bluuebunny/crossref_metadata_2025 huggingface dataset:
Optimal control of the decay of nonequilibrium statistical correlations
Authors: Lavenda B. H.
Published: March 2003

A quasithermodynamic interpretation of the stochastic control of irreversible thermodynamic diffusion processes is presented in which the drift is the control parameter. The joint entropy, considered as a function of the initial data is the negative of the optimal expected total cost, and the generalized Hamilton–Jacobi equation, which it satisfies, is the dynamic programming equation for the optimal stochastic drift control. The two cost functions, proposed by Yasue, are shown to differ by a stochastic gauge transformation and constitute equivalent variational problems. Yasue’s results are shown to apply in two limiting cases: the asymptotic time limit, where the nonequilibrium statistical correlations have worn off, or the weak noise limit, where random thermal fluctuations have a negligible importance. The asymptotic expected total cost is governed by a minimum relative entropy principle and the goodness of the thermodynamic drift control in the stochastic problem is determined.
The stochastic H-theorem
Authors: Santamato E. , Lavenda B. H.
Published: March 2003

The stochastic analogue of the generalized H-theorem is formulated for multidimensional, time homogeneous diffusion processes which asymptotically are characterized by an invariant probability distribution. It applies to both isolated and open thermodynamic systems, the latter being characterized by rotational probability currents. The physical mechanism for the monotonic behavior of the stochastic H-function in time is linked to the decay of statistical correlations between a given nonequilibrium state and those through which the system passes at successive instants in time.
Real solutions of the Yang–Mills field equations in Minkowski space
Authors: Kyriakopoulos E.
Published: March 2003

A system of nonlinear partial differential equations is obtained by considering complex self-dual Yang–Mills fields in Minkowski space and then selecting those fields whose real part is again a solution of the Yang–Mills field equations. From solutions of this system families of real solutions of the Yang–Mills field equations in Minkowski space are obtained, which depend on one or more arbitrary solutions of the two-dimensional Laplace equation and one or more arbitrary functions.
Spacetime metric and Yang–Mills fields unified in a Galilean subspace structure
Authors: Coleman Robert Alan , Mann Robert B.
Published: March 2003

A novel approach to the unification of spacetime metric and Yang–Mills fields is presented. The spacetime metric field appears naturally as part of a first order G-structure, a Galilean subspace structure on a world manifold of higher dimension. There is an a priori distinction between internal space dimensions and spacetime dimensions. The prolongation of the first order Galilean subspace structure to second order is a principal bundle of second order coframes which has additional degrees of freedom in the second order part of its gauge group. The Yang–Mills fields are defined in a natural way as second order gauge fields by a reduction of the second order Galilean subspace structure. The Yang–Mills fields appear as part of a connection on the world manifold rather than on the spacetime manifold. The kinematic foundations of the new model are analyzed using the theory of G-structures and their prolongations. Kaluza–Klein models are also discussed from the G-structure viewpoint and compared with the Galilean subspace model.
Scattering by slightly nonspherical particles in the high frequency limit. II. Transparent particles
Authors: Krebs Jerome
Published: March 2003

The scattering of a scalar plane wave by a slightly nonspherical transparent particle is investigated using a combination of boundary perturbation theory, the Debye expansion, and the modified Watson transformation. Boundary perturbation theory is used to find the perturbed scattering matrix for the problem. The Debye expansion is then substituted into the perturbed S matrix and the modified Watson transformation is used to sum the resulting partial wave expansion in the short wavelength limit. This method is applied to backscattering by a sphere whose shape is perturbed by making the radius a function of θ given by rp(θ)=a[1+δP2(cos θ)], where a is the radius of the unperturbed sphere, δ is the perturbation parameter, and P2 is a Legendre function. This method will be valid when both (ka)1/3≫1 and ‖N−1‖1/2≫1. where k is the wavenumber and N is the index of refraction of the particle.
Large momentum behavior of the Feynman amplitudes in the φ44 -theory
Authors: Pohlmeyer K.
Published: March 2003

The complete asymptotic expansion of the Feynman amplitudes for large values of the scale parameter is derived in the φ44 -theory for Euclidean and Minkowski metrics.
Representation of the active Lorentz transformation for particle dynamics
Authors: Fradkin David M.
Published: March 2003

The rank-2 tensor representation of a passive Lorentz transformation constructed by Krause solely from the four-velocities of two inertial observers is shown to lack sufficient generality to describe unambiguously the active Lorentz transformation completely specifying the dynamic change of a classical particle from an initial state to a later state. This lack of uniqueness is traced to an arbitrary three-parameter little group transformation. For states described both by their four-vector momentum and polarization, we construct a rank-2 tensor representation of the active Lorentz transformation, connecting initial and later states, which is constructed solely from initial and later momenta and polarizations. This representation now contains a single arbitrary parameter. A unique active Lorentz transformation is achieved by further specification of an additional four-vector associated with the initial and later states.
What happens to the position, spin, and parity when the mass goes to zero
Authors: Jordan Thomas F.
Published: March 2003

