bluuebunny/crossref_metadata_2025 huggingface dataset:
Scattering of electromagnetic waves from a perfectly conductive slightly random surface: Depolarization in backscatter
Authors: Nakayama J. , Mitzutani K. , Tsuneoka M.
Published: July 2002

The scattering of electromagnetic waves from a perfectly conductive slightly random surface is studied by a probabilistic method developed recently. For a plane wave incident on a homogeneous, isotropic, Gaussian random surface, a stochastic wave solution involving multiple scattering effects is approximately obtained by use of the Wiener–Hermite expansion technique in the probability theory. Then the backscattering cross section per unit surface is derived for both like and cross polarization in a closed form and is shown in the figures. The surface waves propagating along the random surface are discussed.
Hypervirial theorem and parameter differentiation: Closed formulation for harmonic oscillator integrals
Authors: Morales J. , Lopez-Bonilla J. , Palma A.
Published: July 2002

A simple method has been developed to generate a closed formula for the calculation of matrix elements of arbitrary functions f(x) in the representation of the harmonic oscillator. The proposed algebraic procedure is based on the combined use of the hypervirial theorem with and without the second quantization formalism along with the parameter differentiation technique. The closed formula thus obtained is given in terms of a sum involving the jth derivative of f(x) evaluated at zero.
An initial value gravitational quadrupole radiation theorem
Authors: Winicour Jeffrey
Published: July 2002

A rigorous version of the quadrupole radiation formula is derived using the characteristic initial value formulation of a general relativistic fluid space-time. Starting from initial data for a Newtonian fluid, an algorithm is presented that determines characteristic initial data for a one-parameter family of general relativistic fluid space-times. At the initial time, a one-parameter family of space-times with this initial data osculates the evolution of the Newtonian fluid and has leading order news function equal to the third time derivative of the transverse Newtonian quadrupole moment.
Stochastic quantization of a Fermi field: Fermions as solitons
Authors: Bandyopadhyay P. , Hajra K.
Published: July 2002

It is shown that the stochastic quantization of a fermion introducing an anisotropy in the internal space so that this gives rise to two internal helicities corresponding to particle and antiparticle leads us to describe a fermion as a Skyrme soliton. The Skyrme term appears here as a consequence of this internal anisotropy and can be treated as a quantum effect. Some topological properties of this fermionization are then discussed.
Comment on ‘‘Compact expression for Löwdin’s alpha function’’ [J. Math. Phys. 2
6, 940 (1985)]
Authors: Suzuki Noboru
Published: July 2002

Recently Antone [J. Math. Phys. 26, 940 (1985)] has presented a compact expression for Löwdin’s α function, and expected that, in calculation on the electronic properties of molecules and solids, it is the most convenient of all the expressions available in literature. But, in the present paper, it is shown that the expression for the α function obtained from the expansion formula of Silverstone and Moats [Phys. Rev. A 16, 1731 (1977)] is remarkably more compact and, therefore, more convenient than Antone’s expression. Though not visibly, it is proved with the aid of some manipulation that the formula of Silverstone and Moats can be reduced to the well-known expansion formula of a solid harmonic. In the special case where the center of the function to be expanded and that of the α function both are located on the z axis, some mistakes are found that lead to Antone’s expression for the α function.
Loop gauge theory and group cohomology
Authors: Vourdas A.
Published: July 2002

A generalized fiber bundle model in which the fibers are Hilbert spaces is studied. Unitary transformations are used to define a unitary isomorphism (‘‘parallelism’’) among them. The Weyl group is first used to ‘‘connect’’ the projective Hilbert spaces (ray spaces) and to introduce a one-form connection that defines which coset at a point y is parallel to a given coset at another point x. Then, the central extension of the Weyl group by U(1)′ is studied in order to introduce the most general mapping between the elements of these cosets. This leads to a two-form connection and makes the model a good candidate for a fiber bundle approach to string theories.
Transition amplitude spaces
Authors: Gudder Stanley , Pulmannová Sylvia
Published: July 2002

Motivated by physically plausible axioms, the concept of a transition amplitude space (tas) is defined. Various connections between this framework and other axiomatic approaches to the foundations of quantum mechanics are derived. In particular, transition probability spaces, the algebraic approach, the operational statistics and quantum logic approaches, and traditional Hilbert space quantum mechanics are considered. It is shown that a tas always admits a Hilbert space representation. Results are obtained concerning isomorphisms and automorphisms for tas’s. The concept of an A-form is introduced and the relationship between certain A-forms and bounded linear operators on a Hilbert space are studied. Finally, it is shown that sums and tensor products of tas’s can be formulated in a natural way.
Probability of convergence of perturbation theory for hydrogen photoionization
Authors: Caliceti E. , Goldoni L. , Graffi S.
Published: July 2002

The probability is estimated that at a given frequency ω the action of an external, monochromatic radiation field acting on a hydrogen atom yields a fixed positive convergence radius of the Rayleigh-Schrödinger perturbation expansion for the quasienergy resonances.
The existence of singularities in general relativity despite isolated failures of geodesic focusing
Authors: Borde Arvind
Published: July 2002

