bluuebunny/crossref_metadata_2025 huggingface dataset:
Charge quantization in a Weyl model
Authors: Ranganathan D.
Published: July 2002

An alternative to the Kaluza Klein method for combining gauge groups and gravity based on Weyl’s theory is presented. For a particular geometrical representation of Dirac particles, in terms of two equal Weyl vectors of opposite parity, the following results will be proven. Proper formulation of the initial value problem for gravitation is possible only if one of the Weyl vectors can be decomposed in terms of quaternion-valued spinors. This leads to the model having an SU(2)⊗U(1) symmetry. The charges are fixed and the only permitted values are ±1, ±(1/3), ∓(2/3) times the charge of the ‘‘charged’’ vector boson, on purely geometrical grounds. The hypercharge assignments are calculated for spinors and scalars and shown to be those of the Weinberg–Salam model. Other experimental predictions of the model are discussed.
A simple proof of geodesical completeness for compact space-times of zero curvature
Authors: Yurtsever Ulvi
Published: July 2002

Any Riemannian metric on a compact manifold is geodesically complete. By contrast, it is widely known that incomplete compact Lorentzian manifolds exist. In this article it will be proven that a compact manifold with a smooth Lorentz metric must be complete if the metric is flat everywhere. This question of completeness; which has significant implications for the classification of (compact) Lorentzian space forms, has remained unresolved until quite recently, when it was finally established by Carrière as a special case of an even more general result. Here, a simple, alternative proof of this special case of Carrière’s theorem is given; the proof requires minimal mathematical machinery but still involves the use of some intriguing connections between the topology and global geometry of a compact flat space-time.
Minimal chiral Schwinger model in the matter gauge
Authors: Kim Won-Tae , Kim Jae-Kwan , Park Young-Jai
Published: July 2002

In the gauge-invariant formulation of the minimal chiral Schwinger model, we explicitly show the role of the Wess–Zumino field, which seems to be dynamical in the matter gauge φL=0. Furthermore, in this gauge we show how the left-handed chirality is maintained in the physical Hilbert space.
Simple calculation of Löwdin’s alpha function. IV. Procedure for evaluating the coefficients in expansion of a Slater-type atomic orbital
Authors: Suzuki Noboru
Published: July 2002

By using the explicit expression for the coefficients bKk(LM‖l)[Eq. (16) in J. Math. Phys. 26, 3193 (1985), which is referred to hereafter as Part II], a closed expression for the coefficients cij(NLM‖l) appearing in Löwdin’s alpha function (1/r)αl(NLM‖a,r) for a Slater-type atomic orbital is obtained. By manipulating its expression mathematically, it was manifested that cij(NLM‖l) vanishes if i≥N+L−M+l. For the specific cases that each of i and j takes 0 or 1, cij(NLM‖l) take the same value. From the symmetry relation on bKk(LM‖l) [Eq. (6) in Part II], it was proved that cij(NLM‖l)=cji(NLM‖l), provided M=L. Through some manipulation, the recursion formula for cij(NLM‖l) in N was derived, while that about M was obtained by introducing the recursion formula for bKk(LM‖l) in M [Eq. (24) in Part II] into the expression for cij(NLM‖l). For the special cases where N and M both are equal to L, the expression for cij(NLM‖l) is given in a compact and symmetric form. The use of this expression leads to a recursion formula for cij(LLL‖l) in L. Especially, cij(LLL‖l) for L=0 is expressed by a single term, and a recursion formula for cij(000‖l) in l was obtained in a very simple form. The systematic use of these recursion formulas leads to a procedure for evaluating cij(NLM‖l) successively. Finally, cij(NLM‖l) evaluated by this procedure, with the restriction that 2≥N≥L≥0 and 2≥min{L,l}≥M≥0, are given in a matrix form.
Duality rotation as a Lie–Bäcklund transformation
Authors: Przanowski M. , Maciol/ek-Niedżwiecki A.
Published: July 2002

It is shown that the duality rotation group for Maxwell electrodynamics in vacuum can be considered as a general Lie–Bäcklund transformation group acting on Fourier transforms of the electromagnetic potential. Conserved quantity connected with this group is found to be a consequence of the Noether theorem.
The collision of gravitational waves in a stiff perfect fluid
Authors: Griffiths J. B.
Published: July 2002

Exact solutions are presented which describe the collision and interaction of gravitational waves in a stiff fluid medium. The background region ahead of each wave is conformally flat, and the gravitational waves have constant and aligned polarization. Behind the waves the gravitational field is algebraically general, reflecting the fact that each wave is backscattered as it propagates through the fluid.
Alternative characterizations of unitarity of conformal models with 0<c<1
Authors: Pinson Haru T.
Published: July 2002

It is shown that a physical primary field composed with the adjoint of a physical primary field is single valued only for the unitary conformal models with central charge 0<c<1.
Note on ‘‘Large family of colliding waves in the Einstein–Maxwell theory’’
Authors: Halilsoy M.
Published: July 2002

As a supplementary to the general class of solutions published in this journal [J. Math. Phys. 31, 2694 (1990)] we remark that for a specific choice of our seed function we obtain an interesting solution which reduces to the well-known solutions of Khan–Penrose and Bell–Szekeres in particular limits.
Small oscillations: A new solution based on non-Noetherian symmetries
Authors: Hojman Sergio A.
Published: July 2002

