bluuebunny/crossref_metadata_2025 huggingface dataset:
On the structure of the canonical tensor operators in the unitary groups. I. An extension of the pattern calculus rules and the canonical splitting in U(3)
Authors: Biedenharn L. C. , Louck J. D. , Chacón E. , Ciftan M.
Published: February 2004

The structure of the totally symmetric unit tensor operators (and their conjugates) in U(n) is examined from the viewpoint of the pattern calculus and the factorization lemma. The geometrical properties of the arrow patterns of the fundamental projective (tensor) operators are demonstrated to be the origin of the existence of simple structural expressions for a class of reduced matrix elements of the totally symmetric unit projective operators. An extension of the pattern calculus rules is given whereby these matrix elements can be written out directly. This class of reduced matrix elements is sufficient to permit the construction of the general totally symmetric unit tensor operator. The canonical splitting of the multiplicity in U(3) is similarly shown to be implied uniquely by the geometrical properties of the arrow patterns of the fundamental projective operators and their conjugates. This fact is used to construct explicitly the class of U(3) unit tensor operators having maximal null space. Explicit expressions for a large class of Racah coefficients are also given, and the implications of their limit properties discussed.
On the structure of the canonical tensor operators in the unitary groups. II. The tensor operators in U(3) characterized by maximal null space
Authors: Biedenharn L. C. , Louck J. D.
Published: February 2004

The canonical splitting of the multiplicities of the unit tensor (Wigner) operators in U(3) was used in I to determine explicitly one Wigner operator in each (arbitrary) multiplicity set. The denominator function whose zeroes define the null space of this Wigner operator is presented in a new form from which the complete identification of the null space is made. Using the properties of the intertwining number of U(3), the null spaces of all the U(3) Wigner operators are determined, and it is demonstrated that the null spaces of the operators belonging to a multiplicity set are simply ordered by inclusion. The Wigner operator previously obtained from the canonical splitting is shown to be the one having the maximal null space for its multiplicity set.
Mapping onto Solutions of the Gravitational Initial Value Problem
Authors: York James W.
Published: February 2004

Two approaches to the Einstein initial value problem for vacuum gravitational fields are considered. In the first, the metric of a spacelike slice is prescribed arbitrarily and it is shown that momenta satisfying the constraints can be constructed by exploiting the well-known relation of three of the four constraints to the three-dimensional coordinate transformation group. Specifically, it is shown that there exists a coordinate mapping of a certain specified set of functions onto momenta satisfying the constraints for a specified 3-metric. A further interpretation of this procedure is discussed. In the second approach the 3-geometry of a spacelike slice is specified up to a conformal factor. It is shown that, using a coordinate transformation method similar to the above, transverse traceless momenta can be constructed and that this construction depends essentially only on the conformal geometry of the spacelike hypersurface. The remaining constraint is satisfied by a choice of the conformal factor. As a result, it follows that the initial value equations can be satisfied by mapping certain specified sets of functions onto solutions by using coordinate transformations and a group of scale transformations which include conformal transformation of the metric. This is significant because the unconstrained initial data (gravitational degrees of freedom) are represented by a pair of scale-invariant transverse, traceless tensors of weight53. These objects, in turn, give irreducible representations of the coordinate and scaling groups which are used to effect solutions of the initial value equations.
Deformable Magnetically Saturated Media. I. Field Equations
Authors: Maugin Gérard A. , Eringen A. Cemal
Published: February 2004

In this article we propose a variational approach to the study of nonlinear elastic solids in which magnetization is constant in magnitude. The emphasis is placed upon the application of the different invariances used in modern continuum mechanics: Euclidean invariance, objectivity, and material symmetry. In Part I, a variational treatment is given in the spirit of ``oriented media theory.'' A comparison is made with the results of a direct treatment starting with the postulation of balance laws. Part II is devoted to the development of constitutive equations for a variety of material classes.
Variational Methods in the Wave Operator Formalism: Applications in Variation-Perturbation Theory and the Theory of Energy Bounds
Authors: Brändas Erkki J. , Micha David A.
Published: February 2004

Variational principles of the Lippmann-Schwinger type are used to develop approximations to eigenenergies and eigenfunctions within the wave-operator formalism. The present approach starts with exactly soluble ``primary'' eigenvalue equations to give explicit results valid beyond the limits of conventional perturbation theory. The variational functionals are expressed in terms of resolvents of the primary Hamiltonian, and bounds to the functionals are constructed also for cases where the resolvents are only partly known. Approximations to eigenenergies and eigenfunctions are obtained in terms of quantities in the Brillouin-Wigner perturbation theory. Connections with methods for upper and lower energy bounds are discussed, and the convergence properties of the nonlinear Padé summation is recovered in this way. Closed formulas within the double perturbation theory framework are presented as a logical extension.
One-Center Two-Electron Integrals Arising in Electron-Ion Scattering Calculations
Authors: Ramaker David E.
Published: February 2004