The unitary transformation to the helicity form and the limit of zero mass are examined in terms of the position, spin, parity and time-reversal operators for an irreducible unitary representation of the Poincaré group for positive mass. The position, spin, parity and time-reversal operators do not change as the mass goes to zero, but if the space of particle states becomes smaller as the Poincaré group is reduced to a separate representation for each helicity, the position and spin operators, which are not reduced, will no longer be defined on the particle states. Since the parity operator connects states of opposite helicity, it will be defined on the particle states if they have paired plus and minus helicities.
Anomaly-free complex representations in SU(N)
Authors: Eichten Estia , Kang Kyungsik , Koh In-Gyu
Published: March 2003

We have found all irreducible, anomaly-free and complex representations of SU(N) up to dimension 4×109 and SU(16). None of these representations are asymptotically free. For each SU(N), we have given a complete list of complex reducible representations which satisfy both asymptotic and anomaly freedom. Applications of such solutions are briefly discussed.
Viscous fluid interpretation of electromagnetic fields. II
Authors: Raychaudhuri A. K. , Saha S. K.
Published: March 2003

The paper examines the possibility of interpreting the energy-stress tensor of an electromagnetic field with or without a perfect fluid as due to a viscous fluid without any electromagnetic field. Some results obtained previously by Tupper are recovered and the time irreversibility brought about by viscosity is emphasized.
Electron motion in longitudinal electromagnetic fields
Authors: Bagrov V. G. , Githman D. M. , Shapovalov V. N.
Published: March 2003

A complete study of a charged particles motion in such electromagnetic fields, where vectors of electric and magnetic fields are parallel to each other and to some constant vector, is made. It lists all classes of fields, permitting the solution of the problem by the method of separation of variables, and all concrete kinds of fields in which Dirac’s and Klein–Gordon’s equations can be expressed through the known specifications and are given for the first time.
On the polynomial first integrals of certain second-order differential equations
Authors: Gascón F. G. , Ramos F. B. , Aguirre-Daban E.
Published: March 2003

It is shown that any first integral of type P2(ẋ)—a polynomial of degree 2 in ẋ—of the differential equation ẍ=Vx can be obtained from a pointlike gauge symmetry of the action AL associated to L= 1/2 ẋ2+V(t,x). The same result holds for any first integral of kind Pn(ẋ) when dynamical symmetries of AL polynomials in ẋ are allowed. The neccessary and sufficient conditions that V(t,x) must satisfy in order that ẍ=Vx possesses a first integral of type Pn(ẋ) have been obtained. These conditions reduce (when n=2) to a condition obtained by Leach. The computational advantages and difficulties which appear in order to obtain first integrals for type Pn(ẋ) are also briefly discussed.
The inverse scattering problem for L
C
R
G transmission lines
Authors: Jaulent M.
Published: March 2003

The inverse scattering problem for one-dimensional nonuniform transmission lines with inductance L(z), capacitance C(z), series resistance R(z) and shunt conductance G(z) per unit length (z∈R) is considered. It is reduced to the inverse scattering problem for the Zakharov–Shabat system. It is found that one can construct from the data the following functions of the travel time x: q̃±(x)=[(1/4)(d/dx)(ln(L/C))±(1/2)(R/L−G/C)] ×exp(∓∫x∞(R/L+G/C)dy).
Two-dimensional scattered fields: A description in terms of the zeros of entire functions
Authors: Manolitsakis I.
Published: March 2003

A general description of n-dimensional Fourier transforms is given in terms of their complex zero surfaces. The properties of these surfaces are analyzed and then applied to two-dimensional scattered electromagnetic fields in the Fraunhofer region. It is shown that the properties of two-dimensional fields differ inherently from those of one-dimensional fields and that they lead to a reduced ambiguity for object reconstruction from intensity data. A way of estimating this ambiguity is given.
Implementation of automorphism groups in certain representations of the canonical commutation relations
Authors: Warchall Henry A.
Published: March 2003

Necessary and sufficient conditions are given for the unitary implementability of one-parameter unitary groups of one-particle automorphisms of the CCR algebra in representations symplectically related to the Fock representation. The criteria become particularly simple when the one-particle generator of the unitary group is positive and bounded away from zero; in this case the automorphism group is unitarily implementable only in the representations unitarily equivalent to the Fock representation. If the spectrum of the generator includes zero, however, the situation is more complicated; there then exist representations inequivalent to the Fock representation which admit unitary implementation of the automorphism group. It is also shown that whenever implementation of the automorphism group is possible, the implementing operators can be chosen to be a strongly continuous unitary group, guaranteeing the existence of a ‘‘second-quantized’’ self-adjoint generator.
Irreducible representations of the superalgebras type II
Authors: Hurni J.-P. , Morel B.
Published: March 2003

The representation of the orthosymplectic algebras and the other members of their class are built explicitly, with simple techniques.
Reduction of tensor products with definite permutation symmetry: Embeddings of irreducible representations of Lie groups into fundamental representations of SU(M) and branchings
Authors: Schellekens A. N. , Koh In-Gyu , Kang Kyungsik
Published: March 2003

We consider tensor products made out of a number of identical copies of the defining representations of Lie groups that are asymptotically free and complex. Decomposition of the tensor products into the terms with definite permutation symmetry is made by using the index sum rules and the congruence class. The results can also be used to find the branchings of SU(M) into a Lie group G, where M is equal to the dimension of the defining representation of G. Application of our results to preon dynamics is indicated in two examples.
A class of discontinuous integrals involving Bessel functions
Authors: Schwartz Charles
Published: March 2003

