bluuebunny/crossref_metadata_2025 huggingface dataset:
Magnetic Configuration of a Cylinder with Infinite Conductivity
Authors: Bardotti Graziella , Bertotti Bruno , Gianolio Laura
Published: January 2005

The magnetic configuration of a cylinder with infinite conductivity is computed numerically for different values of the height 2h. The calculation indicates that the current density j(z) diverges at the edges as I(h)/(h2−z2)½ and permits the evaluation of the function I(h). The regular part of j(z) seems to be approximated by an elliptical profile. The case of a cut cylinder is also discussed.
N-Dimensional Total Orbital Angular-Momentum Operator. II. Explicit Representations
Authors: Granzow Kenneth D.
Published: January 2005

A method of generating orthogonal polar coordinate systems in N-dimensional space is given. Commuting angular-momentum operators are easily found in the coordinate systems generated; these operators are of a single form which depends on two parameters. A short table of coordinate systems and the resulting structure of quantum numbers and eigenfunctions is given.
Theorem Relating the Eigenvalue Density for Random Matrices to the Zeros of the Classical Polynomials
Authors: Bronk Burt V.
Published: January 2005

A theorem due to Stielties shows that the problem of locating the zeros of the classical polynomials is equivalent to finding the electrostatic equilibrium positions for a set of interacting point charges. Defining a density function for these same charges we find that the density of zeros for the nth Hermite polynomial is the same as the density of eigenvalues for an ensemble of n-dimensional Hermitian matrices. Similarly the location of the zeros of the nth Laguerre polynomial determines the density of eigenvalues for an ensemble of n-dimensional positive matrices, and the zeros of the ½nth Tchebichef polynomial determine the density for the real part of the eigenvalues for an ensemble of n-dimensional unitary matrices.
High-Field Magnetoresistance of Inhomogeneous Semiconductors and Plasmas. III. Two-Dimensional Inhomogeneity Distributions
Authors: Morrison J. A. , Frisch H. L.
Published: January 2005

In previous papers we have studied the high magnetic field magnetoresistance of a classical model semiconductor (or a plasma) produced by the presence in the sample of more or less random spatial inhomogeneities on a scale small compared to the size of the sample. We extend our computations of the leading terms of the components of the resistivity tensor to the two-dimensional case in which the external magnetic field ℋ is inclined (but not perpendicular) to the plane of variation of the spatial inhomogeneity distribution. The field ℋ is applied along the z axis, and the inhomogeneity distribution is characterized by a sufficiently smooth potential φ(x, z + λy). While the magnetoresistance ratios saturate in the y and z directions, one finds that this ratio is proportional to ℋ2 (as ℋ → ∞) in the x direction.
Numerical Method for the Exact Expansion of Generating Functions
Authors: Isenberg C.
Published: January 2005

A new method is developed for the evaluation of coefficients in multinomial generating functions. This method requires solely numerical techniques to derive the coefficients in the expansion of the generating function, and thus avoids the organizational problems that occur when algebraic methods are used to expand these functions. With the use of a digital computer this method enables the number of coefficients to be extended considerably. As an example of its application some of the coefficients in a four-variable generating function are calculated.
Useful Operator in Plasma Kinetic Theory
Authors: Wu Ching-Sheng
Published: January 2005

An operator which facilitates the derivation of the plasma kinetic equation is introduced and discussed. The operator determines the first integral of the pair correlation function without the necessity for knowledge of the pair correlation function itself. To break through the lengthy algebraic effort which is usually encountered in solving the truncated BBGKY hierarchy equations, the present operator method is found to be far superior to the singular integral equation technique. The mathematical simplification which can be gained from the use of this operator is demostrated by several examples.
Generalized Perturbation Expansion for the Klein-Gordon Equation with a Small Nonlinearity
Authors: Montgomery David
Published: January 2005

A previously given method for deriving secularity-free perturbation expansions for the Klein-Gordon equation with a ``small'' nonlinear term is generalized to include situations in which the lowest-order solution is not restricted to be a monochromatic wave.
Diffraction by Polygonal Cylinders
Authors: Morse Burt Jules
Published: January 2005

Asymptotic solutions for the two-dimensional reduced wave equation in the exterior of a convex polygonal cylinder with both Dirichlet and Neumann boundary conditions are obtained. The method used is the geometrical theory of diffraction. Both the cases of oblique and grazing incidence are treated, and the far fields in all directions including those along shadow and specular lines are found. A feature of the method is that the solutions may be carried to any desired order. The calculation is illustrated for the case of a rectangular cylinder and, for this geometry, cross sections, surface current densities and radiation patterns are obtained. Graphs of some of these results have been included.
Irreducible Tensor Expansion of Solid Spherical Harmonic-Type Operators in Quantum Mechanics
Authors: Chiu Ying-Nan
Published: January 2005

A method is proposed to derive the general one- and two-center expansions of quantum mechanical operators that are in the form of regular or irregular solid spherical harmonics of any integral degree. The expansions are expressed as couplings of irreducible spherical tensors. The physical nature of such coupling and the parallelism to vector addition are illustrated. Possible uses of such expansions in the evaluation of molecular integral and their reduction to simple, known expansions obtained from other methods are briefly discussed.
A No-Interaction Theorem in Classical Relativistic Hamiltonian Particle Dynamics
Authors: Cannon John T. , Jordan Thomas F.
Published: January 2005

