bluuebunny/crossref_metadata_2025 huggingface dataset:
Upper and lower bounds to zeroth order Coulombic hyperangular interaction integrals
Authors: Demiralp Metin , Baykara N. Abdülbaki
Published: March 2003

In recent years it has been shown that the use of hyperspherical coordinate representation of the Schrödinger equation for electrically charged particles necessitates the evaluation of certain kinds of hyperangular interaction integrals. The analytic evaluation of rather simple cases has also been accomplished. On the other hand certain numerical devices have been utilized and the complications that have arisen have been discussed for their computation. We have attempted in this work to find upper and lower bounds for all types of zeroth order hyperangular interaction integrals having Coulombic potentials. A nesting procedure has been developed for obtaining close bounds which can possibly be used to evaluate the desired value of integrals under consideration. In this context a theorem has been established for the evaluation of a similar type of integral and possible ways towards the generalization of the theorem have also been discussed. For three particle systems some applications have also been presented.
Representations of graded Lie groups
Authors: Sitaram B. R. , Tripathy K. C.
Published: March 2003

In this paper we establish the existence of a faithful matrix representation of finite type for every connected simply connected graded Lie group. We also show the 1-1 correspondence between finite-dimensional representations of a graded Lie algebra and the representations of finite type of the corresponding connected simply connected graded Lie group.
Mathematical properties and asymptotic expansion of the generalized quark statistical function
Authors: Chang K. C. , Chew C. K. , Liang T. Y. , Phua K. K. , Low H. B.
Published: March 2003

An asymptotic expansion for the generalized quark statistical distributin function in which quarks are introduced into Chao–Yang statistics is derived. Maythematical properties of the function are also examined.
A characteristic function approach to the discrete spectrum of electrically charged particles
Authors: Demiralp Metin
Published: March 2003

The purpose of this article is to obtain a scalar function the zeros of which give the discrete energy values for a system of electrically charged particles. The relation between the serial expansion of the characteristic function in powers of the system’s eigenvalue and the Stieltjes series has been revealed not only for the electrically charged particles but also generally for any positive (or negative) definite Hermitian operator which has only a discrete spectrum. The use of Padé approximants to express the characteristic function has offered a rapidly convergent scheme to evaluate the system’s eigenvalues. The first few elements of the Padé Table for the reciprocal of the characteristic function of certain systems have been given to verify the presented idea numerically. The determination of these elements needs the values of certain complicated integrals which we name ‘‘Zeroth Order Hyperspherical Spectral Coefficients’’ [HSC(φ0)]. The first two of these coefficients are investigated and their evaluation is realized analytically.
Perturbation expansion of S matrix for background scattering
Authors: Bosanac S.
Published: March 2003

The S matrix near a pole is parametrized into the contribution from the resonance and the background scattering. We develop a perturbation theory for the background scattering, based on the Jost function formalism. A closed expression is found up to the second order in the coupling strength between the channels. A brief comparison with the other formalism is also made and the advantages of the present theory are shown.
The free boson gas in a weak external potential
Authors: Pulè J. V.
Published: March 2003

The equation of state and the barometric formula for a free boson gas in a weak external potential are derived for very general potentials.
Compactificaton partly proven
Authors: Stacey Richard
Published: March 2003

For a restricted class of SU(2) gauge-field structures we show that only integral topological charges can occur, without making any assumptions about the asymptotic behavior of the fields.
Functional integrals in Navier–Stokes incompressible fluid turbulence
Authors: Rosen Gerald
Published: March 2003

A variational principle is formulated for the dynamical evolution of the Hopf characteristic functional Φ=Φ[y(x),t] by employing an appropriate functional integral over all parameter fields y(x). It follows that the ratio of functional integrals Γ≡∫Φ*Φ̇D(y)/∫‖Φ‖2D(y) is an exact constant of the motion during the decay of boundary-free Navier–Stokes incompressible fluid turbulence. Bearing the physical dimensions of inverse time, the constant of the motion Γ is a scalar function of the multipoint velocity correlation tensors embodied in Φ. For statistical situations such that the probability measure over the velocity-field ensemble is semi-Gaussian (i.e., the real part of ln Φ is a quadratic functional of y), Γ is evaluated explicitly in terms of the two-point velocity correlation tensor.
Critical behavior of the two-state doubling algorithm
Authors: Isaacson D. , Isaacson E. L. , Marchesin D. , Paes-Leme P. J.
Published: March 2003

We describe an algorithm which produces K2×K2 matrix approximations to the low energy part of the Schrödinger operator for N coupled oscillators. We carry out the algorithm analytically in the case K=2, for arbitrary N. In particular we show explicitly in this case how the N→∞ limit exhibits critical behavior.
Existence and asymptotic behavior of Padé approximants to the Korteweg–de-Vries multisoliton solutions
Authors: Liverani C. , Turchetti G.
Published: March 2003

The summation procedure of the Padé type is applied to the perturbation expansion of the solution of the potential Korteweg-de-Vries equation (K.d.V.), introduced by Rosales. For the N-soliton solution without background the [(n−1)/n] Padé approximants are shown to exist for n≤N. Their asymptotic behavior is investigated and it is found that it corresponds to a system of n solitons with the leading velocity parameters. The analogous results for the K.d.V. then follow in agreement with some previous numerical observations.
Manifestly parity invariant electromagnetic theory and twisted tensors
Authors: Burke William L.
Published: March 2003