The two-electron integrals which arise in electron-atomic ion scattering theory are expressed as a finite sum of terms each involving a generalized hypergeometric function. We give what is believed to be the first finite expansion known for the exchange integral. The many well-known recursive and transformation features of the hypergeometric functions are then utilized to conveniently and accurately evaluate the integrals with few restrictions on the values of the parameters.
SU (n − 2) × SU (2) × U (1) Bases for SU (n)
Authors: Sharp R. T.
Published: February 2004

Explicit basis dates for the general IR of SU(n) are defined in the scheme SU(n − 2) × SU(2) × U(1); the approach makes use of elementary multiplets.
On the Asymptotic Behavior of Certain Dynamical Systems
Authors: Prosser Reese T.
Published: February 2004

The asymptotic behavior at large times for certain dynamical systems arising in the Hamiltonian formulation of classical mechanics is investigated. It is shown that for potentials which die out sufficiently fast at large distances the unbounded states of the system are asymptotically free. This result complements the corresponding result for quantum mechanical systems, and is obtained by analogous methods. In addition, the existence, differentiability, and asymptotic completeness of the associated wave mappings is established under appropriate further assumptions by classical methods.
Particle Transport in Spherical Media with a Central Black Cavity
Authors: Sheaks O. J.
Published: February 2004

A transform procedure is applied to the integral form of the Boltzmann transport equation to obtain the particle density in a spherically symmetric medium surrounding a central black absorber. The singular eigenfunction expansion technique is applied to provide a general solution, and boundary conditions are derived for the general equation for arbitrary multiplication and source distributions. Specific applications to the spherical Milne problem and a uniform source distribution are presented to demonstrate the application of the general transform technique.
Necessary Conditions for N-Representability of Reduced Density Matrices
Authors: Coleman A. J.
Published: February 2004

In this work a large new class of extreme points of the set of N-representable 2-matrices is obtained. They correspond to the exact ground state of an operator B(g) which generalizes the BCS Hamiltonian. Further, three hitherto unpublished necessary conditions for N-representability are obtained.
Operator Valued Measures in Quantum Mechanics: Finite and Infinite Processes
Authors: Benioff Paul A.
Published: February 2004

In this work, operator valued measures are used to study finite and infinite sequences of measurements. It is shown that to each such process qΔ there is uniquely associated a probability operator measure OqΔ which contains all the statistical properties of the process. In order to make this association for infinite processes, the operator valued equivalent of the Kolmogorov extension theorem is needed. This theorem is given and proved. It is then shown that for each qΔ and each set E of possible outcome sequences, there are two ways to find the probability that carrying out qΔ on a system in state ρ gives an outcome sequence φ in E. The usual method of repeating qΔ on ρ over and over again generates a sequence α of outcome sequences φ. The probability is obtained as the limit relative frequency that α(j) is in E, for j = 0, 1, …. The other, new, method is the repeated measurement of OEqΔ on ρ. The remarkable aspect of this equivalence is that the mathematical procedures of the usual method for determining if α(j) is in E or not `disappear' into the operators OEqΔ of the new method. This is discussed in some detail and examples are given.
Perturbation Calculation of an Algebraic Realization of Spin Waves
Authors: Liu C. J.
Published: February 2004

Via the results of a previous paper on an algebraic realization of spin-wave theory [J. Math. Phys. 12, 2144 (1971)], the Hamiltonian of the Heisenberg model of ferromagnetism is regrouped into a main part and a perturbed part. By introducing a generalized Bethe-Salpeter equation it is shown that the main part can be diagonalized by the single-particle states, two-particle states, and two-particle bound states. To study the scatterings of the perturbed part, an equation for the amplitude of the two-particle scattering states is derived. At low temperatures this equation is solved by power series expansion. The modification of thermodynamic free energy and spontaneous magnetization due to perturbation is equal to the first Born approximation multiplied by a function Q(S).
Timelike Asymptotic Series of Almost Local Fields
Authors: Völkel A. H.
Published: February 2004

Timelike asymptotic series for many-particle matrix elements of products of almost local fields are derived which generalize and extend the Araki-Haag series of quasilocal operators. An interpretation of the asymptotic leading terms in the form of contributions from disconnected intermediate particle states is given. A discussion of the dependence of the asymptotic leading terms on the smearing in the space variables is presented.
The Existence and Completeness of Generalized Wave Operators for Spherically Symmetric, Asymptotically Coulomb Potentials
Authors: Carroll Michael O'
Published: February 2004

By applying a theorem of Kuroda, we prove the existence and continuous completeness of the generalized wave operators W±(H2, H1), W±(H1, H2), where W±(Hj, Hi) = s — limeiHjte−iHit × Pi, in the Hilbert space L2(R3). Pi is the projection operator on the subspace of absolute continuity of Hi. H1 is the self-adjoint Hamiltonian for a particle in a pure Coulomb potential Vc = ze2/|x|, and H2 is the self-adjoint Hamiltonian for a system described by the potential function Vc + V, where V is a real-valued, measurable function of x ε R3, spherically symmetric [V(x) = V(r = |x|)], satisfies the condition ∫ 0Rr2|V(r)|2dr+ ∫ 0∞(1+r)δ|V(r)|idr<∞for some R(0 ≤ R < ∞), some 0 < δ < 1 with i = 1, 2, and is continuous except at r = 0. In conjunction with our result, we obtain a bound for the radial Coulomb Green's function. Dropping the continuity assumption on V, we have absolutely continuous completeness of the wave operators.
A Class of Nonlinear Realizations of the Poincaré Group
Authors: Dresden M. , Albano A.
Published: February 2004

