corresponding quadratic constants of geodesic motion. Included as special cases are relativistic analogs of the Lenz vector and of the quadratic constant of the motion peculiar to the spatial harmonic oscillator.
The mixture of quantum states
Authors: Cornette William M. , Gudder Stanley P.
Published: February 2004

Convex prestructures, a mathematical framework that extends the usual concept of convex subset of a real linear space, are employed to generalize methods used in the study of axiomatic quantum mechanics. A brief summary of the mathematical framework of convex prestructures is given. Convex prestructures are classified, and those which are isomorphic to a convex subset of a real linear space are characterized. The operational quantum mechanics of Davies and Lewis is generalized within the framework of convex prestructures and the existence of a physically motivated orthomodular poset is given. Mielnik's beams and filters are also discussed within the framework of convex prestructures. An error in Mielnik's formulation of beam mixtures is pointed out and it is shown that his beam mixtures and one classification of convex prestructures are equivalent. Also his concept of a filter is generalized in the framework of convex prestructures and geometric requirements needed on the set of normalized states so that they may correspond to a physical system are investigated. Finally, Mackey's axioms are discussed and reformulated in the language of P-convex structures.
Hamiltonian description of relativistically interacting two-particle systems
Authors: Künzle H. P.
Published: February 2004

The state space of an isolated system of two massive point particles (without spin) in instantaneous action-at-a-distance theory is provided with a Poincaré invariant symplectic (Hamiltonian, canonical) structure. This is possible in such a way that the position coordinates commute with respect to the Poisson brackets, and for a nontrivial interaction, if the state space is chosen as the set of initial data not for spacelike, but for lightlike separation of the two particles. The conserved total 4-momentum and polarization vector of the system can be explicitly calculated and used to define a center of momentum frame in which the relative motion is most conveniently described. Under some mild additional restrictions it is shown that the possible invariant Hamiltonian interactions are all obtained by choosing arbitrarily one function of three Lorentz invariant scalars on the state space. Some evidence is presented for the conjecture that for given equations of motion the symplectic structure on the state space is determined up to arbitrary values for the rest masses of the two particles. It also follows that the relative motion of the particles can be described in a plane orthogonal to the 4-momentum and polarization vector. A simple example is given that seems physically interesting, since to first order in the coupling constant the obtained equations of motion agree with those derived from the advanced-retarded Liénard-Wiechert potentials.
Factorizable and infinitely divisible PUA representations of locally compact groups
Authors: Falkowski B. J.
Published: February 2004

Factorizable and infinitely divisible projective unitary-antiunitary representations of locally compact groups are analyzed in terms of their ``expectation values.'' A connection between these and first order cocycles is established. As a consequence a very general analog of the Araki-Woods embedding theorem is proved.
A new system of Casimir operators for U(n)
Authors: Hudson R. L.
Published: February 2004

Explicit formulas are found for the Casimir operators for U(n) whose eigenvalues in the irreducible representation for which the highest weight has components l1 − n + 1, l2 − n + 2,…, ln are the elementary symmetric polynomials in l1, l2,…, ln.
On the stationary gravitational fields
Authors: Kloster S. , Som M. M. , Das A.
Published: February 2004

The stationary gravitational equations in vacuum are expressed in five different forms. A necessary integral condition on the twist potential φ is derived. The Papapetrou-Ehlers class of stationary solutions is rederived in a different way. In the study of the complex potential theory it is proved from the field equations that a body admitting an arbitrary symmetry must satisfy an integral condition analogous to the equilibrium criterion. It is proved that the vanishing of the scalar curvature of the associated space implies the flatness of the space-time metric. A proof is given for the fact that the only analytic functions of the complex potential F which preserve the field equations form a four-parameter Möbius group. It is also shown that any differentiable function of F and F̄ which preserves the field equations must either be an analytic function of F or the conjugate of such a function. Next the conformastationary vacuum metrics are classified. In the study of the axially symmetric stationary fields a class of metrics (outside the Papapetrou-Ehlers class) is found depending on Euclidean harmonic functions.
Complexification of the algebraically special gravitational fields
Authors: Lind Robert W. , Newman Ezra T.
Published: February 2004