It is shown that a relativistically invariant classical mechanical Hamiltonian description of a system of three (spinless) particles admits no interaction between the particles. If a set of ten functions of the canonical variables of the three-particle system satisfies the Poisson bracket relations characteristic of the ten generators of the inhomogeneous Lorentz group, and-with the canonical position variables of the particles-satisfies the Poisson bracket equations which express the familiar transformation properties of the (time-dependent) particle positions under space translation, space rotation, and Lorentz transformation, then this set of ten functions can only describe a system of three free particles. A significant part of the proof is valid for a system containing any fixed number of particles. In this general case, a simplified form is established for the Hamiltonian and generators of Lorentz transformations, and it is shown that the generators of space translations and space rotations can be put in the standard form characteristic of free-particle theories. The proof of the latter involves a generalization from one to many three-vector variables of the angular momentum Helmholtz theorem of Lomont and Moses.
Determinantal Method in Perturbation Theory
Authors: Sasakawa Tatuya
Published: January 2005

The determinantal method of deriving fundamental relations of a new perturbation theory, which the author has presented recently, is demonstrated. This method is simpler than the Green's function method which has been adopted in the previous paper. The Brillouin-Wigner perturbation theory is discussed for comparison.
Spectral Analysis of the Anisotropic Neutron Transport Kernel in Slab Geometry with Applications
Authors: Leonard A. , Mullikin T. W.
Published: January 2005

A spectral analysis of the transport kernel for anisotropic scattering in finite slabs is achieved by first solving a type of generalized scattering problem for a subcritical slab. Initially, the scattering problem is stated as an inhomogeneous integral transport equation with a complex-valued source function. This is readily transformed to singular integral equations and linear constraints in which the space and angle variables enter as parameters. Dual singular equations appear in applications of Case's method to transport problems, but we cannot yet completely explain this duality. The singular equations are transformed to Fredholm equations by an extension of Muskhelishvili's standard method and by analytic continuation. It is shown that, for a wide class of scattering functions, this particular Fredholm reduction yields equations which converge rapidly under iteration for all neutron productions and slab thicknesses. The ultimate solution of the singular equations contains arbitrary constants which, when evaluated by the aforementioned linear constraints, display explicitly the Fredholm determinant and the eigenfunctions of the transport kernel. An immediate consequence of this result is the criticality condition and the associated neutron distribution. Specific applications to linear anisotropic and isotropic scattering in slab geometry are discussed. In addition, it is seen that the case of isotropic scattering in spheres can be treated with this method, and, in fact, the spectral analysis of the kernel for the slab problem immediately applies to the sphere kernel.
Causality Implies the Lorentz Group
Authors: Zeeman E. C.
Published: January 2005

Causality is represented by a partial ordering on Minkowski space, and the group of all automorphisms that preserve this partial ordering is shown to be generated by the inhomogeneous Lorentz group and dilatations.
Boundary Conditions for a Partial-Wave Amplitude
Authors: Balachandran A. P.
Published: January 2005

A partial-wave amplitude is frequently subject to constraints which specify its values at a given set of points. This happens, for instance, when we insist on its correct threshold behavior. We investigate such constraints in this paper and derive a class of inequalities which are necessary conditions for the existence of such an amplitude.
Study of Exactly Soluble One-Dimensional N-Body Problems
Authors: McGuire J. B.
Published: January 2005

In this paper it is shown that several cases of one-dimensional N-body problems are exactly soluble. The first case describes the motion of three one-dimensional particles of arbitrary mass which interact with one another via infinite-strength, repulsive delta-function potentials. It is found in this case that the stationary-state solution of the scattering of the three particles is analogous to an electro-magnetic diffraction problem which has already been solved. The solution to this analogous electro-magnetic problem is interpreted in terms of particles. Next it is shown that the problem of three particles of equal mass interacting with each other via finite- but equal-strength delta-function potentials is exactly soluble. This example exhibits rearrangement and bound-state effects, but no inelastic processes occur. Finally it is shown that the problem of N particles of equal mass all interacting with one another via finite- but equal-strength delta functions is exactly soluble. Again no inelastic processes occur, but various types of rearrangements and an N-particle bound state do occur. These rearrangements and the N-particle bound state are illustrated by means of a series of sample calculations.
Analytic Solution of the Percus-Yevick Equation
Authors: Wertheim M. S.
Published: January 2005