A key ingredient of the singularity theorems of general relativity is that geodesics will focus under certain conditions. While the conditions that are generally imposed are fairly weak and can be expected to hold for most geodesics in any reasonable space-time, the question arises of what the consequences might be if these conditions happen to fail to hold for isolated geodesics. The standard singularity theorems in the literature do not cover such cases. A result is presented here that demonstrates that a singularity will exist even in cases where geodesic focusing does not occur for some geodesics.
Nonpolynomial Yang–Mills local cohomology
Authors: Bandelloni Giuseppe
Published: July 2002

The spectral sequence method is used to find the nonintegrated function cohomology of the BRS Yang–Mills operator in the space of the analytic (a priori nonpolynomial) functions in space-time dimensions.
Chiral symmetry breakdown. I. Gauge dependence in constant vertex approximation
Authors: Atkinson D. , Johnson P. W.
Published: July 2002

An approximate quark propagator equation in a Landau-like gauge is analyzed and it is shown that there is a critical value of the coupling constant, corresponding to the onset of dynamical chiral symmetry breakdown, provided that (a) there is an infrared cutoff, which can be supplied by an effective gluon mass, and (b) there is an ultraviolet cutoff, which may be engendered by a running coupling constant. Dynamical chiral symmetry breakdown is shown not to occur in other gauges under the same circumstances, thus casting doubt upon the approximations commonly used.
Spontaneous splitting and internal isometries of superstring vacua
Authors: McInnes Brett
Published: July 2002

Superstring vacua are normally presumed to be of the form M×K, where dim(M)=4, dim(K)=6, and where × denotes the global Riemannian product. Since, however, one would ultimately wish to understand the external/internal distinction in terms of some dynamical mechanism (‘‘spontaneous splitting’’) involving vacuum expectation values of local fields, it may be preferable to use a local Riemannian product at the outset. Here it is shown that these spaces, which have the same local (block-diagonal) type of metric as M×K, can be described and classified by examining the isometry groups of the Calabi–Yau manifolds which have been proposed as models for the internal superstring vacua.
Yang–Mills solutions in S3×S1
Authors: Villarroel Javier
Published: July 2002

A search is conducted for new solutions to Yang–Mills classical field theory defined on S3×S1 using Witten’s ansatz. Then some sort of non-Abelian plane waves giving rise to a divergent energy are obtained.
Strong cosmic censorship and the strong curvature singularities
Authors: Krȯlak Andrzej
Published: July 2002

Conditions are given under which any asymptotically simple and empty space-time that has a partial Cauchy surface with an asymptotically simple past is globally hyperbolic. It is shown that this result suggests that the Cauchy horizons of the type occurring in Reissner–Nordström and Kerr space-times are unstable. This in turn gives support for the validity of the strong cosmic censorship hypothesis.
On the denominator function for canonical SU(3) tensor operators. II. Explicit polynomial form
Authors: Louck J. D. , Biedenharn L. C. , Lohe M. A.
Published: July 2002

The canonical resolution of the multiplicity problem for tensor operators in SU(3) is equivalent to the map (the denominator mapping) from the set of all SU(3) unit tensor operators to SU(3) invariant functions (the denominator functions). The denominator function vanishes precisely on that characteristic null space that specifies each operator uniquely since [for SU(3)] the characteristic null spaces are known to be simply ordered. Each denominator function can be expressed, up to explicitly known multiplicative factors, as a ratio of two successive polynomials in the set {Gtq}, t=0,1,..., q+1, q=0,1,... . By obtaining explicitly the set of all polynomials {Gtq}, this paper completes the construction of all SU(3) denominator functions.
On canonical irreducible quantum field theories describing bosons and fermions
Authors: Baumann Klaus
Published: July 2002

For a relativistic irreducible quantum field theory (QFT) in which the bosons and fermions fulfill the canonical commutation relation (CCR) and the canonical anticommutation relation (CAR), respectively, it is shown that in n>3 space dimensions Bose and Fermi fields fulfill free field equations. Furthermore which interactions might be compatible with CCR and CAR in lower space dimensions are characterized. The possible candidates are interactions of type Q2(ψ,ψ°)φ+P4(φ) in n=3, Q2(ψ,ψ°)P2(φ)+P6(φ) in n=2, and Q4(ψ,ψ°)F(φ) in n=1 space dimensions, where Qm and Pm are polynomials of degree up to m.
A simplified model for orbifold compactification
Authors: Zabl/ocki Krzysztof
Published: July 2002

The problem of vacuum stability in orbifold compactification is addressed. The spectrum of fermions and the effective potential in a simple model of compactification on the T2/Z2 orbifold with a topologically nontrivial gauge field background is calculated.
Evaluation of Feynman diagrams in the logarithmic approach to quantum field theory
Authors: Bender Carl M. , Jones H. F.
Published: July 2002

The techniques necessary to compute the O(δ2) contributions to the Green’s functions of a scalar field theory with self-interaction λ(φ2)1+δ in d-dimensional space-time are developed. The resulting expressions are evaluated explicitly for d=1, 0, and some negative even dimensions. For d=3 and 4 we calculate their leading behavior in terms of a spatial cutoff a.
The construction of B (1) l in terms of vertex operators and a Lie-admissible not associative algebra
Authors: Cougo-Pinto M. V.
Published: July 2002

The affine nontwisted Kac–Moody algebra B(1)l is constructed in terms of an underlying not associative algebra obtained by tensoring an associative algebra of vertex operators with a given Lie-admissible algebra. The former has its origin in bosonic string theory and the latter is found to be essentially an algebra of contractions used in canonical field theory.
SU(1,1), its connections with SU(2), and the vector model
Authors: de Prunelé E.
Published: July 2002