We develop here the calculus of twisted tensors and in particular twisted differential forms, treating them as tensors with complementary orientations. These geometrical objects give us the proper language for electromagnetic theory in a 3-space plus time representation. The parity properties of the fields are simplified and many graphical illustrations are given.
Type-adapted subduction matrices
Authors: Kasperkovitz P.
Published: March 2003

If an irreducible representation is restricted to a subgroup it becomes reducible in general. The matrices transforming this reducible representation into a direct sum of irreducible constituents are called subduction matrices. Their structure is discussed for real, complex, and quaternionic representations where all these representations are assumed to show a peculiar structure characteristic for the type of this representation (character test +, 0, −). The choice of these type-adapted representations, a convention possible for all compact groups, considerably reduces the number of parameters needed to fix a subduction matrix.
An analytic formula for u(3)-boson matrix elements
Authors: Rosensteel G. , Rowe D. J.
Published: March 2003

The u(3)-boson Lie algebra is the liquid limit of the symplectic algebra sp(3, R). An analytic formula is given for the u(3)-boson matrix elements in irreducible unitary representations corresponding to the sp(3, R) discrete series. The formula also applies to the generators of the mathematically isomorphic, but physically different, interacting boson algebra.
Charged-particle off-shell scattering: common structure of all two-body off-shell scattering quantities for Coulomb plus rational separable potentials
Authors: van Haeringen H.
Published: March 2003

We establish a common structure of all two-body off-shell scattering quantities (expressed in momentum space or coordinate space) associated with Coulomb plus rational separable potentials. We present expressions in so-called maximal-reduced closed form, including new formulas: (i) for the off-shell Jost state for the Coulomb potential, (ii) for the off-shell Jost function associated with the Coulomb plus Yamaguchi potential, and (iii) for the scattering, regular, and Jost states in coordinate representation for Coulomb plus simple separable potentials for all l.
Cluster expansion of the distribution functions for a ground state Fermi system
Authors: Sinha S. K. , Singh Y.
Published: March 2003

The spin-averaged Slater sum of the fermion system is expanded in terms of the square of the ground state wavefunction of a boson system and the ‘‘antisymmetry’’ Ursell function. This expansion is used to obtain the cluster series for the radial distribution function of the fermion system in terms of (−𝒞(n)/S), where 𝒞(n) is sum of chains of (−f/S) and (−fhB2/S) bonds. The series is further expressed in a more compact form using a function L(n) defined by Eq. (55), and the ‘‘modified’’ FHNC approximation for the radial distribution function is presented.
Special properties of the irreducible representations of the proper Lorentz group
Authors: Srinivasa Rao K. N. , Gopala Rao A. V. , Narahari B. S.
Published: March 2003

It is shown that the finite- and infinite-dimensional irreducible representations ( j0, c) of the proper Lorentz group SO(3,1) may be classified into the two categories, namely, the complex-orthogonal and the symplectic representations; while all the integral-j0 representations are equivalent to complex-orthogonal ones, the remaining representations for which j0 is a half-odd integer are symplectic in nature. This implies in particular that all the representations belonging to the complementary series and the subclass of integral-j0 representations belonging to the principal series are equivalent to real-orthogonal representations. The rest of the principal series of representations for which j0 is a half-odd integer are symplectic in addition to being unitary and this in turn implies that the D j representation of SO(3) with half-odd integral j is a subgroup of the unitary symplectic group USp(2 j+1). The infinitesimal operators for the integral-j0 representations are constructed in a suitable basis wherein these are seen to be complex skew-symmetric in general and real skew-symmetric in particular for the unitary representations, exhibiting explicitly the aforementioned properties of the integral-j0 representations. Also, by introducing a suitable real basis, the finite-dimensional ( j0=0, c=n) representations, where n is an integer, are shown to be real-pseudo-orthogonal with the signature (n(n+1)/2, n(n−1)/2). In any general complex basis, these representations (0, n) are also shown to be pseudo-unitary with the same signature (n(n+1)/2, n(n−1)/2). Further it is shown that no other finite-dimensional irreducible representation of SO(3,1) possesses either of these two special properties.
Modeling quantum behavior with standard (nonquantum) probability theory
Authors: Bordley Robert F.
Published: March 2003

This paper argues that quantum behavior can be modeled using standard probability theory. To show this, such a model is constructed in which the Lagrangians associated with different paths are random. (This random Lagrangian formulation is equivalent to constrained entropy maximization.) We assume that the random error term varies as a harmonic oscillator over time. (We attribute this to certain properties of measuring devices.) The result is a formula which provides a good qualitative description of the n-slit interference experiment—indeed the formula is quite similar to the formulas of quantum mechanics. Hence standard probability theory models can describe interference effects so that a quantum probability theory is unnecessary.
The geometric foundations of the integrability property of differential equations and physical systems. I. Lie’s ‘‘function groups’’
Authors: Hermann Robert
Published: March 2003