The properties of the Percus-Yevick approximate integral equation for the pair distribution function in classical statistical mechanics are examined for the class of pair potentials consisting of a hard core plus a short-range tail. For one-dimensional systems, some elementary theorems of complex variable applied to the Laplace-transformed equations enable one to express the direct correlation function in a very simple form, one which becomes explicit and trivial in the absence of a short-range tail. In the presence of the tail, the direct correlation function satisfies a (coupled) integral equation over a finite domain. The impossibility of a phase transition in one dimension is strongly indicated. Analysis of the case of three dimensions proceeds similarly, but is complicated by the appearance of essential parameters other than the density and compressibility. The character of the direct correlation function is qualitatively unchanged. Principal differences in three dimensions are that a phase transition is no longer prohibited, and the pair distribution function cannot be reasonably expressed as a sum of nth-neighbor contributions.
The Influence of Initial Correlations on the Approach to Equilibrium
Authors: Jones Gerald L.
Published: January 2005

The irreversible behavior of a particle under the influence of fixed scattering centers is investigated in the weak coupling limit. An ensemble is introduced which statistically describes the scattering centers as well as the particle. This allows the treatment of correlations between the particle and the scattering centers. A new diagrammatic method is used to investigate high-order terms in the perturbation theory. This method yields quite explicit information about the way in which the influence of initial correlations will disappear. In particular, it is quite clear that as one goes to higher order in the perturbation theory one must wait longer times for the influence of initial correlations to disappear. For completeness, the Boltzmann equation is derived and solved to lowest order in the interaction strength.
Simple Derivation of the Faxén Solution to the Lamm Equation
Authors: Weiss George H.
Published: January 2005

In this paper a Hankel transform technique is used to derive the Faxén solution to the Lamm equation when the sedimentation coefficient is constant and when it varies linearly with concentration.
Norm Invariance of Mass-Zero Equations under the Conformal Group
Authors: Gross Leonard
Published: January 2005

It is known that a suitable collection of solutions of the free-field Maxwell's equations is a Hilbert space with respect to an appropriate norm, and that the inhomogeneous Lorentz group acts on this Hilbert space in a unitary and irreducible manner. It is shown that this representation extends to a unitary representation of the conformal group of Minkowski space. Similar results are obtained for other mass-zero relativistic equations.
Perturbation Theory for Strong Repulsive Potentials
Authors: Weinberg Steven
Published: January 2005

A conformal mapping of the coupling-constant plane is used to rearrange the Born series. The new series is guaranteed to converge for any decent repulsive potential. The first few terms do well in actual calculations of the scattering length.
Quantum Kinetic Equations for Electrons in a Periodic System
Authors: Ron Amiram
Published: January 2005

The approach to equilibrium of a system of electrons in a periodic system is studied by deriving a kinetic equation in the self-consistent field approximation. The derivation based on the introduction of an hierarchy of equations for the s-body density matrices and employing a truncation scheme, valid in the self-consistent field approximation. The irreversibility is introduced by the adiabatic hypothesis of Bogoliubov. The kinetic equation takes proper account of the collective aspects of the electron system and includes the dynamic shielding.
Some Dynamical Properties of an Impurity in the Hard-Sphere Bose Gas
Authors: Soda Toshio
Published: January 2005

The dynamical properties of an impurity in the hard-sphere Bose gas are investigated by extending the pseudopotential method and Hamiltonian of the author's previous work. The interaction potential between two impurities is calculated up to one quasiparticle exchange and is shown to have a Yukawa form of attraction with a range of (16πρa)−1/2 in addition to the hard-core interaction at the origin. (ρ and a are the density of the boson gas and hard-core diameter of the boson, respectively.) Necessary conditions for impurities to have a bound state are also obtained. It is found that the mass of the impurity must be greater than approximately nine times the boson mass, and the density of the boson gas must lie in some range with a maximum and minimum. Then the differential cross section for Compton-type scattering and one quasiparticle production on an impurity are calculated. The Čerenkov radiation of sound quanta is studied when the impurity is traveling very fast in the hard-sphere Bose gas. It is found that there is no radiation unless the velocity v of the impurity is faster than [k2 + (16πρa)]1/2 and the radiation has a maximum for the angle θ0 such that cosθ0 = (k2 + 16πρa)½/v. The cross section for Čerenkov radiation is also calculated. (k is the momentum of the quasiparticle emitted in the Čerenkov radiation.)
Kramers-Wannier Duality for the 2-Dimensional Ising Model as an Instance of Poisson's Summation Formula
Authors: McKean H. P.
Published: January 2005

The well-known Kramers-Wannier high-low-temperature duality for the 2-dimensional Ising model is derived by means of the Poisson summation formula for a commutative group.
Singular Potentials and Peratization. II
Authors: Pais A. , Wu Tai Tsun
Published: January 2005

In a field theory with more than one unrenormalizable interaction (like the W theory with weak and electromagnetic coupling), the important problem arises of resumming multiple series of individually divergent terms. In order to get a first insight in the new questions which arise for multiple as compared to single series, we study the analogous question for a superposition of two singular potentials, using a family of exactly soluble cases. We ask whether one can expand resummed series for the zero-energy scattering amplitude in powers of one coupling constant with coefficients depending on the other. The answer depends both on the relative magnitude of the coupling constants and on the relative degree of singularity of the interactions. Depending on these two conditions one finds three regimes, one where a convergent power expansion holds, another where an asymptotic expansions obtains, and a third where it is impossible to expand in powers of either single constant separately. It is conjectured that a similar situation will be true in a field theory with leading power singularities only (and no logarithmic ones), if such a theory has meaning.
Convergence of Virial Expansions
Authors: Lebowitz J. L. , Penrose O.
Published: January 2005