A relation between representation functions (RF’s) of positive discrete unitary irreducible representations (UIR’s) of SU(1,1) and the RF’s of the UIR’s of SU(2) is given. The classical vector model is worked out for the positive discrete UIR’s of SU(1,1). Classical domains, probability densities, and algorithms for numerical computations of SU(1,1) RF’s and Clebsch–Gordan coefficients are derived, in full analogy with the SU(2) case.
Wigner operator and Racah operator of the Lie superalgebra OSP(1,2)
Authors: Zeng Gao-Jian , Yuan Xiou-Hua
Published: July 2002

Starting with the Wigner–Eckart theorem about the OSP(1,2) irreducible tensor [J. Phys. A: Math Gen. 20, 5423 (1987)], the OSP(1,2) Wigner operator and Racah operator are studied, their general definitions, orthogonality properties, and coupling laws are given, and the connections between them and the corresponding operators of the SO(3) algebra are established. The results obtained in this paper are a natural development of the authors’ theory on the OSP(1,2) irreducible tensor.
Adiabatic switching for time-dependent electric fields
Authors: Scialom Márcia A. G. , Iório Rafael J.
Published: July 2002

In this work the scattering theory associated with the differential equation i(∂ψ/∂t)=(−Δ+e−Ε‖t‖g(t)x1 +q(x))ψ is considered, where x=(x1,x⊥)∈R×R2, Ε≥0, ω>0, α∈R, g(t), t∈R is continuous, periodic with mean value zero over a period, and q(x) approaches to zero sufficiently fast as ‖x‖→∞. In the case Ε>0, it is shown that the usual theory is adequate; however, a limit does not exist when Ε↓0. A modified theory is developed where the limit does exist as Ε↓0. Furthermore, the concepts of bound states and scattering states for Ε≥0 are discussed.
Coherent states for the harmonic oscillator representations of the orthosymplectic supergroup Osp(1/2N,R)
Authors: Balantekin A. B. , Schmitt H. A. , Barrett B. R.
Published: July 2002

Coherent states for the harmonic oscillator representations of the noncompact supergroup Osp(1/2N,R) are introduced and the invariant integration measure is calculated by studying transformation properties of supercoset variables. The generalized Bogoliubov transformation for mixed systems of bosons and fermions is also obtained. An example for the simple harmonic oscillator is given.
Multipole structure of stationary gravitational fields at null infinity
Authors: Kundu Prasun K.
Published: July 2002

The multipole structure of the gravitational field produced by a stationary, isolated source at null infinity is investigated using a Bondi-type null polar coordinate system. The results are connected with the previous works of the author on the multipole expansion of stationary, asymptotically flat, vacuum solutions of the Einstein equations in the framework of the Geroch–Hansen one-point compactification scheme. The present work strongly suggests that all such solutions are analytic in the inverse luminosity distance r−1 in a Bondi chart.
Integrable dynamical systems with hierarchy. II. Solutions
Authors: Okubo Susumu
Published: July 2002

A semisystematic method of finding solutions that satisfy the zero Nijenhuis tensor condition with dual symplectic structure is developed. In this manner, a few solutions, including that of the Toda lattice, have been found. It is also shown that the general solution for the linear problem is intimately connected with nontriviality of the second cohomology group of solvable Lie algebras. Moreover, the case of the quadratic problem requires studies of an algebra involving the triple-linear product system.
Spinorial idempotents in the Clifford algebras of Minkowski spaces
Authors: Kopczyński Wojciech
Published: July 2002

Algebraic spinor spaces determined by spinorial idempotents are considered in the case of two- and four-dimensional, real and complexified Minkowski spaces. The form of the idempotents and their classification is given.
Small oscillations of regular polytopes in d≥4 space dimensions
Authors: Eastaugh A. , van Nieuwenhuizen P.
Published: July 2002

Using the theory of finite groups, the spectrum of a regular ‘‘tetrahedron’’ in four and more space dimensions is analyzed.
Solution of the Dirac equation in Kasner’s space-time
Authors: Srivastava Sushil K.
Published: July 2002

The Dirac equation for the spin- 1/2 field in Kasner’s space-time is discussed and various possible solutions are obtained. For further interpretation of the theory a current vector is derived and Gordon decomposition of the current for massive fields is discussed.
Twistors in 2+1 dimensions
Authors: Ward R. S.
Published: July 2002

The geometry of twistors for (2+1)-dimensional flat space-time is described. Functions on twistor space generate solutions of various field equations in space-time. As an illustrative example, it is shown what a sine–Gordon soliton looks like in this twistor description.
High symmetry solutions of the anti-self-dual Yang–Mills equations
Authors: Chakravarty Sarbarish , Kent S. L. , Newman E. T.
Published: July 2002