A general theorem, which appears to be newly discovered although it is of a very classical sort, gives simple evaluations for a large class of infinite integrals containing Bessel functions in product with other suitably constrained analytic functions.
The commutant of a multiplication operator
Authors: Nasr A. H.
Published: March 2003

We determine the class of all operators commuting with a multiplication operator defined by a general piecewise continuous strictly monotonic function.
Fractional approximations for linear first-order differential equations with polynomial coefficients—application to E1(x)
Authors: Martin Pablo , Zamudio-Cristi Jorge
Published: March 2003

A method is described to obtain fractional approximations for linear first-order differential equations with polynomial coefficients. This approximation can give good accuracy in a large region of the complex variable plane that may include all of the real axis. The parameters of the approximation are solutions of algebraic equations obtained through the coefficients of the higher and lower powers of the variable after the substitution of the fractional approximation in the differential equation. The method is more general than the asymptotical Padé method, and it is not required to determine the power series or asymptotical expansion. A simple approximation for the exponential integral is found, which gives three exact digits for most of the real values of the variable. Approximations of higher accuracy than those of other authors are also obtained.
Maximum of the spin-flip cross section from unitarity and four constraints
Authors: Sakmar I. A.
Published: March 2003

The upper bound on the spin-flip cross section is improved by adding a fourth constraint in a variational calculus. The total cross section, elastic cross section, the forward slope, and the backward slope of the imaginary part of the amplitude form the equality constraints. In addition the unitarity of the partial waves gives inequality constraints.
The electric double layer and electrohydrostatic surface deformation
Authors: Cade R.
Published: March 2003

A study is made of the equilibrium configuration of a liquid surface under surface tension and gravity when additionally, the liquid is electrically conducting, is under a given electrostatic field, and has at the surface an electric double layer. The essential element here is the presence of the double layer, making the problem real in the sense of being distinct from what could be approached by the classical methods, and requiring the application of relatively recent considerations concerning electrostatic force in a continuum. From the point of view of applications, the significant feature is the prediction of a double-layer effect whose dependence upon the field is essentially linear, as compared with the quadratic, purely classical effect, and in specific problems that are solved, quantitative results in this respect are obtained, of possible use experimentally.
Geometric quantization and representations of semisimple Lie groups: spin (2,1) and spin (2,2)
Authors: Sitaram B. R. , Tripathy K. C.
Published: March 2003

The UIR’s of spin (2,1) and spin(2,2) are studied in the light of Kostant–Auslander induction scheme, and compared with those obtained earlier by Harish–Chandra and Schmid.
The Riccati equation and Hamiltonian systems
Authors: Guerrero F. Guil
Published: March 2003

The involutive system of functionals associated by Gel’fand and Dikii to a nth-order scalar differential operator is obtained from a set of solutions of a generalized Riccati equation. These solutions allow us to explain the involutive character of the system of functionals in terms of the Riccati equation properties only.
A global isometry approach to accelerating observers in flat space–time
Authors: Urani John R. , Kemp Marilyn H.
Published: March 2003

A global two-point diffeomorphic extension of Lorentz transformations is constructed which preserves the global Lorentzian metric structure of flat R4. This global mapping induces, as a tangent-space mapping, instantaneous Lorentz transformations parametrized by interframe velocity functions. The elimination of pseudoterms from particle and electromagnetic field equations leads to an exact analytic expression for the affine connection needed for covariant differentiation. Examination of invariant particle equations gives an obvious proof of the equivalence principle in terms of the symmetric part of the acceleration-group connection. Transformation properties of the connection coefficients are shown to be in accord with general covariance requirements. The specific case of the rotating observer is treated exactly where it is seen that the affine connection merely supplies the exact Thomas precession term. Recent work by DeFacio et al. is found to be especially convenient for comparison with the present work. The results of the two approaches agree precisely. A summary of results indicates that the global isometry approach gives results consistent with those obtained via presymmetry arguments.
Random walks on lattices. The problem of visits to a set of points revisited
Authors: Rubin Robert J. , Weiss George H.
Published: March 2003

A general method is outlined for calculating the statistical properties of the number of visits to a set of points in a random walk. In illustrative examples, known results and new results are easily derived.
Hypervirial calculation of integrals involving Bessel functions
Authors: Fernández F. M. , Mesón A. , Castro E. A.
Published: March 2003

A general and simple procedure is presented for evaluating matrix elements that involve Bessel functions. The method is based upon hypervirial relationships for systems subjected to Dirichlet boundary conditions.
Poincaré–Cartan integral invariant and canonical transformations for singular Lagrangians: An addendum
Authors: Dominici D. , Gomis J.
Published: March 2003

The results of a previous work, concerning a method for performing the canonical formalism for constrained systems, are extended when the canonical transformation proposed in that paper is explicitly time dependent.
Structure of asymptotic twistor space
Authors: Lugo Gabriel
Published: March 2003