Some bounds are obtained on ℜ(V), the radius of convergence of the density expansion for the logarithm of the grand partition function of a system of interacting particles in a finite volume V, and on ℜ, the radius of convergence of the corresponding infinite-volume expansion (the virial expansion). A common lower bound on ℜ(V) and ℜ is 0.28952/(u+1)B, where u ≡ exp [−Min s−1Σi<j≤s 2φ(xi−xj)]/KT [so that u ≥ 1, with equality for nonnegative φ(r)], B ≡ ∫|e−φ (r)/KT−1| d3 r, and φ(r) is the binary interaction potential; the irreducible Mayer cluster integrals have the related upper bounds βk ≤ [(u+1)B/0.28952]k/k[u = 1, when φ(r) ≥ 0]. For potentials with hard cores the maximum density is an upper bound on ℜ(V), though possibly not on ℜ; an example shows how both ℜ(V) and ℜ can be less than the maximum density, even if there is no phase transition. A theorem is proved, analogous to Yang and Lee's theorem on uniform convergence in the complex z plane, defining a class of domains in the complex ρ plane within which the operations V → ∞ and d/dρ commute. This theorem is used to show that limV→∞ R(V) ≤ R, and that there is no phase transition for 0 ≤ ρ < 0.28952/(u + 1)B.
Uniqueness of 4- and 8-Dimensional Spaces
Authors: Peaslee D. C.
Published: January 2005

Among rotation groups Rn, the cases n = 4 and 8 are unique in having two inequivalent n × n representations. Mathematically this is related to the uniqueness of quaternions and octonions; physically these groups seem to underlie the real and charge-space symmetries of elementary particles. An attempt is made to interpret this fact by assuming a lack of inherent geometrical preference between Fermi-Dirac and Bose-Einstein statistics. Corollaries are the identity of real and charge-space statistics and the complete disjointness of real and charge-space coordinates.
Correlation Functions and the Critical Region of Simple Fluids
Authors: Fisher Michael E.
Published: January 2005

The ``classical'' (e.g. van der Waals) theories of the gas-liquid critical point are reviewed briefly and the predictions concerning the nature of the singularities of the coexistence curve, the specific heat, and the compressibilities are compared critically with experiment and with the analytical and numerical results for lattice gas models.

The critical singularities are related to the behavior of the pair correlation function G(r) = g(r) − 1 and the Ornstein-Zernike theory of critical scattering is reviewed. Alternative derivations of the theory are discussed and its validity is assessed in relation to experiment and to more detailed theoretical calculations. The nature and magnitude of the expected deviations from the ``classical'' theory are described. The analogies with critical magnetic phenomena are mentioned briefly.
Fluctuations in Multiple Capture Processes
Authors: Petschek Albert G.
Published: January 2005

The fluctuation in the number of many-fold captures by an element exposed to a high neutron flux is computed. It is found that the fluctuations are identical to those that would be obtained by selecting nuclei at random from an infinite supply with the appropriate average composition.
Ising-Model Spin Correlations on the Triangular Lattice
Authors: Stephenson John
Published: January 2005

A Pfaffian representation, of the partition function of the triangular lattice is used to derive expressions for various two, four, and six spin correlations in terms of Pfaffians. The pair correlations along a diagonal are expressed as a Toeplitz determinant whose limiting form yields the spontaneous magnetization. At the ferromagnetic critical point the correlations decay as 1/r12 with approximately radial symmetry. At the antiferromagnetic zero point the ground state is highly degenerate—it has finite entropy—and on a given sublattice the pair correlations along a row decay as ε/r12, where ε=+ε0 on the sublattice containing the origin spin and ε≃−12ε0 on the other two sublattices. Finally, the perpendicular susceptibility, χ⊥, which depends on a finite number of correlations, is calculated; its ferromagnetic behavior is similar to that of the perpendicular susceptibilities of the quadratic and honeycomb lattices, but for an antiferromagnet χ⊥ diverges as 1/T at low temperatures.
Finite and Disconnected Subgroups of SU3 and their Application to the Elementary-Particle Spectrum
Authors: Fairbairn W. M. , Fulton T. , Klink W. H.
Published: January 2005