Beginning with the anti-self-dual Yang–Mills (ASDYM) equations for an arbitrary Lie algebra on Minkowski space, this paper specializes to the case in which the vector potentials are independent of all the space-time coordinates, i.e., are space-time constants. The resulting equations are three algebraic equations on the algebra. These equations are then simplified by using a null basis. Two of the equations can be immediately solved while the third remains, in general, quite difficult to deal with. Two general cases are considered: finite-dimensional Lie groups and the infinite-dimensional diffeomorphism groups on finite-dimensional manifolds. In a few of the special cases, e.g., SL(2,C) and the Virasoro algebra, the solutions can easily be found. The study of the the diffeomorphism groups leads unexpectedly to the Monge–Ampère equation. In particular, the four-dimensional volume preserving diffeomorphism group is identical with the vacuum anti-self-dual Einstein equations. In conclusion, the question of the associated Lax pair equations and its relation to the Riemann–Hilbert splitting problem on S2 is examined.
Symmetry operators and separation of variables for spin-wave equations in oblate spheroidal coordinates
Authors: Kalnins E. G. , Williams G. C.
Published: July 2002

A family of second-order differential operators that characterize the solution of the massless spin s field equations, obtained via separation of variables in oblate spheroidal coordinates and using a null tetrad is found. The first two members of the family also characterize the separable solutions in the Kerr space-time. It is also shown that these operators are symmetry operators of the field equations in empty space-times whenever the space-time admits a second-order Killing–Yano tensor.
Trapped surfaces in monopole-like Cauchy data of Einstein–Yang–Mills–Higgs equations
Authors: Malec Edward , Koc Piotr
Published: July 2002

The non-Abelian monopole solution of Bogomolny, Prasad, and Sommerfield is chosen as a part of the Cauchy data for the evolution of Einstein–Yang–Mills–Higgs equations. Momentarily static spherically symmetric data for gravitational fields are obtained numerically via the Lichnerowicz equation. In the case of generic scaling of fields initial data with trapped surfaces were found.
Representations of the diffeomorphism group describing an infinite Bose gas in the presence of ideal vortex filaments
Authors: Albertin Uwe K. , Morrison Harry L.
Published: July 2002

A number of representations of the group of volume preserving diffeomorphisms of M=S3 in the finite-volume case and M=R3 in the infinite-volume case that describe a Bose gas in the presence of a vortex filament are examined. The core of the vortex is taken to lie along a curve γ. Let Dif  f γμ(M) be the group of volume preserving diffeomorphisms that map γ onto itself, Mγ the manifold M with γ removed, and Map(Mγ,T) the space of smooth maps of Mγ into the complex numbers of modulus unity. It is shown, using the formalism of Klauder [J. Math. Phys. 11, 233 (1970)], that an infinite number of inequivalent representations of Dif  f γμ(M) exist in the infinite-volume limit using cyclic vectors, which are coherent states based on elements in Map(Mγ,T). It is found, however, that these states have questionable physical significance since they appear to violate the continuity equation for quantum probability flow. This leads to the postulation that Dif  f γμ(M) acts as gauge group. The representations of Dif  f γμ(M) are then used to construct induced representations of the full group volume preserving diffeomorphisms of M, which are realized in the Hilbert space over the space of unparametrized loops in M in a natural way. These latter representations are found to be essentially the ones under current study in quantum hydrodynamics [G. A. Goldin, R. Menikoff, and D. H. Sharp, Phys. Rev. Lett. 58, 2162 (1987)].
Symplectic orbits in quantum state space
Authors: Chruściński Dariusz
Published: July 2002

All symplectic orbits of the action of an arbitrary compact connected Lie group on the space of density operators are found. It is shown that there is only one orbit that is Kähler (orbit of coherent states).
On some Racah coefficients of U(n)
Authors: Quesne C.
Published: July 2002

Some U(n) Racah coefficients appearing in various applications of vector coherent state and K-matrix theories are calculated: For such a purpose, use is made of their definition in terms of U(n):U(n−1) reduced Wigner coefficients and U(n−1) Racah coefficients. By starting from known U(2) Racah coefficients, the recursion relations obtained are solved by induction over n.
Auxiliary linear equations for a class of nonlinear partial differential equations via jet-bundle formulation
Authors: Lee You-Quan
Published: July 2002

It is shown that a class of two-variable nonlinear partial differential equations, such as the Liouville equation, the sine–Gordon equation, the Ernst equation, and the Ernst–Maxwell equations, can be Ricatti-type quasilinear systems through maps from J1 (R2, Rn) to J0 (R2, Rl). The auxiliary linear equations (Laxpair) for them are formulated, respectively, by using the W–E prolongation procedure. The Lax pairs for the Liouville equation and the sine–Gordon equation contain an arbitrary parameter besides the usual spectral parameter.
The quantization condition in the presence of a magnetic field and quasiclassical eigenvalues of the Kepler problem with a centrifugal potential and Dirac’s monopole field
Authors: Yoshioka Akira , Ii Kiyotaka
Published: July 2002

In the presence of a magnetic field, the Maslov quantization condition is not available in the original form. An alternative quantization condition is proposed with the aid of a principal U(1) bundle over a phase space and a connection whose curvature form is the charged symplectic form. By means of this quantization condition, quasiclassical eigenvalues of the Kepler problem with a centrifugal potential and Dirac’s monopole field are calculated, which turn out to coincide with the eigenvalues of the quantized problem.
Rotations, squeezing, and the unitary transformation operator from individual particles to Jacobi variables
Authors: Khanna F. C. , Mann A. , Takahashi Y.
Published: July 2002