This series of papers will attempt to discuss in a systematic way when the dynamical differential equations of a physical system have the ‘‘integrability’’ property. This first paper contains two topics: A description of some general properties of ‘‘function groups’’ and the related geometric structures of Poisson-cosymplectic manifolds; and the Lax representations for differential equations as a sort of ‘‘quantization’’ of Lie’s ‘‘function groups.’’ The general geometric setting of the ‘‘integrability’’ material in terms of the theory of Ehresmann pseudogroups is also described.
Higher-order special self-adjoint equations and particle dynamics
Authors: Reid James L. , Ray John R.
Published: March 2003

We exhibit a remarkable connection between a hierarchy of higher-order special self-adjoint ordinary differential equations and the description of motion of a cluster of particles in classical mechanics. The cluster is assumed to consist of equal mass particles all moving in one dimension. In a perturbation schema based on the first-order equation of motion of the center of mass point, the time evolution of the moments of order m−1 is governed by the solution of a special self-adjoint equation of order m. A similar connection exists for the moments of a wave packet in quantum mechanics.
Lagrange equations for a spinning gas cloud
Authors: Shieh S. Y.
Published: March 2003

Lagrange equations are derived for a spinning gas cloud. The rotational and vortex velocities are treated as independent variables and their defining equations as equations of constraint. Application of the formalism of Lagrange multipliers to this case of 27 variables and 18 equations of constraint yields nine final equations which are simple in form and contain only variables explicitly included in the kinetic and potential energy.
A group of coordinate transformations which preserve the metric of Weinhold
Authors: Salamon Peter , Ihrig Ed , Berry R. Stephen
Published: March 2003

Recently Weinhold described a natural metric on the state space of an equilibrium thermodynamic system. We describe the coordinate transformations which preserve both the first law of thermodynamics and this metric.
On topological boundary characteristics in nonabelian gauge theory
Authors: Cronström C. , Mickelsson J.
Published: March 2003

We study a topological classification of gauge potentials based on an examination of the Chern–Simons surface term C(U) at appropriate boundary components of the space-time manifold when the potential approaches a pure gauge dU U−1 at the boundary. We derive an explicit local formula for a 2-form H(U) such that C(U)=dH(U).
Positive-definite self-dual solutions of Einstein’s field equations
Authors: Lorenz-Petzold Dieter
Published: March 2003

We investigate (anti-) self-dual Riemann space-times for diagonal Bianchi types of class A with positive-definite metrics. A general algorithm to find self-dual solutions is presented. Explicit solutions are given for all types of class A.
Structure and motion of the Lee–Yang zeros
Authors: Nishimori Hidetoshi , Griffiths Robert B.
Published: March 2003

For an Ising model satisfying the Lee–Yang condition, the zeros of the partition function Z and those of the associated functions ZA in the space of imaginary magnetic fields at all lattice sites are determined by a single analytic hypersurface. The sense of motion of the zeros of Z as the interactions are varied can be related to the positions of the zeros of the ZA . Contrary to a plausible conjecture, it is not true that all of the zeros of Z in a uniform field tend towards the point ẑ=1 in the complex fugacity plane as the temperature is lowered, but it is possible that the first zero (that nearest to ẑ=1) has a monotone motion. Various simplicity and intertwining properties of the zeros of Z and ZA which generalize earlier results are proved by a new argument which makes direct use of the Lee–Yang property.
Graded tensor calculus
Authors: Scheunert M.
Published: March 2003

We develop a graded tensor calculus corresponding to arbitrary abelian groups of degrees and arbitrary commutation factors. The standard basic constructions and definitions, like tensor products, spaces of multilinear mappings, contractions, symmetrization, symmetric algebra, as well as the transpose, adjoint, and trace of a linear mapping, are generalized to the graded case and a multitude of canonical isomorphisms is presented. Moreover, the graded versions of the classical Lie algebras are introduced, and some of their basic properties are described.
The use of comparison filters in linear filter theory
Authors: Moses Harry E.
Published: March 2003

In the present paper, it is shown how the linear filter equation for a given correlation coefficient can be solved in terms of the solution of the filter equation with a different correlation coefficient. The second filter is called a comparison filter. One obtains an integral equation for the difference of the two filters in terms of the difference of the two correlation functions and the solution of the comparison filter. Thus if the comparison filter is known and its correlation coefficient is close to that of the desired filter, one may regard the comparison filter as being an approximation to it. The difference of the two filters is then small and perturbation expansions or variational principles for the difference may be expected to give better results than if one did not use a comparison filter. The difference in the solutions of the two filter equations may also be regarded as the change (or error) in the filter due to a change (or error) in the correlation coefficient. Our result is obtained by pressing the close analogy of the filter equation to the Gel’fand–Levitan equation of inverse spectral theory. Another result of the use of comparison filters is to show that the filter equation for the difference of filters satisfies a possibly useful grouplike property.
Dirac tensor distributions for moving submanifolds of R
n
Authors: Betounes David E.
Published: March 2003

This paper considers nonclassical fields (tensor distributions) of the form τδΩ̃, where δΩ̃ is the Dirac delta function for a moving p-dimensional submanifold of Rn (0≤ p≤n). The density τ is a classical (smooth), rank-k tensor field on Rn+1. The main result of the paper is the development of formulas for the distributional derivatives of such fields. The derivatives considered are the absolute differential (Levi-Civita connection), the covariant derivative along a given vector field, the divergence operator, the exterior differential, and the exterior codifferential. The resulting derived fields are shown to reflect the underlying geometry of the submanifold Ω as well as the nature of its motion. In the special case p=n, it is seen that the jump conditions on fields at the boundary of the region Ω arise naturally from the distributional calculus.
Generalized Hamiltonian dynamics. I. Formulation on T*Q⊕T
Q
Authors: Skinner Ray , Rusk Raymond
Published: March 2003