We show that asymptotic projective twistor space 𝒫𝒯+ is an Einstein–Kähler manifold of positive curvature. We then use the Chern–Moser theory of hypersurfaces in complex manifolds to show that the Kähler curvature of 𝒫𝒯+ closely related to the CR curvature of its boundary. We also give a proof that the Kähler potential function defining the boundary satisfies the complex Monge–Ampere equations.
Coupled translational and rotational diffusion in liquids
Authors: Steiger Ulrich , Fox Ronald F.
Published: March 2003

The equations for coupled translational and rotational diffusion of asymmetric molecules immersed in a fluid are obtained. The method used begins with the Kramers–Liouville equation and leads to the generalized Smoluchowski equation for diffusion in the presence of potentials. Both external potentials and intermolecular potentials are considered. The contraction of the description from the Kramers–Liouville equation to the Smoluchowski equation is achieved by using a combination of operator calculus and cumulants. Explicit solutions to these equations are obtained for the two-dimensional case. Comparison of our results with earlier literature is also presented.
Simple multiple explode–decay mode solutions of a two-dimensional nonlinear Schrödinger equation
Authors: Nakamura Akira
Published: March 2003

Multiple similarity type explode-decay mode solutions of a two-dimensional (≡2D) nonlinear Schrödinger (≡NLS) equation have been obtained by the bilinear method. From the three examples of the 2D-KdV equation, ordinary cubic 2D-NLS equation, and the present 2D-NLS equation, the expectation is presented such that ’’any 2D nonlinear evolution equation which has multiple soliton solutions simultaneously has simple self-similar-type multiple explode-decay mode solutions so far as the equation has self-similar symmetry.’’
A generalization of the Dirac equation to accelerating reference frames
Authors: Urani John R. , Kemp Marilyn H.
Published: March 2003

Using a recently developed global isometry method for treating accelerating observers, the induced tangent space transformation on flat Lorentzian R4 is mapped homomorphically onto a time-dependent D(1/2,0) ⊕ D(0,1/2) representation of SL (2,C). The Dirac equation is shown to take on pseudoterms via this mapping. Eliminating the pseudoterms by identifying an affine connection, an exact analytic expression for the covariant derivative is found for general cases of arbitrary C2 timelike observers. The transformation properties of the connection are shown to satisfy the conditions imposed by a general tetrad formalism. The specific case of the rotating observer is considered wherein the exact expression for the boosted Dirac equation is found.
The stationary coordinate systems in flat spacetime
Authors: Letaw John R. , Pfautsch Jonathan D.
Published: March 2003

The stationary metrics in flat spacetime are derived using a recent classification of the timelike Killing vector field trajectories. The metrics fall into six classes. A ’’simple’’ coordinate system from each class is selected as representative. Three of these systems are rectangular Minkowski coordinates, pseudocylindrical (’’accelerating’’) coordinates, and rotating coordinates. The remaining three appear to be new coordinate types which will be useful in exploring coordinate-dependent effects in quantum field theory.
Singular boundaries of space–times
Authors: Geroch Robert , Can-bin Liang , Wald Robert M.
Published: March 2003

We give an example of a causally well-behaved, singular space–time for which all singular-boundary constructions which fall in a certain wide class—a class which includes both the g-boundary and b-boundary—yield pathological topological properties. Specifically, for such a construction as applied to this example, a singular boundary point fails to be T1-related to an event of the original space–time. This example suggests that there may not exist any useful, generally applicable notion of the singular boundary of a space–time.
Quantization of spinor fields. II. Meaning of ’’bosonization’’ in 1+1 and 1+3 dimensions
Authors: Garbaczewski Piotr
Published: March 2003

We demonstrate that the correspondence principle allowing us to relate the classical (c number) and quantum levels of spinor fields in 1+1 and 1+3 dimensions, involves free Bose systems with unbounded from below Hamiltonians. The necessary condition for the quantum spinor fields to be ’’bosonized’’ on the ’’physical’’ space is that for the related free Bose systems, only the non-negative part of the spectrum persists, due to constraints. Compared with the bosonization formulas, the number of independent Bose degrees of freedom necessary for a consistent formulation of the correspondence principle is doubled.
Reduction of the super phase space for a massless Dirac particle
Authors: Nilsson Bengt E. W.
Published: March 2003

We show how to get the reduced super phase space for a classical spinning particle and how to quantize this theory. This technique introduces a Grassmannian ’’Hamiltonian’’ and a corresponding Grassmannian ’’time’’ parameter.
Long-range order in the spin van der Waals model
Authors: Lee M. Howard
Published: March 2003

Long-range order in the spin van der Waals model is considered when the number of spins is finite and also when infinite. We show explicitly that a finite system cannot support long-range order. An infinite system at high temperatures is found to be dominated by the entropy of degenerate states of the system and, as a result, the system behaves essentially like an ideal system. In an infinite system at low temperatures, long-range order exists, fully reflecting the spin symmetry of the Hamiltonian. For the XY-like regime (J≳Jz ), mx is finite but mz vanishes, where mx and mz are reduced order parameters for the transverse and longitudinal directions, respectively. For the Ising-like regime (J<Jz), mx vanishes but mz is finite. The isotropic interaction (Jz = J) behaves as a singularity and it must be considered separately. A physical interpretation of the behavior of long-range order is offered using the geometry of spin space.
Mickelsson lowering operators for the symplectic group
Authors: Bincer Adam M.
Published: March 2003