A unitary operator for the transformation from individual particles to Jacobi variables is constructed explicitly for particles of arbitrary masses. It is expressed as a product of rotation and squeezing operators using only canonical variables.
The asymptotic localization of position probability in quantum mechanics
Authors: Farina J. E. G. , Mosley S. N.
Published: July 2002

The method of stationary phase is discussed in a mathematically rigorous way. A resulting lemma is used to derive the asymptotic localization of position probability under the evolution operator Ut=F−1 exp(−iωt)F, where ω is a continuous function of the wave vector k=(k1,...,kN) (N=1,2,...) with continuous first and second derivatives. The measurement of velocity is discussed, and the interpretation of the self-adjoint operator v̂i=F−1∇iωF as representing the ith component of velocity is also discussed.
Anisotropic cosmological models with energy density dependent bulk viscosity
Authors: Huang Wung-Hong
Published: July 2002

An analysis is presented of the Bianchi type I cosmological models with a bulk viscosity when the universe is filled with the stiff fluid p=ε while the viscosity is a power function of the energy density, such as η=α‖ε‖n. Although the exact solutions are obtainable only when the 2n is an integer, the characteristics of evolution can be clarified for the models with arbitrary value of n. It is shown that, except for the n=0 model that has solutions with infinite energy density at initial state, the anisotropic solutions that evolve to positive Hubble functions in the later stage will begin with Kasner-type curvature singularity and zero energy density at finite past for the n≥1 models, and with finite Hubble functions and finite negative energy density at infinite past for the n<1 models. In the course of evolution, matters are created and the anisotropies of the universe are smoothed out. At the final stage, cosmologies are driven to infinite expansion state, de Sitter space-time, or Friedman universe asymptotically. However, the de Sitter space-time is the only attractor state for the n< (1)/(2) models. The solutions that are free of cosmological singularity for any finite proper time are singled out. The extension to the higher-dimensional models is also discussed.
The Dirac equation in a non-Riemannian manifold: II. An analysis using an internal local n-dimensional space of the Yang–Mills type
Authors: Marques-Bonham S.
Published: July 2002

The geometrical properties of a flat tangent space-time local to the generalized manifold of the Einstein–Schrödinger nonsymmetric theory, with an internal n-dimensional space with the SU(n) symmetry group, is developed here. As an application of the theory, a generalized Dirac equation, where the electromagnetic and the Yang–Mills fields are included in a more complex field equation, is then obtained. When the two-dimensional case is considered, the theory can be immediately interpreted through the algebra of quaternions, which, through the Hurwitz theorem, presupposes a generalization of the theory using the algebra of octonions.
New method for deriving nonlinear integrable systems
Authors: Mel’nikov V. K.
Published: July 2002

A new approach is proposed to derive nonlinear integrable systems. It is used to obtain several new nonlinear integrable systems. The above results are relevant to some problems of hydrodynamics, plasma physics, solid-state physics, etc.
Shifted tableaux, Schur’s Q functions, and Kronecker products of S
n spin irreps
Authors: Salam M. A. , Wybourne B. G.
Published: July 2002

Properties of shifted tableaux have been explored in order to improve the algorithm for the calculation of Q function outer products. A simple technique has been established for finding out the highest and lowest partitions in the expansion of Q function outer products. Using these techniques and Young’s raising operators, we have completed the Kronecker product for Sn spin irreps.
Nonexistence and existence of various order integrals for two- and three-dimensional polynomial potentials
Authors: Cleary Paul W.
Published: July 2002

The nonexistence of integrals of the motion, which are sixth and fourth degree polynomials in the velocities, was established for a range of polynomial potentials. The first known systematic search for sixth-order integrals was performed for cubic and quartic polynomial potentials. It revealed that there exist no nondegenerate cases with such integrals for either potential. Similarly, there exists no nondegenerate fifth or sixth degree polynomial potentials possessing quartic invariants. A complete list of three-dimensional cubic potentials with quadratic integrals is given. All these integrable three-dimensional potentials can be interpreted as orthogonal superpositions of known integrable two-dimensional potentials possessing quadratic integrals. They correspond to 3 of 11 possible coordinate systems in which three-dimensional potentials separate.
A new perturbative approach to nonlinear partial differential equations
Authors: Bender Carl M. , Boettcher Stefan , Milton Kimball A.
Published: July 2002

This paper shows how to solve some nonlinear wave equations as perturbation expansions in powers of a parameter that expresses the degree of nonlinearity. For the case of the Burgers equation ut+uux=uxx, the general nonlinear equation ut+uδux=uxx is considered and expanded in powers of δ. The coefficients of the δ series to sixth order in powers of δ is determined and Padé summation is used to evaluate the perturbation series for large values of δ. The numerical results are accurate and the method is very general; it applies to other well-studied partial differential equations such as the Korteweg–de Vries equation, ut+uux =uxxx.
Quantum three-body scattering problem in the adiabatic hyperspherical representation
Authors: Kvitsinsky Andrei A. , Kostrykin Vadim V.
Published: July 2002

The adiabatic hyperspherical (AH) approach to the quantum three-body problem is considered. It is proven that the AH harmonics are complete and differentiable with respect to the hyperradius for a large class of two-body potentials. For the case of short-range potentials, the scattering theory is studied in the framework of the AH approach. The asymptotics of the AH potential curves, harmonics, and coupling matrix elements are derived, as well as the structure of the three-body wave operators and, the S-matrix in the AH representation is investigated.
Boson–fermion and baryon mapping of multiquark states
Authors: Meyer Jutta
Published: July 2002