The Dirac–Bergmann generalized Hamiltonian dynamics for a degenerate-Lagrangian system is formulated on the Whitney sum T*Q⊕TQ of the phase space T*Q and the velocity space TQ over the configuration space Q. The formulation is related to those on T*Q and TQ. Some ambiguities concerning generalized dynamics that have appeared in the literature are clarified.
Generalized Hamiltonian dynamics. II. Gauge transformations
Authors: Skinner Ray , Rusk Raymond
Published: March 2003

Generalized Hamiltonian dynamics is the finite-dimensional version of gauge field theory and possesses invariance properties corresponding to gauge invariances. It is argued herein that a proper description of the finite-dimensional gauge transformations requires a time-dependent formalism. With this, local and global gauge transformations can be distinguished, and the insight obtained from this distinction clarifies some ambiguities that have appeared in the literature. In particular, the time-dependent formalism provides a precise statement for Dirac’s conjecture concerning the form of the generalized Hamiltonian on phase space.
B*-algebra representations in a quaternionic Hilbert module
Authors: Soffer A. , Horwitz L. P.
Published: March 2003

It is shown that the Gel’fand–Naimark–Segal (GNS) construction can be generalized to real B*-algebras containing an algebra *-isomorphic to the quaternion algebra by the use of quaternion linear functionals and Hilbert Q-modules. An extension of the Hahn–Banach theorem to such functionals is proved.
Conformal QED
Authors: Binegar B. , Fronsdal C. , Heidenreich W.
Published: March 2003

A conformally invariant quantum electrodynamics is constructed. The setting is realistic space-time (rather than Euclidean), and a complete Gupta–Bleuler quantization scheme is carried out. Conformal invariance of the quantum field theory (as opposed to either classical field theory or to a theory defined by its Feynman rules) requires a richer Gupta–Bleuler structure than has been considered previously. Yet the essential features of this structure are preserved. The requirement that the wave equation be of second order fixes a unique action that already contains the gauge-fixing terms that are required in any complete quantum field theory. The ‘‘Lorentz condition’’ turns out to be the transversality condition yαaα(y)=0 (in the manifestly covariant six-dimensional notation); this condition has to be treated in the same way as the Lorentz condition ∂μAμ(x)=0 (four-dimensional notation), as a boundary condition on the physical states.
On the Ohm–Navier–Stokes system in magnetohydrodynamics
Authors: Yoshida Zensho , Giga Yoshikazu
Published: March 2003

We study a mathematical structure of the Ohm–Navier–Stokes system that describes the incompressible dissipative evolution of a plasma. We apply the nonlinear semigroup theory and construct a unique regular solution which satisfies the system at least locally-in-time. We show that, for small initial data, this solution solves the system globally-in-time. We also introduce another scheme to construct solutions for less regular initial data.
Transformation coefficients of permutation groups
Authors: Chen Jin-Quan , Collinson David F. , Gao Mei-Juan
Published: March 2003

The eigenfunction method is used to calculate the transformation coefficients 〈[ν]m‖[ν],τ[ν1][ν2]m1 m2〉 from the Yamanouchi basis of the permutation group Sf1+f2 to the Sf1+f2⊃Sf1⊗Sf2 irreducible basis. A program in fortran is written, and tables of the transformation coefficients for the permutation group Sf up to f=6 are given. Possible applications of the transformation coefficients are sketched.
A new semiclassical interpretation of the Lamb shift
Authors: Barwick John T. F.
Published: March 2003

A modification of a previous semiclassical explanation of the Lamb shift is shown to be applicable to all levels in hydrogenic ions. The phenomenon responsible for the level shifts has not been considered explicitly in other quantum electrodynamic or semiclassical theories, but it is shown that it should be a source of observable energy changes. An approximate calculation for hydrogen s states gives ΔE1s=0.25748 cm−1 (experimental ΔE1s=0.2722 cm−1), ΔE2s=0.03755 cm−1 =1125.7 MHz (experimental ΔE2s=0.03528 cm−1), and ΔE3s=0.01166 cm−1 (experimental ΔE3s =0.0088 cm−1), but more important is the demonstration of an effect which should apparently be involved in any theory of the Lamb shift.
Conditions of existence for a class of self-dual solutions of the Einstein equations
Authors: Caderni N. , Martellini M. , Salmistraro F.
Published: March 2003

We study the integrability of the Einstein equations for a class of empty homogeneous space-times (Bianchi class A), once the self-duality constraints are imposed on the space-time itself. This system is integrable in the case of Bianchi type I and is a subset of Bianchi types VI0 and VII0. Bianchi type II space-times do not admit self-dual solutions and for the case of Bianchi VIII and IX we were unable to find a general integrability condition.
On Riemannian spaces with conformal symmetries or a tool for the study of generalized Kaluza–Klein theories
Authors: Moreschi Osvaldo M. , Sparling George A. J.
Published: March 2003