An attempt is made to fit the symmetries of the currently observed elementary-particle spectrum into the structure of finite or disconnected subgroups of SU3. Surprisingly, the detailed properties of these subgroups have not been elucidated previously. As a first step, therefore, character tables and other relevant properties are derived for these groups. Next, the classification of elementary particles is made on the basis of the representations of the groups discussed. The techniques previously employed by Case, Karplus, and Yang for the application of finite subgroups of SU2 to isotopic spin are extended to the subgroups of SU3. The structure of SU3 is utilized to suggest how charge and hypercharge operators are to be assigned in the subgroups. The results obtained are similar to those of SU2 and isotopic spin. There is an upper limit, for any given group, to the dimension of the irreducible representation. For some of the groups considered, these upper limits are eight and even ten. There exist finite groups which can accommodate the eight baryons in one of the irreducible representations. However, when one looks at scattering problems, use of the finite groups, as expected, gives charge or hypercharge conservation only modulo an integer determined by the group. Charge independence is also lost. In a representative group analyzed in detail, the imposition of exact charge conservation leads automatically to the exact conservation of hypercharge and to the full SU3 symmetry. Exact charge and hypercharge conservation can be maintained for the disconnected groups, but the maximum dimension of the irreducible representations is six, and only charge symmetry, not charge independence, is satisfied. A short discussion of the representations of the group SU3/C is included in the appendix.
Linear Heisenberg Model of Ferro- and Antiferromagnetism
Authors: Katsura Shigetoshi , Inawashiro Sakari
Published: January 2005

The partition function of the one-dimensional Heisenberg model is considered. Hamiltonian of the system H=−12 ∑ [J⊥(σlxσl+1x+σlyσl+1y)+J∥σlzσl+1z]−mH ∑ σlzis expressed in terms of Fermi operators. The term which contains J∥, the quartic term and a part of quadratic term in Fermi operators, have been regarded as perturbation, keeping the symmetry with respect to the magnetic field. Linked-cluster expansion in an appropriate form for this case has been developed and the partition function has been obtained up to the third order in J∥. Numerical values of energy, specific heat, and susceptibility up to second order in J∥ are shown. The ground-state energy is EN|J⊥|=−2π−2π2(J∥|J⊥|)−16π3(16−π2144)(J∥J⊥)2+O[(J∥J⊥)3].E/N|J∥| for the antiferromagnetic case J∥ = −|J∥| = J is −0.8899. Agreement with the exact value, −0.8863, is quite satisfactory.
Exact Critical Percolation Probabilities for Site and Bond Problems in Two Dimensions
Authors: Sykes M. F. , Essam J. W.
Published: January 2005

An exact method for determining the critical percolation probability, pc, for a number of two-dimensional site and bond problems is described. For the site problem on the plane triangular lattice pc = ½. For the bond problem on the triangular, simple quadratic, and honeycomb lattices, pc=2 sin (118π),12,1−2 sin (118π), respectively. A matching theorem for the mean number of finite clusters on certain two-dimensional lattices, somewhat analogous to the duality transformation for the partition function of the Ising model, is described.
Linear Representation of Spinor Fields by Antisymmetric Tensors
Authors: Klauder John R.
Published: January 2005

A redundant, linear representation of four-component spinors ψ(x) by antisymmetric tensors fμν(x) is proposed on the basis of the relation ψ=12fμνγμνυ, where γμν is the skew product of gamma matrices and ν is a constant fiducial spinor. The redundant degrees of freedom in fμν as well as the particular choice of ν are both treated as unobservable ``gauges,'' and the appropriate gauge groups are discussed. As part of this analysis, we demonstrate that the possibility that tensors can behave as spinors is intimately connected with the existence of two coordinate-invariant, gauge-covariant subsidiary conditions. A linear, tensorial reformulation of the Dirac equation is given, and shown to be the Euler-Lagrange equation of the conventional action functional for spinor fields. Finally covariance under arbitrary space-dependent coordinate and gauge transformations is discussed, and a generally covariant, tensorial form of the Dirac equation is proposed differing from the conventional generally covariant equation in the degree of arbitrariness in the (spin) connection.
Solution of a Singular Integral Equation from Scattering Theory
Authors: Kenschaft R. P. , Amado R. D.
Published: January 2005

The solution of a singular integral equation of the form ψ(ω,ω0)=−1ω−1π ∫ μ∞ρ(ω1,ω0)ψ(ω1,ω0) dω1ω1+ω−ω0−iεis obtained. The equation first appeared in the attempt of Källén and Pauli to solve V − θ scattering in the Lee model. The methods developed by one of us to solve that problem are turned to solving the integral equation itself.
Solution of Einstein's Field Equations for a Rotating, Stationary, and Dust-Filled Universe
Authors: Wright James P.
Published: January 2005

The solution of Einstein's field equations, Rij−12gijR=8πκρuiuj+λgij, for a line element of the form ds2=(dx0)2−δ2(x1)(dx1)2+2β(x1)dx0dx2−γ2(x1)(dx2)−α2(x1)(dx3)2 is found. The density, ρ, may be a function of position, and the cosmological constant λ is not necessary in order to have a finite density. The solution reduces to that of Gödel if the variable α is constant. If the requirement for an empty universe is made (Rij = 0), the solution is conformally flat. The characteristics of the conformal curvature tensor are also obtained.
Method for Treating Fluctuation of Dynamical Variables
Authors: Jones Gerald L.
Published: January 2005

An upper bound, on the probability that a fluctuation of a given size will occur in given time interval, has been derived. The bound is useful because it is small for some cases of interest. The fluctuations of the kinetic energy in a canonical ensemble have been considered as an example.
Complete High-Energy Behavior for Certain Planar Graphs
Authors: Martinis M.
Published: January 2005