The generalized Dyson boson mapping is extended to multifermion systems containing three-particle substructures as occurring in nuclear matter. Two different approaches are described. The first one leads to a mapping involving equal numbers of bosons and fermions, where each boson, as usual, represents a fermion pair. The second possibility consists of the introduction of new kinds of fermions carrying the quantum numbers of the original three-fermion subsystems. Both transformations are nonunitary.
New method of integration for the Dirac equation on a curved space-time
Authors: Bagrov V. G. , Obukhov V. V.
Published: July 2002

A new method of integration of the Dirac equation on curved space-time is presented. The method is based on diagonalization and on separation of variables. The diagonalization allows the use of the well-known method of variables separation of scalar equations for integration of the Dirac equation. All conditions of diagonalization are found. All metrics and potentials admitting the method are presented.
Spinor equations in relativistic quantum mechanics
Authors: Marx Egon
Published: July 2002

A set of two first-order equations for classical spinor fields are used to formulate the relativistic quantum mechanics (RQM) of a single massive spin-1/2 particle. These equations are generalized Weyl equations and they are not equivalent to the Dirac equation. They lead to a conserved charge that is not positive definite, thus allowing for a probabilistic interpretation of the wave function in RQM. The charge is also conserved when the fields interact with a scalar field through the charge-current densities.
Painlevé test and exact similarity solutions of a class of nonlinear diffusion equations
Authors: Glöckle W. G. , Baumann G. , Nonnenmacher T. F.
Published: July 2002

For (1+1)-dimensional diffusion equations where the diffusion coefficient is an arbitrary power of the dependent variable, a Painlevé test is performed on both the partial differential equation and the similarity reductions. The invariance of the Painlevé property under a large class of similarity reductions is shown. For the reductions with the Painlevé property, the explicit similarity solutions are given. It is demonstrated how results of a Painlevé analysis can be used to obtain further exact similarity solutions, even in cases without the Painlevé property.
Two-point quasifractional approximant in physics: Method improvement and application to Jν(x)
Authors: Chalbaud Eduardo , Martín Pablo
Published: July 2002

An improved two-point quasifractional approximant method is presented that includes a free parameter in the denominator. This parameter is determined by minimizing the theoretical truncation error bound, thus ensuring high accuracy. An added advantage of introducing a free parameter is that defects that are usual in Padé approximants are always avoided. The method is applied to the fractional Bessel functions Jν(x), obtaining a unique approximant, valid for all positive x, that is more accurate than previously published.
Neutrino in the presence of gravitational fields: Separation of variables
Authors: Shishkin German V. , Villalba Víctor M.
Published: July 2002

It is well known that the most complete information about single-particle states is contained in its wave function. For spin-1/2 particles this means that it is necessary to have exact solutions of the Dirac equation. In particular, in the case of neutrinos in the presence of gravity, it is necessary to solve the covariant Dirac equation. At present, the existence of neither massless neutrinos (electron neutrinos) nor massive neutrinos (muon and τ neutrinos) cannot be excluded. Since for massless neutrinos any solution of the Dirac equation is also a solution of the Weyl equation, there exists the possibility of studying, from a unified point of view, massive as well as massless neutrinos by means of the Dirac equation. In the search of exact solutions of systems of partial differential equations one can proceed as follows: (a) separation of variables and (b) solution of the corresponding ordinary differential equations. In the present paper, a complete analysis of the separation of variables in the Dirac equation for massive as well as for massless neutrinos is carried out by means of the algebraic method [J. Math. Phys. 30, 2132 (1989)]. It is found that for the massless neutrinos, there are further possibilities of separation of variables, not valid for the massive case.
Hamiltonization of the Lorentz force equation for a massive particle with spin: A twistorial approach
Authors: Bette Andreas
Published: July 2002

A twistor formulation of the Lorentz force equation is presented. To prepare for its quantization a Poincaré covariant symplectic structure Ω and a Hamiltonian Poincaré scalar function H on T×T (direct product of two twistor spaces less the diagonal, i.e., less the set of points in T×T, where the two twistors coincide), such that the Lorentz force equation for a massive particle with spin corresponds to a (Liouville) flow in T×T generated by H and canonical with respect Ω is introduced.
Representations of the quantum algebras 𝒰q(u
r,s) and 𝒰q(u
r+s) related to the quantum hyperboloid and sphere
Authors: Klimyk A. U. , Pakuliak S. Z.
Published: July 2002

Representations πΛμ of the principal degenerate series of the quantum algebra 𝒰q(ur,s) are introduced. Structure of these representations is studied. Several classes of unitary irreducible representations of the algebra 𝒰q(ur,s) are separated in the set of irreducible representations πΛμ and irreducible constituents of reducible representations πΛμ. The formulas of action of operators of irreducible representations of the quantum algebra 𝒰q(ur+s) in the basis corresponding to restriction of representations onto the subalgebra 𝒰q(ur+us) are given.
A superversion of quasifree second quantization. I. Charged particles
Authors: Grosse H. , Langmann E.
Published: July 2002