A class of nonlinear space-time transformations is exhibited, which forms a nonlinear realization of the Poincaré group. The transformations leave the expression I = x2+f(xμ/x0) invariant; f is an arbitrary function of the ratios xμ/x0. The infinitesimal generators are constructed as differential operators in the Minkowski space. The transformations are defined only in a restricted region A (the allowed region) of the Minkowski space. By introducing auxiliary variables, the transformations can be recast in their usual linear form; this, however, is in general possible only in a region L (the linear region) which is different from A. The region structure is analyzed in general and given explicitly for a special form of the function f. Among the physical ideas suggested by the nonlinear formalism is the notion of ``relativity of coincidence.'' This expresses the fact that events coincident (or having arbitrary small Minkowski separation) in one frame of reference will not be coincident (or will have finite Minkowski separation) in a transformed frame.
Hamiltonian Formalism for General Lagrangian Systems in an Exceptional Case
Authors: Ryan C.
Published: February 2004

It is shown that in the exceptional case of a Lagrangian system, where the highest derivative of a generalized coordinate cannot be expressed in terms of the lower derivatives and the generalized momenta, the procedure to adopt in setting up the Hamiltonian formalism for the system (and consequently the quantization of the system) is to pass to an equivalent Lagrangian which does not have this defect and to use this rather than the original Lagrangian.
Random Walks in Polytype Structures
Authors: Thorpe M. F.
Published: February 2004

It is shown that the total number of walks, starting and ending at the same point and having the same number of steps, is the same for all polytype structures in the fcc, hcp series and in the zincblende, wurtzite series and is independent of the starting point. This result is proved by showing that the eigenvalues of a simple Hamiltonian are the same within the two series considered. A relation is found between random walks in the two series of structures that is useful in extending currently available tables of random walks for the zincblende structure.
Moments and Correlation Functions of Solutions of Some Stochastic Matrix Differential Equations
Authors: Morrison J. A.
Published: February 2004

The (not necessarily linear) vector differential equationdudz=f(u(z),M(z),z),u(0)=g[M(0)]is first considered, where M(z) is a finite-state Markov process which has, in general, a nonstationary transition mechanism. The joint process {u(z), M(z)} is a Markov process, and forward and backward Kolmogorov equations are derived for the transition probability density functions. Attention is then turned to the linear matrix differential equationdWdz=A(M(z),z)W(z),W(0)=γ[M(0)],where W and γ are n×m matrices and A is an n×n matrix. The forward equations for the corresponding probability density functions are used to obtain two different, but equivalent, formulations for the calculation of the moments of any given order, and of the correlation functions, of the solution. The calculation of the moments and correlation functions is reduced to the solution of systems of linear ordinary differential equations, with prescribed initial conditions. The inhomogeneous matrix equation dYdz=A(M(z),z)Y(z)+B(M(z),z),Y(0)=γ[M(0)]is also considered. Some applications, in particular to the calculation of the average modal powers in randomly coupled transmission lines, will be given elsewhere.
Projective Representations and the Relation of Internal to Space-Time Symmetries
Authors: Warren Russell E. , Klink William H.
Published: February 2004

The relation of space-time to internal symmetries in relativistic quantum mechanics is investigated using the Mackey theory of induced projective representations of group extensions. Representation multipliers are found for semidirect products of the Poincaré group and arbitrary internal symmetry groups. Upon investigating a typical example, it is found that when relations such as UπUC=(−1)2J UCUπ, obtained from field theory, are assumed, a unique choice of representation multiplier follows; in particular, this multiplier requires UCπt2=1 for all J. Representations relative to this multiplier are computed.
Position Operators as ``Internal'' Symmetries
Authors: Warren Russell E. , Klink William H.
Published: February 2004

Space-time variables are generated as representation labels of an underlying group, the group itself being combined with the Poincaré group in a manner reminiscent of the way in which internal symmetries are combined with the Poincaré group. After representations of the group are found, a transform is introduced which allows one to pass from spinor to Wigner wavefunctions in a boost independent manner, exhibiting clearly the spin dependence of the wavefunctions.
Normalization of Certain Higher-Order Phase-Integral Approximations for Wavefunctions of Bound States in a Potential Well. II
Authors: Yngve Staffan
Published: February 2004

Using a formula derived from equations given by Furry for the normalization integral of the wavefunction corresponding to a bound state, we derive the normalization factor for the higher-order phase-integral approximations introduced by N. Fröman. The present treatment is based on the method developed by N. Fröman and P.O. Fröman, in which one uses exact formulas in the calculations and makes the approximations in the final stage. We particularize the resulting general formula to the case of a single-well potential previously discussed by the present author and to the case of a double-well potential, which has been treated in a series of papers from this institute.
Constants of Motion and Lie Group Actions
Authors: Andrié M. , Simms D. J.
Published: February 2004