Elementary lowering operators for the symplectic group, for which a graphical algorithm was given by Mickelsson, are obtained in the form of tensor operators. The resultant simple analytic expressions are analogous to the corresponding ones found previously for the unitary and orthogonal groups.
Boson–fermion representations of Lie superalgebras: The example of osp(1,2)
Authors: Blank Jiří , Havlíček Miloslav , Exner Pavel , Lassner Wolfgang
Published: March 2003

A method for constructing infinite-dimensional representations of Lie superalgebras employing boson representations of their Lie subalgebras is outlined. As an example the osp(1,2) superalgebra is considered; explicit formulae for its generators in terms of one pair of boson operators, at most one pair of fermion ones, and at most one parameter are obtained, the Casimir operator being represented by a multiple of unity. The restriction of these representations to the real form of osp(1,2) is skew-symmetric in the even part and can be regarded as a natural generalization of skew-symmetric representations of real Lie algebras. Some other aspects of the presented construction are discussed.
Remarks on certain dual series equations involving the Konhauser biorthogonal polynomials
Authors: Srivastava H. M.
Published: March 2003

It is observed, in the present note, that the literature contains erroneous results concerning the solutions of certain dual (and triple) equations involving series of the Konhauser biorthogonal polynomials. For example, the main results proved recently by K. R. Patil and N. K Thakare [J. Math. Phys. 18, 1724 (1977)] are shown to be invalid except in their already-known special cases. The errors are traced to the misuse of a certain Weyl fractional integral which holds true only in the case of the classical Laguerre polynomials.
The bi-Hamiltonian structure of some nonlinear fifth- and seventh-order differential equations and recursion formulas for their symmetries and conserved covariants
Authors: Fuchssteiner Benno , Oevel Walter
Published: March 2003

Using a bi-Hamiltonian formulation we give explicit formulas for the conserved quantities and infinitesimal generators of symmetries for some nonlinear fifth- and seventh-order nonlinear partial differential equations; among them, the Caudrey–Dodd–Gibbon–Sawada–Kotera equation and the Kupershmidt equation. We show that the Lie algebras of the symmetry groups of these equations are of a very special form: Among the C∞ vector fields they are generated from two given commuting vector fields by a recursive application of a single operator. Furthermore, for some higher order equations, those multisoliton solutions, which for ‖t‖→∞ asymptotically decompose into traveling wave solutions, are characterized as eigenvector decompositions of certain operators.
Recurrence relations for the coefficients of perturbation expansions
Authors: Müller-Kirsten H. J. W. , Sharma L. K.
Published: March 2003

Exact recurrence relations are derived for the coefficients of the perturbation expansion of the Schrödinger wavefunction for large classes of potentials. The terms of the eigenvalue expansion can then be expressed in terms of these coefficients which therefore allow other investigations such as the large-order behavior of the expansion.
Theta functions, Gaussian series, and spatially periodic solutions of the Korteweg–de Vries equation
Authors: Boyd John P.
Published: March 2003

It has been shown by Novikov [Funct. Anal. Appl. 8, 236 (1974)], Dubrovin et al. [Russian Math. Surveys 31, 59 (1976)], Lax [Commun. Pure Appl. Math. 28, 141 (1975)], McKean and van Moerbeke [Inv. Math. 30, 217 (1975)], and others that the nonlinear evolution equations which admit solitary waves also have spatially periodic exact solutions (’’polycnoidal waves’’) which can be expressed in terms of multidimensional Riemann theta functions. Here, it is shown that via Poisson summation, the Fourier series that define the theta functions can be transformed into an infinite series of Gaussian functions. Because the lowest terms of the Gaussian series generate the usual solitary waves, it is possible to intimately explore the relationship between solitary waves and these spatially periodic ’’polycnoidal’’ waves. Also, by using the Gaussian series, one can perturbatively calculate phase velocities and wave structure for the ’’polycnoidal’’ wave even in the strongly nonlinear regime for which the soliton (or multisoliton) is the lowest order approximation. It is further shown that the Fourier series and the complementary Gaussian series both converge so rapidly in the intermediate regime of moderate nonlinearity that one may loosely state that a solitary wave is almost a linear wave, and a linear wave almost a soliton. Thus, by using both series together, one can obtain a very complete description of these stable, finite amplitude, periodic solutions. For expository simplicity, this first discussion of the Gaussian series approach to ’’polycnoidal’’ waves will concentrate on the most elementary example: the ordinary ’’cnoidal’’ wave of the Korteweg–de Vries equation. The great virtue of the Poisson method, however, is that it extends almost trivially to other equations (the Nonlinear Schrödinger equation, the Sine–Gordon equation, and a multitude of others) and also to periodic solutions of these equations that are describable in terms of higher dimensional theta functions (’’polycnoidal’’ waves). The next to last section proves a number of generalizations of the theorems of Hirota [Prog. Theor. Phys. 52, 1498 (1974)], applicable both to ’’cnoidal’’ and ’’polycnoidal’’ solutions without restriction, and explains how these extensions will work.
Sine-Gordon and modified Korteweg–de Vries charges
Authors: Case K. M. , Roos A. M.
Published: March 2003