A formalism comprising and extending quasifree second quantization of charged bosons and fermions is presented. The second quantization of one-particle observables leads to current superalgebras, and a super-Schwinger term shows up. Anticommuting parameters are introduced in order to construct super-Bogoliubov transformations mixing bosons and fermions. As an application, representations of Lie superalgebras are given which are semidirect products of extensions of affine Kac–Moody algebras and the Virasoro algebra, and of the super-Virasoro algebra.
Braid group representations arising from quantum supergroups with arbitrary q and link polynomials
Authors: Zhang R. B.
Published: July 2002

The theory of quantum supergroups is applied to the construction of braid group representations and link invariants. A method developed in an earlier publication is reviewed, which produces link polynomials from braid group representations generated by quantum supergroup invariant Ř matrices. When q is a generic complex parameter, this method, applied to the universal R matrices, yields hierarchies of link polynomials associated with different irreps of quantum supergroups. When q is a root of unity, suitable constraints are imposed on quantum supergroups to turn them into finite-dimensional quasitriangular Z2-graded Hopf algebras. The corresponding universal R matrices are obtained, which, in turn, lead to series of link polynomials upon using the above mentioned method. As concrete examples, the link polynomials related to the vector irreps of the quantum supergroups Uq(osp(M/2n)), all the irreps of Uq(osp(1/2)) with generic q, and a class of doubly atypical irreps of Uq(gl(2/1)) with q a root of unity are studied in detail.
The resonator with narrow slit and the model based on the operator extensions theory
Authors: Popov I. Yu.
Published: July 2002

The model of zero width slits based on the operator’s extension theory in an indefinite metric space for the wave scattering by a resonator with a narrow slit is constructed.
General method for reducing the two-body Dirac equation
Authors: Galeão A. P. , Ferreira P. Leal
Published: July 2002

A semirelativistic two-body Dirac equation with an enlarged set of phenomenological potentials, including Breit-type terms, is investigated for the general case of unequal masses. Solutions corresponding to definite total angular momentum and parity are shown to fall into two classes, each one being obtained by solving a system of four coupled first-order radial differential equations. The reduction of each of these systems to a pair of coupled Schrödinger-type equations is also discussed.
Semiclassical mechanics for time-dependent Wigner functions
Authors: Robinson Sam L.
Published: July 2002

An explicit and computable asymptotic integral representation is obtained for the time-dependent Wigner distribution associated with the initial quantum state ψ(x,0)=f(x) eiS(x)/ℏ in the semiclassical (ℏ→0) limit. The approximations are valid to arbitrarily high order in ℏ over any finite time interval. The leading order term is further analyzed to obtain a classically determined phase space function which is related to a classical probability density on phase space. The results hold for a large class of time-dependent potentials.
On certain quantum deformations of gl(N,R)
Authors: Fairlie David B. , Nuyts Jean
Published: July 2002

In this article all deformations of the general linear group, subject to certain restrictions which in particular ensure a smooth passage to the Lie group limit, are obtained. Representations are given in terms of certains sets of creation and annihilation operators. These creation and annihilation operators may belong to a generalization of the q-quark type or q-hadronic type with q-boson or q-fermion behavior. This leads to a natural definition of q-direct sums of q-algebras.
Nonstandard scalar quantum fields
Authors: Gudder Stanley
Published: July 2002

This article presents a theory of scalar quantum fields based on nonstandard analysis. Free scalar momentum fields and free Klein–Gordon fields are treated first. It is shown that the nonrigorous formalism of the standard theory can be replaced by a mathematically rigorous nonstandard theory. The second quantized energy–momentum operators are derived and the free quantum fields are diagonalized. Interacting scalar fields are considered and a nonstandard scattering operator is derived. A nonstandard counterpart to Wick’s theorem is developed and the φ4 interaction is briefly discussed.
Proof of Jacobi identity in generalized quantum dynamics
Authors: Adler Stephen L. , Bhanot Gyan V. , Weckel John D.
Published: July 2002

It is proven that the Jacobi identity for the generalized Poisson bracket is satisfied in the generalization of Heisenberg picture quantum mechanics recently proposed by one of the authors. The identity holds for any combination of fermionic and bosonic fields, and requires no assumptions about their mutual commutativity.
Dynamical evolution of the projector induced from the generalized squeezed state
Authors: Arai Takahiro
Published: July 2002

The quantum and classical time evolution of the approximate simultaneous observable on phase space (it is merely called a projector) induced from the generalized squeezed state is considered herein. The purpose of this article is to give a trace norm estimate of the difference between these two types of time evolutions of the projectors. As a consequence of this result, it is shown that this trace norm estimate converges to 0 as ℏ→0.
A Borel-like estimate for the rest of the heat kernel expansion
Authors: Malbouisson A. P. C.
Published: July 2002

It is shown that under some simple assumptions the rest of the truncated asymptotic expansion for the heat kernel has the form required for Borel summability, if N, the number of terms in the truncation, is sufficiently large. Rigorously speaking this result does not imply Borel summability, which requires a uniform bound in N, but it could be useful as a starting point for further investigation on global estimates for the zeta function.
On the arbitrariness of the general solution of an involutive partial differential equation
Authors: Seiler Werner M.
Published: July 2002