A classical Hamiltonian dynamical system with 2N-dimensional phase space is studied in the case when a Lie algebra of constants of the motion exists which contains 2N −- 1 functionally independent elements and when each constant of motion generates a complete integral curve. It is proved that a connected (global) Lie group G acts on the phase space and acts transitively on each connected component of each surface of constant energy. When G is compact, each component of the space of time orbits corresponding to a fixed energy is shown to be a (2N − 2)-dimensional compact symplectic manifold diffeomorphic to an orbit of G in the dual of the adjoint representation. It is shown that a (global) Lie group does act in the case of the harmonic oscillator, but does not act in the case of the negative energy Kepler problem.
Commuting Polynomials in Quantum Canonical Operators and Realizations of Lie Algebras
Authors: Joseph A.
Published: February 2004

It is pointed out that the problem of realizing Lie algebras through polynomials in quantum canonical operators is not equivalent to its classical counterpart because the polynomial Lie algebras taken with respect to the classical and quantum Lie brackets are not isomorphic. Yet there are still many results which are common to both. To show this, the properties of commuting polynomials in quantum canonical operators are analyzed. This makes possible an extension from the classical to the quantum domain of a number of theorems on realizations of semisimple Lie algebras. At the same time it is stressed that differences can arise in the classical and quantum solutions, and some of these are described.
Stochastic Master Equations: A Perturbative Approach
Authors: Besieris Ioannis M.
Published: February 2004

Linear stochastic master equations for wave propagation in a continuous random medium are derived along the lines of the resolvent theory used in nonequilibrium statistical mechanics. Equations for the mean and fluctuating fields are subsequently obtained by operating directly on the stochastic master equations with statistical projection operators. The findings are compared with the results determined using the method of renormalization and the method of smoothing.
On Wave Propagation In Inhomogeneous Media
Authors: Case K. M.
Published: February 2004

Familiar relations between phase and group velocity for wave propagation in homogeneous media are generalized to the inhomogeneous case. The constant velocity ``c'' is merely replaced by an appropriate weighted average. The key tool lies in the stationary property of the frequency as a functional of the wavefunction.
Quantum Theory of Heat Transport in an Isotopically Substituted, One-Dimensional, Harmonic Crystal
Authors: Greer William L. , Rubin Robert J.
Published: February 2004

We present a quantum mechanical treatment of thermal transport in a one-dimensional isotopically substituted harmonic lattice. This work is an extension of a classical mechanical treatment. We find that the difference between the quantum and classical expressions for the thermal conductivity of a random chain vanishes in the limit N → ∞, where N is the number of isotopes. Thus, as in the classical treatment, the thermal conductivity diverges as N1/2. For a periodic diatomic lattice, we derive explicit formulas for the heat current as a function of temperature. At very low temperatures, this quantum mechanical current exhibits Kapitsa behavior.
The Angular Spectrum Representation of Electromagnetic Fields in Crystals. II. Biaxial Crystals
Authors: Lalor Éamon
Published: February 2004

The electromagnetic field in a linear, nonmagnetic nonabsorbing biaxial crystal which fills the entire half-space z ≥ 0 and which has one of its principal dielectric axes perpendicular to the plane z = 0 is represented as an angular spectrum of plane waves. The angular spectrum representation consists of a superposition of plane waves expressed as the sum of two integrals. Each integral contains in general both homogeneous and evanescent plane waves. Each plane wave of the angular spectrum (whether homogeneous or evanescent) satisfies the identical equations which are obeyed by the entire field. The spectral amplitudes of the field are explicitly expressed in terms of the Fourier transform of the field in the plane z = 0. The special case of a uniaxial crystal whose optic axis is parallel to the plane z = 0 is treated in some detail. The far zone structure of the field in such a crystal is determined using the method of stationary phase. The field in the far zone is expressed explicitly in terms of the Fourier transform of the field in the plane z = 0.
An Analytical Approach to the Theory of Internal Conical Refraction
Authors: Lalor Éamon
Published: February 2004

An analytical, quantitative treatment of internal conical refraction is presented. The recently derived angular spectrum representation of electromagnetic fields in biaxial crystals is employed. Explicit expressions for the electric field in the far zone of a conically refracted beam of light are found by applying the principle of stationary phase to the integrals of the representation. A close examination of the expressions for the field in the far zone yields all the known results of internal conical refraction including the Poggendorf dark band. The present treatment, however, goes beyond previous studies since, with our expressions, it is possible to investigate the detailed structure of the conically refracted field.
Internal Labeling and the Group G2
Authors: Wybourne B. G.
Published: February 2004

The states associated with the group-subgroup R7⊃G2 are unambiguously representable as the stretched product states of just seven elementary multiplets. This result is used to derive a number of branching rules for the decomposition R7 → G2 in a simpler manner than hitherto available. An example of the decomposition of the spin representations of R7 is given.
On the Existence of Relations among the Eigenvalues of Difference Equations
Authors: Tsilimigras P.
Published: February 2004

By translating the eigenvalue problem of a difference equation to one of abstract operators, we give a method of finding relations among the eigenvalues of the difference equations.
Exact and Simultaneous Measurements
Authors: Deliyannis Platon C.
Published: February 2004