The results obtained by Polkinghorne for the set of ladder diagrams is generalized to a certain set of planar graphs. The leading asymptotic term behaves as s−1(ln s)p, and then the complete set of terms s−1(ln s)m is summed over m. The final result allows the writing of an equation for the Regge trajectory function.
Unitary Symmetry of Oscillators and the Talmi Transformation
Authors: Kaufman Bruria , Noack Cornelius
Published: January 2005

The Hamiltonian of an isotropic harmonic oscillator is invariant under unitary transformations in three dimensions. This well-known invariance is exploited in a treatment of the Talmi transformation, viz., the transformation of two-particle oscillator functions to center-of-mass and relative coordinates. A simple and transparent form of this transformation in terms of rotation matrices and Wigner coefficients of SU3 is given. The calculation of these Wigner coefficients is described and the problem of degeneracies discussed.
Existence of Proper Modes of Helicon Oscillations
Authors: Legéndy C. R.
Published: January 2005

In this paper it is shown that the class of electromagnetic problems for which the operator i(∂/∂t) (where t denotes time) is self-adjoint extends beyond problems involving only insulators and perfect conductors. The class includes problems in which the perfect conductor is generalized to a medium with antisymmetric resistivity tensor. The latter medium approximates media in which helicon waves can propagate. Helicon waves are known to propagate in good conductors in a strong magnetic field B0; it will be found that two necessary conditions for self-adjointness of the operator i(∂/∂t) are that the sample carrying helicons must not have a finite portion parallel to B0, and it must be surrounded by a reflecting surface that prevents energy from escaping.
On the Reduction Formula of Feinberg and Pais
Authors: Bollini C. G. , Giambiagi J. J. , Domínguez A. González
Published: January 2005

Feinberg and Pais have considered a ``reduction'' formula for the Fourier transform of functions which depend only on the hyperbolic distance. They have shown that the formula is valid in particular cases and stated that it should be valid in general.

We show that it is valid for any causal distribution and furthermore that it is actually an extension of the well-known Bochner Theorem on the Fourier transform of radial functions.
Improved Self-Consistent Configuration Interaction
Authors: Fraga Serafin
Published: January 2005

Using general coupling operators the configuration interaction method is reformulated. The new formulation proves that the configuration interaction procedure leads to self-consistent results for the set of configurations chosen and makes it possible to include a self-consistent contribution of the continuum in practical calculations.
Covariant Higher-Spin Equations
Authors: Berg R. A.
Published: January 2005

Covariant wave equations are derived for nonzero-mass particles of arbitrary spin, with wave-functions that involve no redundant components. The Dirac equation is seen to be the first of these, for spin ½; the Proca vector meson equations for spin 1 are the next set. The derivation is based on synthesizing higher-spin particles from particles of lower spin.
Position and Intrinsic Spin Operators in Quantum Theory
Authors: Berg R. A.
Published: January 2005

The problem of defining position and intrinsic spin operators in terms of the generators of the inhomogeneous Lorentz group is considered. These operators are taken to have the properties usually attributed to them in nonrelativistic quantum theory: their commutation relations must have the commonly accepted form. These commutation relations are then shown to define the intrinsic spin uniquely. The position operator is shown to be also essentially uniquely determined. Explicit forms of the spin and position operators for some special representations are exhibited. The relation of these operators to the spin and position operators of the spin-½ Dirac theory in the Foldy-Wouthuysen representation is considered. An Appendix gives a heuristic derivation of the spin operator.
On the Number of Bound States of a Given Interaction
Authors: Ghirardi Gian Carlo , Rimini Alberto
Published: January 2005

A method for deriving bounds to the number of bound states of a given interaction is built up. The class of interactions for which the method works includes the nonlocal interactions besides the local ones. Problems with many channels and spin-dependent interactions can also be treated. Some bounds are explicitly given.
Correlation Functionals
Authors: Ruelle D.
Published: January 2005

The correlations between positions of particles in classical equilibrium statistical mechanics are usually expressed by correlation functions. It can be seen that if the correlation functions of a system are known, its configurational entropy per unit volume is already determined (independently of the interaction potential or other thermodynamical parameters). In this paper we consider all sequences of functions of an increasing number of variables (these functions are candidates for correlation functions) for which an entropy per unit volume may be defined. These sequences are called correlation functionals and are investigated in detail. They prove useful to the study of the limit of an infinite system in statistical mechanics (thermodynamic limit). Furthermore they allow the segregation of certain thermodynamic systems into phases to be made evident.
Reduced Density Matrices of Quantum Gases. II. Cluster Property
Authors: Ginibre Jean
Published: January 2005

The reduced density matrices of quantum gases are studied by means of a Wiener integral representation described in a previous paper. They are shown to satisfy a cluster property in the form of an absolute integrability condition of the natural quantum analogues of the Ursell functions, considered as functions of the differences of their arguments. Use is made of the natural transposition to the quantum case of the algebraic formalism introduced by Ruelle in the classical case. By-products are two results on the signs of the coefficients of the Mayer expansion, in the case of Maxwell-Boltzmann and Fermi-Dirac statistics, respectively.
Some Constants of the Linearized Motion of Vlasov Plasmas
Authors: Oberman C. , Kruskal M.
Published: January 2005