The Riemann geometry of a space with conformal symmetries is written in terms of intrinsic objects defined from the action of the symmetries. Its application in the study of generalized Kaluza–Klein theories is discussed.
Exact results for the diffusion in a class of asymmetric bistable potentials
Authors: Hongler M.-O. , Zheng W. M.
Published: March 2003

We solve the Fokker–Planck equations with drifts deriving from a class of asymmetric nonharmonic potentials which include bistable cases. An analytical expression for the probability current over the potential barrier is obtained. Finally, we compare our exact results with those obtained by Kramers’ approximation.
Multiple fiber bundles and gauge theories of higher order
Authors: Kerner Richard
Published: March 2003

We investigate a theory of gauge fields over multiple bundles, i.e., principal bundles constructed over base spaces which are principal bundles themselves. The Higgs–Kibble field is introduced geometrically, together with the quartic potential. Results of Forgács and Manton are interpreted in this scheme. We also discuss a spherically symmetric ansatz which yields the quartic potential introduced by ‘t Hooft.
Graded gauge theories over supersymmetric space
Authors: Kerner Richard , da Silva Maia Ema Manuela
Published: March 2003

We generalize the usual gauge theories, as well as the supergauge theories, in the following way. We construct a graded group associated with a compact semisimple Lie group G. This graded group contains G and the linear space of anticommuting G-spinors on which G acts through a highly reducible representation. The graded group generalizes the notion of the super-Poincaré group. Next we construct a fiber bundle the basis of which is the superspace, the structural group being the graded group. Then we introduce the connection, curvature, and calculate the corresponding Yang–Mills Lagrangian. The nontrivial content of such a theory is put forward if we impose the Grassmann parity condition on our connection and curvature; we supposed here that both Grassmann parities (i.e., the one in the superspace and that in the graded group) add up to define the Grassmann parity of the corresponding field components. Together with the Hermiticity condition this supergauge leaves almost no room for arbitrariness in the expansion of the superconnection; it contains only the usual gauge field, the adjoint Higgs multiplet, and the spinor multiplet belonging to the spinorial representation of G. The conformal symmetry of the Lagrangian is broken, and the mass terms appear for the Higgs scalar and the spinor multiplet. The Yukawa and current–current interactions are also obtained, together with the Fermi four-point interaction term. The theory yields the ratio of the Higgs scalar mass versus the bare spinor mass equal to 27/40; the strengths of other couplings depend on the group via the decomposition of the spinor multiplet into the irreducible representations.
Exact solutions to the valley problem in inverse scattering
Authors: Pechenick Kay R. , Cohen Jeffrey M.
Published: March 2003

Standard approximate methods involving the Abel integral equation do not allow the ionospheric electron density to be determined in the ‘‘valley’’ between two electron density peaks. Here we present analytic solutions to the Gel’fand–Levitan equation, which occurs in the exact full-wave inverse scattering theory. These exact analytic solutions exhibit multiple peaks in the electron density as a function of height and provide a solution to the valley problem.
Representations of the groups Sp(n,R) and Sp(n) in a U(n) basis
Authors: Klimyk Anatoli U.
Published: March 2003

The explicit expressions for the infinitesimal operators and the (finite) matrix elements with respect to a U(n) basis are obtained for the representations of the most degenerate series of Sp(n,R) and for the irreducible unitary representations of Sp(n) with the highest weights (M,0,...,0).
An integral transform related to quantization. II. Some mathematical properties
Authors: Daubechies I. , Grossmann A. , Reignier J.
Published: March 2003

We study in more detail the mathematical properties of the integral transform relating the matrix elements between coherent states of a quantum operator to the corresponding classical function. Explicit families of Hilbert spaces are constructed between which the integral transform is an isomorphism.
Covariance and geometrical invariance in *quantization
Authors: Arnal D. , Cortet J. C. , Molin P. , Pinczon G.
Published: March 2003

Several notions of invariance and covariance for * products with respect to Lie algebras and Lie groups are investigated. Some examples, including the Poincaré group, are given. The passage from the Lie-algebra invariance to the Lie-group covariance is performed. The compact and nilpotent cases are treated.
Interaction-set scattering equations
Authors: Kowalski K. L. , Picklesimer A.
Published: March 2003

The generalization of the pair-labeled Rosenberg equations for many-particle scattering are found in the case where there are arbitrary multiparticle interactions. These are called interaction-set equations because they involve auxiliary transition operators which are labeled by the same set of partitions which characterizes the various connectivities of the interparticle interactions. The technique which we employ also provides the analogous extension of a recently proposed set of connected-kernel multiple scattering equations for the Watson-type transition operators. Further, the structure of the interaction-set equations leads to the identification of an entire class of interaction-set connected-kernel scattering integral equations, each of which is based upon a distinct choice of unperturbed Green’s function and its associated connectivity structure. The generalized Rosenberg equations and the connected-kernel Watson-type multiple scattering equations, which are limiting members of this class, correspond to the choice of the N-free-particle and two-cluster-channel unperturbed Green’s functions, respectively.
Improvement of the Froissart–Martin bound for complex scattering angles
Authors: Chaichian Masud , Fischer Jan , Nelipa N. F. , Vrkoč Ivo
Published: March 2003