The observables which can be determined through their states of exact measurement are characterized, and a criterion for the set of states in which two observables are both measured exactly is established so that the two observables will be compatible.
Sliced Extensions, Irreducible Extensions, and Associated Graphs: An Analysis of Lie Algebra Extensions. I. General Theory
Authors: Cattaneo U.
Published: February 2004

The Lie algebra extension problem is investigated and incorporated into a formalism which allows for a visualization of the algebraic structures involved. A finer analysis than the usual mathematical one is sometimes required for the physical applications. This brings about the consideration of sliced extensions, i.e., of extensions provided with sections. Some of these, the ω-sliced extensions, are particularly interesting. They are directly connected with natural Levi decompositions of the Lie algebras obtained from extensions. Graphs are associated with ω-sliced extensions. This is especially suitable for the study of irreducible extensions, which are the basic ones among the extensions. Their structure may be described in terms of graph theory. A subset is picked out from the set of all irreducible extensions of an arbitrary Lie algebra. Its elements, the primitive extensions, have the simplest extension structure and are characterized by the empty graph or by one-vertex graphs.
Sliced Extensions, Irreducible Extensions, and Associated Graphs: An Analysis of Lie Algebra Extensions. II. Application to Euclidean, Poincaré, and Galilean Algebras
Authors: Cattaneo U.
Published: February 2004

The results of a preceding paper on Lie algebra extensions and sliced extensions are applied to the Lie algebras E(3),P,and G of the Euclidean, resp. Poincaré and Galilean groups. The primitive extensions are analyzed in detail. A procedure for the construction of irreducible extensions is illustrated by some examples, using diagrams which picture the graphs of the extensions. It is proved that all extensions by E(3),P,and G are inessential.
Generalization of Euler Angles to N-Dimensional Orthogonal Matrices
Authors: Hoffman David K. , Raffenetti Richard C. , Ruedenberg Klaus
Published: February 2004

An algorithm is presented whereby an N-dimensional orthogonal matrix can be represented in terms of ½N(N − 1) independent parameters θk(ν)[ν=2,3,…,N;k=1,2,…,(ν−1)]. The parameters have the character of angles, whose compact domains are defined in a manner such that there exists a one-to-one correspondence between the points in the parameter space and the group of orthogonal matrices. Explicit formulas are given which express all matrix elements in terms of the angles, and formulas are given which express the angles in terms of the matrix elements. Special choices of angles give block-diagonal matrices. For three-dimensional matrices, the parametrization is equivalent to that of Euler.
Dynamical Quantization
Authors: Onofri E. , Pauri M.
Published: February 2004

An intrinsic quantization procedure based on higher symmetries of classical dynamical systems and utilizing the techniques of van Hove and Souriau is proposed. The procedure is intrinsically Hamiltonian but not explicitly canonical in that the Heisenberg algebra plays no fundamental role. The proposed method is applied to the n-dimensional harmonic oscillator and to the n-dimensional hydrogen atom. This approach seems to provide the first intrinsic justification of the success of ordinary correspondential quantization for this last system.
Note on the Angular Momentum and Mass of Gravitational Geons
Authors: Cohen Jeffrey M. , Wald Robert M.
Published: February 2004

It is shown that (1) the angular momentum of a gravitational geon must be zero if it is axisymmetric and (2) the mass of a gravitational geon must be zero if it is stationary, i.e., if the space-time possesses a Killing vector which is timelike at infinity. Here angular momentum and mass are defined in terms of the asymptotic form of the metric at large distances; they are physical quantities which can be experimentally measured by distant observers. Since the gravitational geons previously considered are highly dynamical on a small scale, our result on the vanishing mass of a stationary geon does not conflict with previous analyses showing that gravitational geons can have mass. Similarly, our results do not exclude the possibility of gravitational geons having nonvanishing angular momentum if they are not strictly axisymmetric.
The Einstein Equations of Evolution-A Geometric Approach
Authors: Fischer Arthur E. , Marsden Jerrold E.
Published: February 2004