The sine-Gordon and the integrated modified Korteweg–de Vries equations are shown to conserve the same infinite set of charges. The charges are determined by a recursion relation. As a consequence, the solutions of all the equations generated by the charges have in common all time-independent properties.
Classical mechanics of nonspherical bodies. I. Binary collisions in two dimensions
Authors: Elskens Yves , Speiser David
Published: March 2003

In order to discuss the statistical mechanics and to prove an H-theorem for two-dimensional, nonspherical bodies, which possess only a symmetry axis, the mechanics of collisions of such bodies are investigated in detail, starting from the collision formulae of D. Bernoulli and Euler.
Direct and inverse scattering problems of the nonlinear intermediate long wave equation
Authors: Kodama Y. , Ablowitz M. J. , Satsuma J.
Published: March 2003

The inverse scattering transformation method associated with a nonlinear singular integrodifferential equation is discussed. The equation describes long internal gravity waves in a stratified fluid of finite depth, and reduces to the Korteweg–de Vries equation as shallow water limit and the Benjamin–Ono equation as deep water limit. Both limits of the method and novel aspects of the theory are also discussed.
Parabolic approximations to the time-independent elastic wave equation
Authors: Corones J. , DeFacio B. , Krueger R. J.
Published: March 2003

A splitting matrix method is used to derive two parabolic-approximation partial differential equations to the three-dimensional, linear, elastic wave equation in isotropic, inhomogeneous media. The derivation is valid for media whose Lamé parameters vary slowly on the length scale of the wavelength of the elastic waves. Next an integral form of the full wave equation is derived based on the splitting matrix and the parabolic approximation solution. Iteration of this equation gives a three-dimensional vector-valued series which generalizes the one-dimensional Bremmer series (which was used in the study of second-order ordinary differential equations). These results are expected to have applications to geophysical modeling and nondestructive evaluation.
Inverse scattering. IV. Three dimensions: generalized Marchenko construction with bound states, and generalized Gel’fand–Levitan equations
Authors: Newton Roger G.
Published: March 2003

This paper represents the final installment in a series on the solution of the inverse scattering problem for the Schrödinger equation in three dimensions. The potential is constructed from a given scattering amplitude without assuming its existence, even in the presence of bound states. For exponentially decreasing potentials, properties of the Jost function and of the regular solution are derived that are sufficient to establish the triangularity of the kernel on which the generalized Gel’fand–Levitan (GL) equation is based. Other generalized GL equations, for nonzero reference potentials, and a nonlinear equation are derived, and for central potentials they are shown to reduce to the well-known radial equations. The contents of the series of papers is summarized.
Consistency of the Cauchy initial value problem in a nonsymmetric theory of gravitation
Authors: McDow J. C. , Moffat J. W.
Published: March 2003

The consistency of the Cauchy initial value problem in a theory of gravity based on a nonsymmetric metric is investigated. It is demonstrated that the dynamical equations preserve the constraint equations as the evolution of the initial data occurs. The consistency is shown rigorously using the full field equations rather than the series expansion used previously.
Kerr-like metric in Brans–Dicke theory
Authors: Krori K. D. , Bhattacharjee D. R.
Published: March 2003

A Kerr-like metric is obtained by means of a complex coordinate transformation in the Brans–Dicke theory.
On the structure of the generalized Tjon–Wu equations
Authors: Turchetti G.
Published: March 2003

The kinetic equations proposed by Ziff are analyzed and their connection with the homogeneous Boltzmann equation is discussed. For a family of models generalizing the Tjon–Wu and Bobylev–Krook–Wu equations, the ordinary and Laguerre moment equations are considered. Beyond the existence of a unique solution in L1, conditions for the convergence of the Laguerre expansion are found and asymptotic estimates are given.
Geometric quantization and UIR’s of semisimple Lie groups. III. Principal and supplementary series
Authors: Sitaram B. R. , Tripathy K. C.
Published: March 2003

The principal and supplementary series representations of arbitrary semisimple Lie groups is analyzed in the framework of Auslander and Kostant’s theory of UIR’s of solvable Lie groups. As an illustration, we discuss a physically relevant symmetry group, Spin (4,2).
Anomalies and eigenvalues of Casimir operators for Lie groups and supergroups
Authors: Balantekin A. Baha
Published: March 2003

An expression for the anomaly of any representation of the SU(N) groups and SU(N/M) supergroups is presented. Some anomaly free complex representations of SU(N) and SU(N/M) are pointed out. For SU(N) these occur for N?5 and for large dimensions. For SU(N/M) they already occur for low dimensions. Also a generating function to obtain the eigenvalues of all Casimir operators of SU(N/M) is given and an extension to other supergroups is pointed out.
Dimensions of orbits and strata in complex and real classical Lie algebras
Authors: Patera J. , Rousseau C. , Schlomiuk D.
Published: March 2003

Explicit expressions for codimensions of orbits and strata of elements of complex Lie algebras gl(n, C), o(n, C), sp(2n, C) and real Lie algebras gl(n, R), gl(n, H), u( p, q), o( p, q), o*(2n), sp(2n, R), and sp(2p, 2q) are given. They make it possible to list easily all dimensions of orbits and strata in a given Lie algebra. The dimension of an orbit or stratum of a given matrix, an element of one of the Lie algebras in its natural representation, can be determined from our formulas after the matrix has been transformed into its Jordan normal form in gl(n, C), gl(n, R), or gl(n, H). Stratification of the Lie algebra in the vicinity of a singular element is discussed.
Nonlinear superposition, higher-order nonlinear equations, and classical linear invariants
Authors: Reid James L. , Ray John R.
Published: March 2003