A new class of nonlocal constants for the linearized Vlasov equations is presented. These are constants which, in general, are not expressible as simple phase-space integrals of a locally defined integrand. The relevance of these constants to stability considerations is indicated.
Mathematical Methods for Evaluating Three-Body Interactions Between Closed-Shell Atoms or Ions
Authors: Zimering Samson
Published: January 2005

The mathematical methods involved in the evaluation of three-body interactions between rare-gas atoms or alkali-halide ions with Gaussian type electron wavefunctions are outlined in first and second orders of perturbation theory. These methods are of general applicability for the analysis of many-center coulombic and exchange integrals occurring in problems of atomic and solid-state physics in which Gaussian functions can be used as a basis.
Calculation of Certain Phase-Space Integrals
Authors: Krzywicki A.
Published: January 2005

We give the result of an approximate calculation of the phase-space integral Ωn(Q)= ∫ δ4(Q−Σiki) Πi δ(ki2−μi2)ϑ(ki0)fi(kiT) d4ki,which appears when one takes into account the fact that only a part of the kinematically allowed phase-space is accessible to particles produced in high-energy collisions, because of the observed smallness of their transverse momenta.
Composite Particles in a Relativistic Model of Two-Body Scattering
Authors: Redei L. B.
Published: January 2005

The relativistic model of two-particle scattering recently described by Jordan, Macfarlane, and Sudarshan is extended to include bound states. The projection operator associated with the boundstate manifold is explicitly given. This relates the structure of the composite particle to the scattering amplitude. There is a discussion of the conditions the phase shifts have to satisfy in order that they can be fitted with the model. Explicit solutions are derived for a large class of phase shifts.
Microcausality in Asymptotic Quantum Field Theory
Authors: Rohrlich F. , Stoddart J. C.
Published: January 2005

Asymptotic quantum field theory can be formulated without the axiom of microcausality, (strong local commutativity). It is shown here that in certain cases microcausality is nevertheless a consequence of the remaining assumptions of the theory. These cases are the ones for which solutions of the basic equations can be obtained in perturbation expansion, i.e., the scalar, spin ½, and neutral vector field. For the charged vector boson, for example, the microscopic causality condition cannot be proved from the basic postulates. In the provable cases the functional derivative in the Bogoliubov causality condition can be defined explicitly, and this condition can then be derived from the postulates of asymptotic quantum field theory. In the other cases, Bogoliubov causality cannot be defined explicitly.
Approach to Stability of a Plasma
Authors: Abraham B. W.
Published: January 2005

The stabilization of a spatially homogeneous plasma by the collision term of the new kinetic equation of Balescu for a weakly unstable plasma is shown for a simplified model. The one-particle velocity distribution consists of two symmetrically displaced Lorentz distribution functions in which the displacement velocity and velocity spread are functions of time. For this distribution function, the collision term decreases the displacement velocity and increases the velocity spread until the plasma is quite stable. Physically this process can be viewed as conversion of relative energy to kinetic energy. This is demonstrated to be equivalent to the passage of the zero of the plus dielectric constant from the upper half complex plane, characterizing an unstable plasma, to the lower half complex plane, characterizing a stable plasma.
Property of the Vertex Function in Potential Theory
Authors: Rockmore R.
Published: January 2005

The vertex function of an s-wave bound state in potential theory is discussed in terms of a non-relativistic Bethe-Salpeter formalism. It is shown that the Born series defining the off-shell amplitude, Γ(k2, P0), has the property that Γ(k2, k2/m)=Γ0/D(k2,λ), where D(k2, λ) is the Jost function for potential strength λ, and where the bare (Γ0) and physical (Γc) couplings are related by Γ0 = ΓcZ1, with Z1, the vertex renormalization constant equal to D(−α2, λ). The particular proof presented derives from a detailed comparison in momentum space of alternative, but equivalent, coordinate space definitions of the Jost function originating with Jost and Pais.
Necessary Condition on the Radial Distribution Function
Authors: Feenberg Eugene
Published: January 2005

Trial functions g(r) may be used as radial distribution functions to study the ground-state properties of a uniform extended quantum fluid (liquid He, nuclear matter). A result obtained by Wigner and Seitz in the study of the charged electron gas imposes an integral inequality on any assumed g(r). The relation is ∫0∞[1−g(r)]r dr/[∫0∞[1−g(r)r2 dr]23<1.792/313=1.243. This inequality places an effective constraint on the location, magnitude, and width of the nearest-neighbor peak.
Algebraic Tabulation of Clebsch-Gordan Coefficients of SU3 for the Product (λ, μ)⊗ (1, 1) of Representations of SU3
Authors: Kuriyan J. G. , Lurié D. , Macfarlane A. J.
Published: January 2005