In this paper the exterior Einstein equations are explored from a differential geometric point of view. Using methods of global analysis and infinite-dimensional geometry, we answer sharply the question: ``In what sense are the Einstein equations, written as equations of evolution, a Lagrangian dynamical system?'' By using our global methods, several aspects of the lapse function and shift vector field are clarified. The geometrical significance of the shift becomes apparent when the Einstein evolution equations are written using Lie derivatives. The evolution equations are then interpreted as evolution equations as seen by an observer in space coordinates. Using the notion of body-space transitions, we then find the relationship between solutions with different shifts by finding the flow of a time-dependent vector field. The use of body and space coordinates is shown to be somewhat analogous to the use of such coordinates in Euler's equations for a rigid body and the use of Eulerian and Lagrangian coordinates in hydrodynamics. We also explore the geometry of the lapse function, and show how one can pass from one lapse function to another by integrating ordinary differential equations. This involves integrating what we call the ``intrinsic shift vector field.'' The essence of our method is to extend the usual configuration space M=Riem(M) of Riemannian metrics to T×D×M, where T=C∞(M,R) is the group of relativistic time translations and D=Diff(M) is the group of spatial coordinate transformations of M. The lapse and shift then enter the dynamical picture naturally as the velocities canonically conjugate to the configuration fields (ξt,ηt)∈T×D. On this extended configuration space, a degenerate Lagrangian system is constructed which allows precisely for the arbitrary specification of the lapse and shift functions. We reinterpret a metric given by DeWitt for M as a degenerate metric on D×M. On D×M, however, the metric is quadratic in the velocity variables. The groups T and D also serve as symmetry groups for our dynamical system. We establish that the associated conserved quantities are just the usual ``constraint equations.'' A precise theorem is given for a remark of Misner that in an empty space-time we must have H=0. We study the relationship between the evolution equations for the time-dependent metric gt and the Ricci flat condition of the reconstructed Lorentz metric gL. Finally, we make some remarks about a possible ``superphase space'' for general relativity and how our treatment on T×D×M is related to ordinary superspace and superphase space.
Scintillation of Randomized Electromagnetic Fields
Authors: Taylor Leonard S.
Published: February 2004

The propagation of a randomized electromagnetic field in a uniform medium is considered and expressions are derived for the autocorrelation and spectrum of intensity fluctuations in terms of the fourth-order coherence function on the initial plane.
A Functional Equation in the Theory of Fluids
Authors: Penrose O. , Lebowitz J. L.
Published: February 2004

Two functional equations of the form ψ2(s) − E(s)φ2(s) = V(s), where s is a complex variable and E(s) and V(s) are given even polynomials, are solved for the even entire functions ψ and φ which are required to behave like cosh[αs + o(s)] for large |Rls|. Two cases are considered: (i) V of degree zero and E of degree two and (ii) V of degree eight and E of degree six. In the second case the polynomials must satisfy a condition in order for ψ and φ to have the right asymptotic behavior. These functional equations arise in solving the Percus-Yevick equation for a mixture of hard spheres with nonadditive diameters.
Asymptotic Behavior of Sturm-Liouville Systems
Authors: Canosa José
Published: February 2004

It is shown that the bound-state solutions of regular and singular Sturm-Liouville systems have the same asymptotic behavior, in the limit of infinitely deep potential wells. This conclusion is illustrated explicity by showing the profound similarity that exists between two seemingly unconnected problems: Mathieu's equation in a finite domain and Schrödinger's equation with Morse's potential.
Multipole Radiation Solutions for a Class of Massive Particle Wave Equations
Authors: Hajj Jack P. , Weaver David L.
Published: February 2004

In this paper, the multipole radiation solutions are derived for the integer and half-integer spin massive particle wave equations of Weaver, Hammer, and Good. The rest system and massless limits of the solutions are found, the latter limit being shown to coincide with previous work by the present authors. Finally, as an application, the massive particle description is second quantized in terms of the multipole solutions and compared with some other formulations.
On the Structure of Relativity Groups
Authors: Lugiato Luigi A. , Gorini Vittorio
Published: February 2004

In this paper an attempt is made to define the class of equivalent reference frames in special relativity in terms of a purely kinematical characterization of the notion of free material point and using homogeneity of space and time, isotropy of space, and unidirectional time flow. The problem of finding the possible forms of the relativity group and the significance of a ``space-time homogeneity axiom'' which was used in previous papers are discussed.
Elementary Spinorial Excitations in a Model Universe
Authors: Rañada Antonio F. , Soler Mario
Published: February 2004

The generalized covariant Dirac equation for a certain five-dimensional universe is studied. If a torsion invariant is included in the free Lagrangian, it is shown that particlelike stable solutions exist having definite positive rest energy, spin, and corresponding antiparticles. The treatment is throughout classical.
Complete Solution of the Inverse Scattering Problem at Fixed Energy
Authors: Sabatier Pierre C.
Published: February 2004

Let D be the class of functions which are bounded by Cr−1+ε and Cr−3−ε, E the class of potentials V(r) such that V(v), rV′(r), and r2 V″(r) belong to D. E is dense in the class of potentials U with finite norm ∫0∞ρ|V(ρ)|dρ in which almost all the results of potential scattering are derived. In this paper a complete solution of the inverse scattering problem at fixed energy is given in a class Ẽ of potentials which contains E. This means that given any set of phase shifts bounded by Cl−1−ε, we construct all the potentials of Ẽ which fit this set of phase shifts. They depend on an arbitrary function. The fundamental tool in the solution is the ``scattering structure function.'' The method is derived in such a way that an approximation theory and numerical computations are feasible. These, together with various studies of the solutions, are the object of forthcoming papers.
An Approximate Solution for the Static, Spherically Symmetric Metric Due to a Point Charged Mass in Brans-Dicke Theory
Authors: Mahanta M. N. , Reddy D. R. K.
Published: February 2004

An approximate solution of the field equations of Brans-Dicke theory is obtained for a static, spherically symmetric metric due to a charged point mass which can be considered to be an analog of the Reissner-Nordstrom metric in Einstein's theory.
Two-Time Spin-Pair Correlation Function of the Heisenberg Magnet at Infinite Temperature. II
Authors: Morita Tohru
Published: February 2004