Extension of the Froissart–Martin bound for complex scattering angles is improved using the solution of the Dirichlet boundary value problem for doubly connected domains. The Froissart–Martin bound for physical scattering angles is used as input value on one of the two boundaries. The obtained bound is valid in an ellipse smaller than the Lehmann–Martin one. Possibilities for further improvements and applications are discussed.
Plane symmetric charged dust distribution
Authors: De Utpal Kumar , Ray Dipankar
Published: March 2003

An attempt is made to obtain the complete set of solutions of Einstein’s equations for a nonstatic charged dust distribution with a comoving system of coordinates and the most general plane symmetric metric, i.e., ds2=exp [2u(x,t)]dt2 −exp[2v(x,t)]dx2−exp [2w(x,t)](dy2+dz2). The field equations have been reduced to a single ordinary differential equation which is integrated in a particular case.
Boundary effects in the dimer problem on a non-Bravais lattice
Authors: Grensing D. , Grensing G.
Published: March 2003

The dimer problem on the hexagonal lattice is solved for various boundary shapes. The number of arrangements of dimers in the asymptotic limit of large lattices proves to be very sensitive to the precise form of the lattice boundary. If N is the number of lattice points and (for large N) WN/2 the number of dimer configurations, then the molecular freedom W reduces to 1 in the case of standard boundaries (parallelogram, rectangle), and there is, in the thermodynamic limit, no freedom in placing a dimer at all. But in the case of a hexagonal lattice which has been given the shape of a macroscopic honeycomb and which thus exhibits the symmetry properties of the unit cell, the molecular freedom is found to tend to W=(3/4)√3 =1.299 for N→∞. Investigating various other boundary forms, the regular hexagon proves to be a convenient surface shape with a maximum molecular freedom which differs markedly from the known value W=1.381 for the hexagonal lattice wrapped on a torus.
Factorized S matrices and generalized Baxter models
Authors: Bovier Anton
Published: March 2003

We prove that solutions of the factorization equations for S matrices with Zn symmetry can be given in terms of theta functions. We present a class of vertex models based on A-symmetric S matrices (A being an abelian group) as natural generalizations of the Baxter model. The mapping of these models into spin systems is described.
Mechanisms of the ‘‘fermion–boson reciprocity’’
Authors: Garbaczewski Piotr
Published: March 2003

We analyze two completely integrable quantized systems: the nonlinear Schrödinger and sine–Gordon ones, with the aim explicitly to recover the (spin-1/2 approximation) mechanisms responsible for their being allowed in the continuum limit equivalence with Fermi systems.
Complex, self-dual Euclidean SU(2) gauge fields with finite real actions
Authors: Chakrabarti A. , Comtet A. , Koukiou F.
Published: March 2003

A class of complex, self-dual Euclidean SU(2) gauge field configurations are obtained. The action is finite and real. In a simple scaling limit, of infinite action, this class reduces to the complex, static monopoles of Manton. Various special features of these solutions are discussed.
Some solutions of the Yang–Mills equations generalizing the Wu–Yang monopole
Authors: Hogan P. A.
Published: March 2003

We present a new form of the Wu–Yang magnetic monopole solution of the SU(2) Yang–Mills equations on S2 which is generalized to yield a solution of the SU(n+1) Yang–Mills equations on CPn for each integer n≥1.
Normalization of Bethe-ansatz states in the chiral-invariant Gross–Neveu model
Authors: Destri C. , Lowenstein J. H.
Published: March 2003

The norms of the Bethe-ansatz eigenstates of the chiral-invariant Gross–Neveu Hamiltonian are calculated.
External boundary perturbations in neutron transport theory
Authors: Rahnema F. , Pomraning G. C.
Published: March 2003

Two formalisms are presented for estimating the change in the fundamental eigenvalue (the criticality) of the neutron transport equation due to a perturbation in the exterior boundary of the system. The first-order perturbation formulas are derived within the context of energy-dependent transport theory and its energy-dependent diffusion approximation. Several numerical examples are given.
Strong fluctuations in the spinor wave optics. Intensity covariance function
Authors: Hillion P. , Quinnez S.
Published: March 2003

In this paper, which is a continuation of the preceding paper, we consider in the framework of the spinor wave optics the intensity covariance function of a light field propagating in a strong turbulent medium. In the preceding paper, for the second-order moments we had a 4-vector corresponding to intensity and to the Poynting vector; similarly, here we obtain a second-rank tensor with 16 components. But we limit ourselves to the zeroth-order approximation with respect to the parameter ε=ω0l−1, where ω0 is a transverse characteristic of the light beam and l the diffraction length. So only four components are needed, and provided that a particular assumption is made on the statistical behavior of the light beam, we get for the intensity covariance function the usual result obtained for a plane wave in the framework of the parabolic approximation. The interpretation of this result is discussed.
Real axis integration of Sommerfeld integrals with applications to printed circuit antennas
Authors: Katehi P. B. , Alexopoulos N. G.
Published: March 2003