An algebraic tabulation is made of the Clebsch-Gordan (CG) coefficients of SU3 which occur in the reduction into irreducible representations of the direct product (λ, μ)⊗ (1, 1) of irreducible representations of SU3. Full explanation is made of the method of handling the complications associated with the possible double occurrence of the representation (λ, μ) itself in the direct product. The phase convention employed is an explicitly stated generalization of the well-known Condon and Shortley phase convention for SU2. The relationship of the CG coefficients associated with the direct product (1, 1)⊗ (λ, μ) to those coefficients already mentioned is also exhibited.
Multipole Matrix Elements of the Translation Operator
Authors: Danos M. , Maximon L. C.
Published: January 2005

Formulas are given for the expansion of multipole fields of arbitrary tensorial character into multipole fields about a shifted origin. The expansion coefficients are given as matrix elements of the translation operator. In analogy to the matrix elements of the rotation operator, we introduce for these matrix elements a standard form which represents a parallel displacement of the coordinate system along the z axis. Any arbitrary translation of the coordinate system then consists of a consecutive application of a rotation, a standard translation, and a rotation. Since the multipole fields form a complete set any arbitrary function can in principle be expressed in a shifted coordinate system by means of the given formulas. All mathematical derivations are given.
Variational Principle for Saturated Magnetoelastic Insulators
Authors: Tiersten H. F.
Published: January 2005

In a previous paper, a system of nonlinear differential equations and boundary conditions governing the macroscopic behavior of arbitrarily anisotropic nonconducting magnetically saturated media undergoing large deformations, was derived. The derivation utilized the classical procedure of defining field vectors and determining the equations relating them by applying energy and momentum conservation theorems. The macroscopic effect of the quantum mechanical exchange interaction was included as was dissipation and the associated thermodynamics. The magnetic field was assumed to be quasistationary. In this paper a variational principle is presented, which is shown to yield the aforementioned system of equations and boundary conditions in the absence of dissipation and heat flow.
Lagrangian Theory for the Second-Rank Tensor Field
Authors: Barnes K. J.
Published: January 2005

The second-rank tensor field φμν is decomposed into its various subspaces under the Lorentz group and the appropriate projection operators are exhibited explicitly. The most general local, Hermitian, free-field Lagrangian which can be formed from this field is written down, and the corresponding equations of motion and subsidiary conditions are derived by means of a variational principle. Finally some possible applications of this theory are discussed (in particular spin-2 boson theory), and all the possible couplings of this field to a Dirac particle are listed in full.
Exact Bootstrap Solutions in Some Static Models of Meson-Baryon Scattering
Authors: Huang Kerson , Low Francis E.
Published: January 2005

We study the exact bootstrap solutions to four well-known models of meson-baryon scattering in the nonrecoil, one-meson approximation. The models are the neutral scalar theory, the charged scalar theory, the symmetric scalar theory, and the neutral pseudoscalar theory. A bootstrap solution is defined to be a solution satisfying Levinson's theorem of potential scattering. It is found that the existence of a bootstrap solution depends crucially on the high-energy conditions, which enter the problem through a cutoff function and through subtractions in the dispersion relations. In all the models considered there is no bootstrap solution with no subtraction. With one subtraction there exists more than one bootstrap solution. However, the requirements that (a) the meson-baryon coupling constant should be different from zero, and (b) there should be no inelastic threshold below the elastic threshold, render the bootstrap solution unique. Positions of bound states and their coupling constants depend on two arbitrary parameters, which may be taken to be the cutoff momentum and the subtraction constant.
Problem of Subtractions in Potential Scattering
Authors: Bessis D.
Published: January 2005

We study the problem of subtractions in potential scattering theory. We show that the single spectral functions can be obtained by analytic continuation of the Mellin transform of the double spectral function. The N/D method could thus be avoided, in principle.
Note on Non-Landau Singularities
Authors: Federbush Paul
Published: January 2005

Some non-Landau singularities are discussed using the formalism of Fotiadi, Froissart, Lascoux, and Pham. The simple cases of self-energy and vertex diagrams are treated, as well as the sixth-order scattering ladder diagram.
Conserved Quantities Associated with Symmetry Transformations of Relativistic Free-Particle Equations of Motion
Authors: Fradkin D. M.
Published: January 2005

A general technique is presented for associating conservation laws with the symmetry transformations that leave invariant the relativistic equations of motion for a free particle. These transformations may be either continuous with the identity (such as infinitesimal transformations) or discontinuous (such as reflections). It is found that for each transformation there exist two classes of conservation laws. The number of separate laws within a class depends on the spin of the particle. The particular cases of the Dirac equation and Maxwell's equations are investigated in some detail. For the Dirac equation, conserved quantities involving discontinuous transformations and also matrix elements between particle and antiparticle states are obtained, in addition to the usual conservation laws. Application of the general method to Maxwell's equations yields not only the usual conserved quantities and Lipkin's ``zilch,'' but also twenty new gauge-independent conserved quantities and other additional integrals associated with discontinuous transformations.
Structure of Gravitational Sources
Authors: Janis A. I. , Newman E. T.
Published: January 2005

The purpose of this paper is to propose a definition of multipole structure of gravitational sources in terms of the characteristic initial data for asymptotic solutions of the field equations. This definition is based upon a detailed study of the corresponding data for the linearized equations and upon the close analogy between the Maxwell and the linearized gravitational fields.