The two-time spin-pair correlation function σ(R,t) is expressed as a product of a Gaussian distribution function and a power series with respect to time. The width of the Gaussian distribution function is determined by the second derivative with respect to time of the autocorrelation function σ(0,t). The coefficients of the power series are determined up to terms of order t8 for the square and s.c. isotropic Heisenberg and XY magnets of spin ½ at infinite temperature, and up to terms of t10 for the linear magnets. The expressions obtained by truncating the power series to the exactly known terms give a very good fit at short times to the exact expression for the linear XY model, and to the results of the computer simulation due to Windsor for the s.c. Heisenberg ferromagnet. The Fourier-time transforms of the expressions thus obtained are shown to be the Gram-Charlier expansions. Thus we conclude that the Gram-Charlier expansion of the Fourier-time transform of σ(R,t),σ̃(R,ω), and that of its Fourier-space transform I(k,t),S(k,ω), is especially useful in the cases when the short-time behavior of σ(R,t) or I(k,t) is considered important; generally speaking, this is the case at large k or at ω which is not very small. When the width of the Gaussian distribution function is determined by the second derivative of I(k,t), a convergent result is not obtained for small values of k. For larger k, the convergence is as good as for the case when the width is determined by the autocorrelation function.
Eigenvalue Problem for Lagrangian Systems. VI
Authors: Barston E. M.
Published: February 2004

The gyroscopic Lagrangian system ξ¨+Aξ̇+Hξ(t)=0 on the finite-dimensional complex Hilbert space E is shown to be stable if and only if there exist Hermitian operators iα and P > 0 such that A = Pα + αP and H = P(¼ + α2)P. Structural stability is shown to be equivalent to the uniqueness of P and α, and to the existence of a Liapunov operator on E × E of the form Lp(T), where L=(−iA−ii0), T=(0−iiHiA), and p(x) is a real polynomial of degree not exceeding the least of the quantities 2 dim E − 1 and 4N + 1, where N denotes the number of negative eigenvalues of H.
Exchange Interaction Model of Ferromagnetism
Authors: Chen H. H. , Joseph R. K.
Published: February 2004

The Schrödinger exchange operator for arbitrary spin has been used to form an interaction Hamiltonian for a nearest-neighbor model of ferromagnetism. Through use of the cluster expansion method and new group theoretic results in conjunction with the diagrammatic method, eight terms in the high temperature series for the zero-field partition function and the low-field susceptibility are obtained for arbitrary spin and general crystal lattice. Critical parameters are estimated from these series by means of various ratio tests and Padé approximants. For the cubic lattices the Curie temperature Tc and the critical index γ are given by kBTC/J=0.547(q−1.6)(Y−1+0.21)and γ=0.48+2.16Y−1 for S>12;=1.41±0.02 for S=12,respectively, where Y = 2S + 1. Comparison of these results with those appropriate to the Heisenberg model as well as to experimental values is made. The concept of multipolar ordering is also discussed. It is shown that for the present model all of the 2S ``independent'' multipolar phase transitions are exactly degenerate with the usual dipolar transition.
Pulse Propagation in a Dispersive Medium with Moving Density Profile
Authors: Whitman G. M. , Felsen L. B.
Published: February 2004

Space-time ray methods are developed and employed to obtain asymptotic solutions for pulse propagation in media with slow spatial and temporal inhomogeneities. Emphasis is placed on cold isotropic plasmas whose plasma frequency ωp has a space-time dependence of the form (z−Vt), thereby simulating ordered profile motion. Asymptotic results are constructed directly by the ray method, are related to those in a spatially inhomogeneous but temporally invariant plasma by the Lorentz transformation, and are also compared with an exact closed form solution for the special case of exponential variation of ωp(z − Vt). The presentation stresses physical attributes of the propagation process through extensive use of space-time ray diagrams and plane wave dispersion surfaces.
A Bubble-Time Canonical Formalism for Geometrodynamics
Authors: Kuchař Karel
Published: February 2004

A functional differential version of the ADM canonical formalism is proposed. The existence of a canonical transformation separating canonical variables into internal coordinates, energy-momentum densities, and two pairs of true dynamical variables is assumed. The evolution of dynamical variables is governed by functional differential Hamilton's equations. They satisfy certain integrability conditions ensuring the internal path independence of dynamical evolution. The change of dynamical variables along any spacelike hypersurface is given by their Lie derivatives. This allows an elimination of 3∞3 components of the Hamilton equation, leading to a functional differential Hamilton equation based on a single bubble time. The Hamilton-Jacobi theory is built along the same lines. The formalism is illustrated in the mini-phase-space of the cylindrical Einstein-Rosen wave.
A Property of Zeros of the Partition Function for Ising Spin Systems
Authors: Lieb Elliott H. , Ruelle David
Published: February 2004