The fact that the Maxwell equations can be analytically extended into complex Minkowski space is used to show that a class of solutions to the real Maxwell equations exists which can be viewed as arising from a monopole source moving along a complex world line in the complex Minkowski space. This class of solutions is the natural analog of the class of regular, algebraically special type II, twisting metrics in Einstein's general theory of relativity, in that the two cases are characterized geometrically by the fact that the Maxwell and Weyl tensors, respectively, both possess a shear-free, diverging, geodesic principal null vector field l, which is twisting. By analytically extending the algebraically special metrics into a complex manifold, we show that the analogy runs even deeper than this. Aside from the constants, charge and mass, the solutions in both cases are completely determined by a single complex function φ. In both analytically extended manifolds the surfaces, φ=const, are complex null surfaces and the complexified versions of both the Maxwell and Weyl tensors now have a nontwisting principal null vector field l*, equal to the gradient of φ. We introduce the natural coordinate and tetrad systems associated with l and l* and show the relationship between them in both the flat and curved complex manifolds. The class of solutions to the Maxwell equations is solved in both systems. The algebraically special metrics are treated in detail, and the Kerr metric is given as an explicit example.
Relativistic Grad polynomials
Authors: Anderson James L.
Published: February 2004

A new method for constructing the relativistic Grad polynomials employed in relativistic kinetic theory is presented. It simplifies considerably the labor involved in their construction compared to previous methods and at the same time exhibits orthogonality properties between the components of the polynomials that were not apparent from the forms obtained by these earlier methods.
Spinor connections in general relativity
Authors: Luehr C. P. , Rosenbaum M.
Published: February 2004

An axiomatic foundation is provided for the theory of spinor calculus on the space-time manifold of general relativity. The methods, which deal directly with concepts in a coordinate free manner, allow not only elegant and compact statements of definitions and formulas but also have served as powerful analytical tools for the derivation of some interesting new results and for the unification and clarification of the previous work of other authors. The most general spinor connections are defined and related to the standard spinor connection (the unique spinor connection which is compatible with the spinor inner product and generates the Riemann 4-vector connection). By means of the intrinsic formalism presented here an interpretation is given to the spinor theory of Infeld and van der Waerden. The most general spinor curvature tensors are derived, and two alternate expressions result from two bispinor connections which satisfy the desirable requirement of producing the standard 4-vector connection by two different prescriptions. Another application of the techniques developed here results in an interesting expression for the spinor connection coefficients in terms of Dirac gamma matrices for four component spinors and arbitrary spinor connections which is much simpler and more general than others given in the literature.
On the inverse problem in radiative transfer
Authors: McCormick N. J. , Kuščer I.
Published: February 2004

The inverse problem in monochromatic radiative transfer is considered for an infinite medium with anisotropic scattering. It is shown that each Legendre coefficient of the scattering function can be related independently of the others to an appropriate integral over space and angles of the intensity due to a monodirectional plane source. This result offers some advantage over the analogous one for an isotropic plane source if the medium is weakly absorbing.
On the geometrization of neutrino fields. I
Authors: Ludwig Garry
Published: February 2004

Necessary and sufficient algebraic and differential conditions are obtained for a geometry to have as its source a neutrino field whose energy density relative to any observer is positive or negative definite.
Application of infinite order perturbation theory in linear systems. II. The frequency spectrum of disordered chains
Authors: Wu Shi-yu
Published: February 2004

A formulation is presented such that the ensemble average of the diagonal elements of the Green's function for a one-dimensional disordered system can be calculated to arbitrary accuracy. The method is illustrated with an application to an isotopically disordered chain. An approximate solution to the frequency spectrum of a disordered binary chain is also discussed.
Scattering theory, orthogonal polynomials, and the transport equation
Authors: Case K. M.
Published: February 2004

It is shown that under rather weak restrictions the discrete eigenvalues occurring in one-velocity transport theory are real or purely imaginary, simple, ≥ 1 in magnitude, finite in number, and occur in ± pairs. Proofs are obtained using methods of scattering theory applied to orthogonal polynomials.
A simple proof of certain FKG inequalities
Authors: Monroe James L.
Published: February 2004

We present a proof of a set of FKG inequalities, namely, 〈Πj=1N(ρi)νi Πj=1N(ρj)δj〉 −〈Πi=1N(ρi)νi〉 〈Πj=1N(ρj)δj〉≥0. The proof is obtained using Gaussian random variables and holds for systems whose Hamiltonian contains a positive quadratic form and one-body interactions on which no restrictions are placed.