Printed circuit antennas are becoming an integral part of imaging arrays in microwave, millimeter, and submillimeter wave frequencies. The electrical characteristics of such antennas can be analyzed by solving integral equations of the Fredholm first kind. The kernel involves Sommerfeld integrals which are particularly difficult to solve when source and field points lie on an electrical discontinuity, as it occurs in the determination of the characteristics of printed circuit antennas. An analytic-numeric real axis integration technique has been developed for such integrals and it is combined with piece-wise sinusoidal expansions to solve the Fredholm integral equation for the unknown current density.
A generalized Weyl correspondence. II. Some general results
Authors: Gadella M.
Published: March 2003

After defining a generalized Weyl correspondence, we give some general results. These are presented as comments on a theorem. They mainly refer to the finite-dimensional, unbounded, and non-self-adjoint cases.
On the correspondence between classical and quantum mechanics. I
Authors: Prosser Reese T.
Published: March 2003

We consider here a general procedure for implementing the correspondence between classical and quantum mechanical systems of finitely many degrees of freedom. We show that corresponding systems may be formulated within a common framework in such a way that the kinematic, statistical, dynamical, and covariance features may be easily compared.
Angular momentum analyticity of Schrödinger energy levels for quark confining potentials
Authors: Datta D. P. , Mukherjee S.
Published: March 2003

Using the Kato–Rellich perturbation theory for linear operators, the analyticity of the Schrödinger energy levels En(l) in the half-plane Re l>− 1/2 has been proved for a large class of quark-confining potentials.
Partitioning ‘‘opposite’’ bounds for potential scattering phase shifts
Authors: Abdel-Raouf M. A.
Published: March 2003

It is shown that the partitioning technique (PT) provides us with upper (lower) bounds for the scattering phase shifts under the same conditions where Schwinger’s variational method (SVM) leads to lower (upper) bounds.
Symmetries of stationary axially symmetric vacuum Einstein equations and the new family of exact solutions
Authors: Nakamura Yoshimasa
Published: March 2003

A new family of exact solutions of the stationary axially symmetric vacuum Einstein equations is presented. The internal symmetries, SL(2,R) rotation, and duality of parametrization, are combined to construct a Bäcklund transformation. For the special ansatz of the field equations, the Bäcklund transformation can be integrated and the hierarchy of ansatz is generated, recursively. The Riemann–Hilbert problem is also discussed for the inverse scattering formulas generating nonlocal symmetries.
A unified theory of the point groups. IV. The general corepresentations of the crystallographic and noncrystallographic Shubnikov point groups
Authors: Kim Shoon K.
Published: March 2003

A new system of classification for all the Shubnikov point groups Gs is presented, which is best suited for describing their isomorphisms as well as their construction. By the new classification and the modified form of the corepresentations, there are presented the simple general expressions of the irreducible corepresentations for the 10 minimum sets of proper Gs, from which all coirreps of the remaining Gs follow. (Icosahedral groups are excluded.)
The Racah algebra for groups with time reversal symmetry. III
Authors: Newmarch J. D. , Golding R. M.
Published: March 2003

The coupling of basis vectors and the recoupling of irreducible corepresentations is considered. The difference between the coupling coefficient and 3jm tensors leads to a variety of 6j and recoupling tensors.
On the symmetries of the 6j symbol
Authors: Newmarch J. D.
Published: March 2003

The 6j tensor for compact groups is shown to transform as a basis vector for the identity representation of the permutation group S4. This allows character theory to be used to determine the minimum number of independent components and a projection operator to determine the relations between components—the symmetry properties.
The Clebsch–Gordan coefficients of the three-dimensional Lorentz algebra in the parabolic basis
Authors: Basu Debabrata , Wolf Kurt Bernardo
Published: March 2003

Starting from the oscillator representation of the three-dimensional Lorentz algebra so(2,1), we build a Lie algebra of second-order differential operators which realizes all series of self-adjoint irreducible representations. The choice of the common self-adjoint extention over a two-chart function space determines whether they lead to single- or multivalued representations over the corresponding Lie group. The diagonal operator defining the basis is the parabolic subgroup generator. The direct product of two such algebras allows for the calculation of all Clebsch–Gordan coefficients explicitly, as solutions of Schrödinger equations for Pöschl–Teller potentials over one (𝒟×𝒟), two (𝒟×𝒞), or three (𝒞×𝒞) charts. All coefficients are given in terms of up to two 2F1 hypergeometric functions.
Upper and lower bounds for eigenvalues of nonlinear elliptic equations: I. The lowest eigenvalue
Authors: Benguria Rafael , Depassier M. Cristina
Published: March 2003

We give a method for finding bounds for the lowest eigenvalue of nonlinear elliptic equations with monotone, local, nonlinearities. This is an extension to nonlinear problems of Barta’s method for linear elliptic operators.
Evolution equations with high order conservation laws
Authors: Abellanas L. , Galindo A.
Published: March 2003

An asymptotic algorithm presented in a previous paper is applied to investigate the possible structures of evolution equations ut=uM+K(u,...,uM−1),  M=3,5, which could be compatible with the existence of a conserved density ρ0(u), depending only on u, and with the existence as well of conserved densities with arbitrarily high-order derivatives. For M=3 it is shown that the Calogero–Degasperis–Fokas equation is essentially the only nonpolynomial equation of that type. For the case ut=D[u4+Q], with Q(u,...,u3) a polynomial, we find a very narrow class of admissible structures for Q, typified by the few particular examples known up to date. Actually, there is in this case an essentially unique structure, modulo a Miura transformation.
Kaluza–Klein theories on bundles with homogeneous fibers. I
Authors: Percacci R. , Randjbar-Daemi S.
Published: March 2003