The relationship between the strength of a differential equation as introduced by Einstein, its Cartan characters, and its Hilbert polynomial is studied. Using the framework of formal theory previous results are extended to nonlinear equations of arbitrary order and to overdetermined systems. The problem of computing the number of arbitrary functions in the general solution is treated. Finally, the effect of gauge symmetries is considered.
On the projected bases for Sp(4)⊇U(2) and the orthogonalization problem
Authors: Ališauskas S. , Berej W.
Published: July 2002

The mutual expansion and overlaps of the projected (Smirnov–Tolstoy and Szpikowski–Berej) bases for the irreducible representations (irreps) of Sp(4) restricted to U(2) are considered. The equivalence relation connecting the overlaps of both (ST and SB) bases after the definite substitution of parameters (up to an elementary factor) is presented. The overlaps of the Szpikowski–Berej basis states are rearranged to double sums, restricted by the parameters characterizing the multiplicities of the repeating irreps of subgroup and thus representable in polynomial forms. The Regge-type symmetry of these new expressions allows the proof of the earlier conjectured symmetry of the orthogonalization coefficients (OC) for the family of the biorthogonal bases of Sp(4)⊇U(2), SU(4)⊇SU(2)×SU(2) and SU(n)⊇SO(n) for two parametric irreps. The structure of the orthogonalization coefficients for the Szpikowski–Berej basis is also considered. The symmetry of the Bα(c′abde) functions (as the conjectured numerator polynomials of OC) has been verified by means of computer algebra for some nontrivial cases.
Constrained hyperbolicity and discontinuity waves
Authors: Bampi Franco , Zordan Clara
Published: July 2002

The consequence of imposing stationary constraints on first-order hyperbolic differential systems is analyzed in detail and it is proved that such constraints can be compatible only with systems admitting zero-speed waves. The definition of constrained hyperbolicity is presented and examined with a view to its implications in the theory of wave propagation and in connection with second-order hyperbolic systems.
Statistical conception of quantum field theory
Authors: Rylov Yuri
Published: July 2002

Two equivalent modes of statistical description of stochastic particle production are considered, exclusive and inclusive. Information about particle production processes are distributed inside exclusive and inclusive descriptions in different ways. The exclusive description realizes an ‘‘all or nothing’’ investigation strategy, whereas the inclusive description realizes the ‘‘step by step’’ investigation strategy. Conventional quantum field theory is shown to use essentially an exclusive description. The possibility of a transition to a more reasonable investigation strategy (inclusive description) of particle production description is discussed.
q-deformation of high-order Virasoro algebra
Authors: Zha Chao-Zheng
Published: July 2002

The high-order Virasoro algebra (HOVA) is deformed on a quantum plane C2‖0 in a formalism reducible to the ordinary HOVA when q→1. After introducing the ‘‘associator,’’ the Jacobi identity and central extensions are also investigated. The q-deformed HOVA possesses a Hopf algebra structure within the framework of q-product algebra. The W∞-algebra expressed in terms of linear combinations of HOVA can thus be q-deformed and possess a Hopf algebra structure.
Adjoint boson realization of SU(N) and a family of structural zeros of 6j coefficients
Authors: Van der Jeugt J.
Published: July 2002

For the fundamental boson realization of SU(N) in its principal SO(3) basis, the generators of SU(N) are SO(3) tensor operators constructed out of one single type of boson, namely a boson with SO(3) multiplet label (N−1)/2. Here, the adjoint boson realization of SU(N) is given: this time the SO(3) tensor operators are constructed by means of N−1 types of bosons [those with SO(3) labels 1,2,..., N−1]. The validity of this realization depends upon a new identity between 6j coefficients. From this realization, or equivalently from this new identity, one can deduce the existence of a family of structural zeros of 6j coefficients.
The Hurwitz transformation: Nonbilinear version
Authors: Davtyan Levon S. , Sissakian Aleksey N. , Ter-Antonyan Valery M.
Published: July 2002

An alternative approach to the Hurwitz (H) transformation reducing Euclidean space E8 to Euclidean space E5 is developed. It is shown how refusal of the bilinearity condition leads to the replacement of the H-transformation by its modified nonbilinear (left and right) version: HL- and HR-transformations. The HL(HR)-transformation of the specific type eight-dimensional hyperspherical coordinates is investigated. The radial coordinate u and the polar angle θ/2, in this approach, transform into u2 and θ, respectively, like in the H-case. Action of these transformations on the remaining hyperspherical coordinates, unlike in the H-case, is equivalent to the invariance (shutting) of one angular triplet and the shutting (invariance) of another triplet. The connection of HL and HR with H is established and the structure of the H-transformation itself is revealed on this basis.
Towards a classification of su(2)⊕...⊕su(2) modular invariant partition functions
Authors: Gannon Terry
Published: July 2002

The complete classification of Wess–Zumino–Novikov–Witten modular invariant partition functions is known for very few affine algebras and levels, the most significant being all levels of A1 and A2 and level 1 of all simple algebras. Here, the classification problem is addressed for the nicest high rank semisimple affine algebras: (A1(1))⊕r. Among other things, all automorphism invariants are found explicitly for all levels k=(k1,...,kr), and the classification for A(1)1⊕A(1)1 is completed for all levels k1, k2. The classification problem for (A1(1))⊕r is also solved for any levels ki with the property that for i ≠ j each gcd(ki+2,kj+2)≤3. In addition, some physical invariants are found which seem to be new. Together with some recent work by Stanev, the classification for all (A1(1))k⊕r could now be within sight.