Given an Ising antiferromagnet on a lattice with an AB substructure (bipartite lattice), one can consider the associated ferromagnet in which all the exchange constants are negated. Suppose the ferromagnet is above its critical temperature in the sense that there is an arc (−θ, θ) of the unit circle on which the partition function has no zeros in z = exp(2βH). We prove that the original antiferromagnet partition function will have no zeros in z in the disc orthogonal to the unit disc and passing through the two end points of the arc. In other words, the antiferromagnet free energy is analytic in the magnetic field for small fields.
Path Integrals, Asymptotics, and Singular Perturbations
Authors: McLaughlin David W.
Published: February 2004

In this paper we evaluate several Feynman path integrals asymptotically with respect to various parameters in order to gain mathematical insight into the asymptotic evaluation of function space integrals with oscillatory integrands, a type of integral which is beginning to appear in areas of physics other than quantum mechanics. In each integral studied, the integrand factors into a product of two functionals, one of which is dominant in the limit under consideration. By systematically exploiting this feature, we obtain the asymptotic behavior of path integrals for the physical situations of (1) weakly complex potentials, (2) high energy and complex potentials, (3) weak real potentials, and (4) strong real potentials. In the complex cases, the techniques indicate a means to handle (complex valued) turning points. In the sections treating strong and weak potentials, we relate the relative ease with which one may exploit the factorization of the integrand to the theories of regular and singular perturbations. In the singular case, several examples are presented, one of which is a high energy evaluation of the path integral associated with the ``Langer transformed'' radial equation. Finally, using more conventional techniques, we construct the complete asymptotic series for each case, thus formally establishing that we have obtained the leading term in an asymptotic expansion of the path integral.
Generalized Mechanics
Authors: Tesser Herbert
Published: February 2004

The quantization scheme for generalized Hamiltonians recently proposed by Hayes is shown to be inconsistent. The theory of constraints developed by Dirac is used and leads to a consistent theory.
Noncommutative Probability on von Neumann Algebras
Authors: Gudder S. , Marchand J.-P.
Published: February 2004

We generalize ordinary probability theory to those von Neumann algebras A, for which Dye's generalized version of the Radon-Nikodym theorem holds. This includes the classical case in which A is an Abelian von Neumann algebra generated by an observable or complete set of commuting observables. Via Gleason's theorem, this also includes the case of ordinary quantum mechanics, in which A=B(H) is the von Neumann algebra of all bounded operators on a separable Hilbert space H. Particular consideration is given to the concepts of conditioning, sufficient statistics, coarse-graining, and filtering.
N-Particle Noninteracting Green's Function
Authors: Cooper W. Grant , Kouri Donald J.
Published: February 2004

A prescription is given for obtaining the Green's function for N free particles which can have different masses. The approach is systematic and straightforward. A coordinate transformation of the Fourier integral representation of the N-particle noninteracting Green's function facilitates the integration over 3N-1 angular variables of wavenumber space. A single radial integral can then be evaluated. The resulting Green's function representation may be of use in applying the integral form of Schrödinger's equation to calculate the ground and excited states of atoms.
Spectrum Generating Algebras and Symmetries in Mechanics. II
Authors: Hermann Robert
Published: February 2004

In case a group of symmetries of a classical mechanics system acts on a locally transitive way on the energy surface, it is shown how the time evolution of the system is related to orbits of one-parameter subgroups of the symmetry group. In particular, this provides a group-theoretic interpretation of certain types of regularization of collisions. Generalizations of this phenomenon to quantum mechanics are also discussed.
Expansion of the Master Equation for One-Dimensional Random Walks with Boundary
Authors: van Kampen N. G. , Oppenheim Irwin
Published: February 2004

In order to understand the behavior of coarse-grained equations in the presence of a boundary, the following model is investigated. A homogeneous one-dimensional random walk is bounded on one side by some boundary conditions of rather arbitrary form. The corresponding master equation is approximated by the Fokker-Planck equation plus partial differential equations for the higher orders. The boundary condition for the Fokker-Planck approximation is well known; but those for the higher order terms are here derived. To the second order they amount to a virtual displacement of the boundary. The case of a two-step random walk, however, gives rise to an unexpected complication, inasmuch as nonpropagating solutions of the master equation cannot be ignored in the boundary condition, although they do not contribute to the differential equations themselves.
Calculation of a Certain Type of 6j-Symbol
Authors: de Vries E. , van Zanten A. J.
Published: February 2004

It is shown that, for an arbitrary finite simply reducible group, it is possible to express a certain type of 6j-symbol in which one of the representations is one-dimensional in terms of 3j-symbols {j k l}.
A Class of Stationary Electromagnetic Vacuum Fields
Authors: Israel Werner , Wilson Gordon A.
Published: February 2004

It is shown how a new class of stationary electromagnetic vacuum fields can be generated from solutions of Laplace's equation. These fields are a stationary generalization of the static electromagnetic vacuum fields of Weyl, Majumdar, and Papapetrou, and are plausibly interpreted as exterior fields of static or steadily moving distributions of charged dust having numerically equal charge and mass densities.
The Four-Dimensionality of Space and the Einstein Tensor
Authors: Lovelock David
Published: February 2004

All tensors of contravariant valency two, which are divergence free on one index and which are concomitants of the metric tensor, together with its first two derivatives, are constructed in the four-dimensional case. The Einstein and metric tensors are the only possibilities.