We find a class of nonlinear ordinary differential equations, in ρ, of any order m?2 whose solutions are given by the nonlinear superposition law ρ(t) = x(t)r(τ), dτ = μ(t)dt, where dmr/dτm = F(r, r ′,...) and x(t) satisfies a special self-adjoint linear equation of order m. The coefficients of the self-adjoint equation in x, which are identical to those of the nonlinear equations in ρ, can be deduced from the well known invariants of the classical theory of linear differential equations.
On one method of solving the Helmholtz equation
Authors: Verbitskii I. L.
Published: March 2003

This paper, Paper II of a series, presents a transformation technique that enables one to substantially simplify the form of the matrix elements of the simultaneous equations to which the two-dimensional Helmholtz equation was reduced in Paper I. The explicit passage to the limit was also carried out for the case of the normally incident wave.
Mathematical problems of irreversible statistical mechanics for quantum systems. II: On the singularities of (Ψ(z)−z)−1 and the pseudo-Markovian equation. Application to Lee model
Authors: Courbage M.
Published: March 2003

We study in the frame of the superspace of the Hilbert–Schmidt operators the contributions of some complex singularities of the analytic continuation of (Ψ(z)−z)−1 to the diagonal part of the solution of the Liouville–von Neumann equation. Under some conditions, the θ̄ operator of the pseudo-Markovian master equation can be explicitly constructed. It is necessary to specify the diagonal representation and the class of initial conditions having regularity properties. This Hilbertian structure does not allow the construction of a closed subspace which reduces the Liouville–von Neumann operator L, giving an exact irreversible subdynamics; more elaborated mathematical structures are therefore necessary. The above methods are illustrated in the case of the Lee model.
Solutions of the wave equation for superposed potentials with application to charmonium spectroscopy
Authors: Sharma L. K. , Iyer V. P. , Mehta Sheilly , Kulkarni S. V. , Choubey Jyoti
Published: March 2003

In this paper complete solutions of the Schrödinger equation for three different superposed potentials have been obtained. In particular high-energy asymptotic expansions of the bound-state eigenfunctions and eigenvalues are derived. Various properties of these expansions have been examined including the behavior of Regge trajectories. Finally the relevance of these investigations to various aspects of the spectroscopy of heavy quark composites is discussed in detail.
Quantum mechanical scattering theory for potentials of the form V(r) = (sin r)/r β , 1/3<β≤1/2
Authors: Bourgeois Brian
Published: March 2003

A rigorous nonrelativistic time dependent quantum-mechanical scattering theory for a single particle is developed for potentials of the form V(r) = (sin r)/r β , 1/3<β⩽ 1/2 . The positive-energy solutions of the radial Schrödinger equation are used to construct modified wave operators which converge as t→±∞ on a dense set of states to the familiar time-independent formulas for the wave operators.
Eigenvalues of an anharmonic oscillator. II
Authors: Kesarwani R. N. , Varshni Y. P.
Published: March 2003

An expression is derived for the sixth nonzero term in the WKBJ approximation. The six-term WKBJ approximation is applied to calculate the eigenvalues for the potential V(x) = 1/2 kx2+ax4, k≳0 and a≳0. At low values of λ[ = ah//( μk3)1/2], the calculated results are in excellent agreement, to 15 significant figures, with those of Banerjee et al. for all quantum numbers. At medium and high values of λ, the calculated results are poor at low quantum numbers, but improve rapidly as n increases. A 15-significant-figure accuracy is achieved at n = 10 for λ = 0.05, and at about n = 15 for λ = 20 000. For λ = 0.5, eigenvalues are calculated to 20 significant figures and an argument is presented to show that by n = 50, the calculated value is correct to 19 significant figures. The accuracy further improves at higher quantum numbers.
The character table for the corepresentations of magnetic groups
Authors: Newmarch J. D. , Golding R. M.
Published: March 2003

A square character table is shown to exist for all finite magnetic groups. The table possesses row and column orthogonality properties similar to the character table for linear groups.
A mechanical model with constraints
Authors: Capri A. Z. , Kobayashi M.
Published: March 2003

We analyze a dynamical system with a finite number of degrees of freedom. A complete analysis is presented both for first class constraints as well as for second class constraints. The results are applicable to Yang–Mills fields as well as higher spin fields.
Supermanifolds and BRS transformations
Authors: Bonora L. , Pasti P. , Tonin M.
Published: March 2003

We use a supermanifold formalism to support a geometrical interpretation of a recently proposed superfield formulation of BRS (Becchi–Ronet–Stora) and anti-BRS transformations.
The holonomy group and spontaneous symmetry breaking
Authors: Ross D. K.
Published: March 2003