We analyze some geometric aspects of Kaluza–Klein theories under the assumption that the (4+d)-dimensional space is a bundle over space–time M with fiber G/H. We formulate the most general metric in the bundle which leads, upon dimensional reduction of the Ricci scalar, to a G-gauge invariant Lagrangian. We find that the treatment of Brans–Dicke-like scalars given by some authors is inconsistent with the bundle-theoretic interpretation.
Error estimates of solutions and mean of solutions of stochastic differential systems
Authors: Ladde G. S. , Sambandham M.
Published: March 2003

Stochastic differential equations are considered. Estimates in terms of statistical properties are given for the difference between the solutions and solutions of the mean of stochastic differential systems. For this purpose necessary theorems are developed and sufficient conditions are given to obtain error estimates. A few examples are worked out to demonstrate the usefulness of the results.
Explicit suspensions of diffeomorphisms—An inverse problem in classical dynamics
Authors: Channell Paul J.
Published: March 2003

Presented in this paper is a set of explicit prescriptions for associating with a given map of Rn, which is C2-isotopic to the identity, a time-dependent vector field whose time-1 map is the given one. Also shown is how to apply additional restrictions to the vector field including that it be (1) periodic in time, (2) Hamiltonian, and (3) of potential form; several examples show numerical verification of the theory.
Operator formalism equivalent to the Feynman quantization technique
Authors: Janiš V. , Souček J. , Souček V.
Published: March 2003

The concept of a Fock–Stueckelberg space of quantum states and a procedure of an operator quantization using only Lagrangians (kinematical quantization) are introduced. A propagator operator 𝒦, matrix elements of which are Green’s functions, is used, and an equation of motion for it is derived. We prove that kinematical quantization is an operator (coordinate-free) form of the Feynman quantization technique. The Feynman path integral (FPI) is obtained as a spectral representation of the operator 𝒦 in a coordinate basis. The connection of a representation of commutation relations in this scheme, the domain of integration in FPI, and causality is mentioned.
A generalization of Cohen’s theorem
Authors: Groblicki Roman
Published: March 2003

The theorem due to L. Cohen, which implies that quantum mechanics cannot be formulated as a stochastic theory in phase space, is generalized. The assumption that the phase-space representatives of the density operators satisfy the quantum mechanical marginals is replaced by the weaker condition of Ω-representability.
Weight vector representatives for SO(2N)
Authors: Soni S. K.
Published: March 2003

Following Mohapatra and Sakita, it is convenient to rewrite the algebra of 2Nγ-matrices in terms of N annihilation operators and N creation operators. We find them useful in representing weight vectors in the spinorial σN σNc and the irreducible subcomponents of σN×σN and σN×σNc operators. Though their Dynkin labels are readily accessible, a natural basis for the enumeration of their complete set of weights is given by N positive weights of the vectorial representation. Their subgroup content under SU(N)⊆SO(2N) and SO(2m)⊗SO(2N−2m)⊆SO(2N) is made obvious by using a simple identity. Conjugation and Yukawa couplings are touched on briefly.
Cartesian polytensors
Authors: Applequist Jon
Published: March 2003

A Cartesian polytensor is defined as a set of Cartesian tensors in a sequence of increasing rank. A matrix formulation of polytensors is given to express arrays of direct tensor products and series of tensor contractions in concise form. The transformation of a polytensor under rotation of coordinate axes is shown to be accomplished by means of an orthogonal matrix. The special properties of compressed polytensors, composed of totally symmetric tensors with redundant components deleted, are demonstrated. The use of polytensors is illustrated by an application to the problem of interactions among polarizable electric charge distributions.
On the 3j symmetries
Authors: Newmarch J. D.
Published: March 2003

The symmetry properties of the 3jm tensor for any finite or compact linear group are discussed using a wreath product construction. This is shown to provide a complete group theoretic explanation for all symmetry properties whether ‘‘essential’’ or ‘‘arbitrary.’’ The link with the similar—but distinct—method of inner plethysms is considered.
A theorem on orbit structures (strata) of compact linear Lie groups
Authors: Sartori G.
Published: March 2003

We present a comprehensive constructive proof of a theorem characterizing the tangent space to a stratum (orbit structure) of the Euclidean space Rn, seat of an orthogonal representation of a compact group G. The characterization is made in terms of gradients of a complete set (integrity basis) of G-invariant polynomials. In a recent paper [M. Abud and G. Sartori, Phys. Lett. B 104, 147 (1981)], the theorem, which may be considered a generalization of a theorem by Michel [C. R. Acad. Sci. Ser. A 272, 433 (1971)], has been shown to be effective in the determination of the equations of the strata and in the determination of natural extrema of G-invariant functions.
A coordinate-free derivation of a generalized geodesic deviation equation
Authors: Swaminarayan N. S. , Safko J. L.
Published: March 2003

A simple, coordinate-free exact derivation of the geodesic deviation equation is given. This result includes the possibility of nonvanishing torsion. We then show that this form of the geodesic deviation equation can be specialized to various results given previously in the literature.