We show that the residual symmetry group after spontaneous symmetry breaking must either be the holonomy group H of the connection or contain H as a subgroup. Since H is a connected, normal Lie subgroup of the gauge group G, knowing the dimension of H is often sufficient to determine H itself. We develop an algorithm for determining dim H for any gauge theory given the structure constants of the gauge group. This algorithm is then applied to a fiber bundle with an SU2 or SU3 gauge group.
Biconical receiving antenna
Authors: Grimes Dale M.
Published: March 2003

The modal solution to a biconical receiving antenna with arbitrary arm angles and lengths is presented in the form of sums over special functions; sums which are exact in the sense that no electromagnetic approximations are made. The antenna load is confined within a sphere of small radius centered at the apices of the cones. The analytical formulation is presented, along with solutions for ψ very small and very large, and certain selected numerical data. The general solution permits calculation of all detailed fields near and far, both receiving and transmitting current modes on the antenna arms and caps and the power and the momentum absorbed by the antenna from an incoming plane wave. It is shown that the receiving current modes are necessary for electromagnetic momentum to be conserved during power reception. Detailed calculation of comparative receiving and transmitting admittances confirms that they are identical, as predicted by the reciprocity theorem. The radiation patterns, however, for retransmission during reception and for transmission differ.
On boson condensation into an infinite number of low-lying levels
Authors: van den Berg M.
Published: March 2003

The complicated structure of the condensate of a free boson gas in two dimensions with mixed boundary conditions is examined.
Higher spin one-dimensional Ising lattice in arbitrary external field
Authors: Percus J. K.
Published: March 2003

We consider an integer lattice in one dimension whose site variables take on the values ν = 0,1,...,D with a fixed nearest neighbor interaction but an arbitrary site-dependent external potential. By first eliminating the external potential in favor of the site probability density, an expression is found in principle for the potential as a functional of the density. This relation is worked out in detail for basic spin 1/2 model, Z3 lattice, random walk ensemble, and a special continuous spin model. The direct correlation function in all cases has only nearest neighbor support, and the thermodynamic potential as a functional of the density couples only nearest neighbor sites.
An SL(2,C )-invariant representation of the Dirac equation
Authors: Hostler Levere C.
Published: March 2003

The relativistic Pauli-type equation {ΠμΠμ+m2+ieσ⋅(E+iB)}φ = 0 (one of a pair of second order equations that follow from the Dirac equation) is investigated. Here φ is a 2×1 Pauli spinor, and σa , a = 1,2,3, are the usual Pauli spin matrices. We investigate the correspondence between a description of a Dirac particle based on this second order equation and a single 2×1 spinor wave function φ, and a description employing the conventional Dirac equation. To this end, a representation is derived that expresses the exact interacting Dirac propagator of the Pauli-type equation. Techniques for discussing scattering of a Dirac particle using the above wave equation are presented. The Feynman rules, at least for the external c-number field problems considered here, are basically those of scalar electrodynamics. A notable difference is the replacement of the factor −ie(Pfμ+piμ) for the one-photon vertex of scalar electrodynamics by the new factor −ie(pfν(δνμ+iσνμ)+(δμ ν +iσμν)piν) for our one-photon vertex. σμφ is a self-dual spin tensor whose components are the usual Pauli matrices, times ±1.
Complete set of SU(5) monopole solutions
Authors: Koh I. G. , Kim Y. D. , Park Y. J. , Kim C. H. , Kim Y. S.
Published: March 2003

The manifestly nonsingular asymptotic forms of the most general possible pointlike SU(5) monopoles are found by using the magnetic symmetry introduced by Cho. New magnetic tensor representations greatly expedite the computations. These magnetic tensors explicitly exhibit the full homotopy class of the mappings classifying the arbitrary allowed magnetic charges.
Shift operator techniques for the classification of multipole–photon states. X. P 0l eigenstate and eigenvalue determination in G2
Authors: De Meyer H. E. , Vanden Berghe G. , Van der Jeugt J.
Published: March 2003

On account of previously derived relations between quadratic shift operator products in the group G2, part of the eigenvalue spectrum of the scalar shift operator P0l is derived in closed form. The corresponding eigenstates which are closely related to the octupole–phonon states are defined in terms of angular momentum lowering shift operator actions upon the maximum angular momentum state.
A new approach to permutation group representation
Authors: Chen Jin-Quan , Gao Mei-Juan
Published: March 2003

The new approach to group representation theory is applied to the treatment of the permutation group. It is shown that obtaining (1) the primary characters and the fractional parentage coefficients, (2) the Yamanouchi bases and the Clebsch–Gordan coefficients, and (3) the irreducible matrix elements of the permutation group S ( f), are all simplified to a unified procedure — diagonalizing a certain operator in the corresponding representation. The operator to be diagonalized for the above three problems is (1) the 2-cycle class operator Cf of S ( f), (2) an appropriate linear combination of the f-1 2-cycle class operators Cf, Cf−1,...,C2 of the group chain S( f)⊇ S( f−1)⊇...⊇ S(2), and (3) an appropriate linear combination of 2f−3  2-cycle class operators Cf, Cf−1,...,C2, 𝒞f−1,...,𝒞2, 𝒞i being the 2-cycle class operator of the subgroup 𝒮(i) of the state permutation group 𝒮(f), respectively. This method, the eigenfunction method, is simpler in concept, yet more powerful in practical calculations.