A new (non-Noetherian) symmetry transformation for the small oscillations problem is exhibited. A novel way to solve this classical problem, based on conservation laws constructed using the new symmetry, is presented. Applications of these results to other fields of physics are outlined.
Comments on space–time signature
Authors: Coll Bartolomé , Morales Juan Antonio
Published: July 2002

In terms of three signs associated to two vectors and to a 2-plane, a formula for the signature of any four-dimensional metric is given. In the process, a simple expression for the sign of the Lorentzian metric signature is obtained. The relationship between these results and those already known are commented upon.
Some new spinor representations of quantum groups B
q(n), C
q(n), G
q(2)
Authors: Hakobyan T. S. , Sedrakyan A. G.
Published: July 2002

Using the known realizations of the quantum algebras Aq(n), Dq(n) in terms of quantum Clifford algebra and folding procedure of Lie algebras we construct some new spinor representations of Bq(n), Cq(n), Gq(2).
Simultaneous reconstruction of material and transient source parameters using the invariant imbedding method
Authors: Corones James , Sun Zhiming
Published: July 2002

This paper extends the time domain wave splitting and invariant imbedding method to an inhomogeneous wave equation with a source term: uxx−utt+A(x)ux=2D(x)i′(t). The direct scattering and inverse source problems of this equation are studied. Operators J̃± that map the source function into the scattered waves at the edges of the slab are defined. A system of coupled nonlinear integrodifferential equations for these scattering operator kernels is obtained. The direct scattering problem is to obtain the scattering operator kernels J± and R+ when parameters A and D are given. The inverse problem is to simultaneously reconstruct A(x) and D(x) from the scattering operator kernels R+(0,t), 0≤t≤2 and J−(0,t), 0≤t≤1. Both numerical inversion algorithms and the small time approximate reconstruction method are presented. A Green’s function technique is used to derive Green’s operator kernel equations for the calculation of the internal field. It provides an alternative effective and fast way to compute the scattering kernels J±. For constant A and D the Green’s operator kernels and source scattering kernels are expressed in closed form. Several numerical examples are given.
Obtaining magnetic monopole solutions by use of the Laplace transform
Authors: Fitzsimmons Sean
Published: July 2002

We solve the modified Toda molecule equation by use of a Laplace transform technique for the Lie algebras An, Bn, Cn, and G2 with the appropriate boundary conditions for obtaining magnetic monopole solutions.
A formulation of supergravity based on Cartan’s connection
Authors: Zardecki Andrew
Published: July 2002

The supergravity is formulated as a gauge theory with the Yang–Mills Lagrangian quadratic in curvature. To arrive at such a description, the super fiber bundle based on a superspace with the OSP(n/4) symmetry group is introduced. The connection in this bundle becomes the Cartan connection when OSP(n/4) is broken to SL(2,C)⊗SO(n). In the reduced bundle, this leads automatically to curvature and torsion. Explicit calculations of the Lagrangian are carried out in terms of the Cartan–Killing metrics and the curvature form for n=1 and n=8. The final theory describes the coupling of geometry to fermion fields. These fields emerge as solder forms of the Cartan connection.
Unitarity and complete reducibility of certain modules over quantized affine Lie algebras
Authors: Zhang Y.-Z. , Gould M. D.
Published: July 2002

Let Uq(𝒢̂) denote the quantized affine Lie algebra and Uq(𝒢(1)) the quantized nontwisted affine Lie algebra. Let 𝒪fin be the category defined in Sec. III. It is shown that when the deformation parameter q is not a root of unit all integrable representations of Uq(𝒢̂) in the category 𝒪fin are completely reducible and that every integrable irreducible highest weight module over Uq(𝒢(1)) corresponding to q≳0 is equivalent to a unitary module.
C-integrable nonlinear partial differential equations. III
Authors: Calogero F. , Xiaoda Ji
Published: July 2002

A technique based on a change of dependent variables, used in a previous paper to generate C-integrable nonlinear partial differential equations (PDEs) (i.e., nonlinear PDEs linearizable by an appropriate Change of variables) in 1+1 dimensions (one time and one space variables), is extended to the case of more than one space dimension. Several examples of evolution C-integrable PDEs in 1+2 dimensions (one time and two space variables) are exhibited.
Schwinger terms and cyclic cohomology for massive 1+1-dimensional fermions and Virasoro algebras
Authors: Grosse Harald , Maderner Walter , Reitberger Christian
Published: July 2002

An important example of characters on two-summable Fredholm modules are Schwinger terms arising in the commutators between charge and axial-charge operators. 1+1-dimensional massive fermions are discussed using the language of quasifree second quantization and for a large class of models the usual δ′-Schwinger term is obtained. The results confirm calculations within the massive Schwinger model at finite temperature but disagree with a conjecture concerning anomaly meltdown. The dependence of the Virasoro cocycle in the quasifree second-quantization framework on traceclass perturbations (like charging and thermalizing) are also investigated.
On the absence of the Painlevé property in Petrov type III Robinson–Trautman solutions
Authors: Garcia-Díaz A. , Plebański J. F. , Sibgatullin N. R.
Published: July 2002

It is shown that solutions of the exact reduced generalized Liouville-like equation, determining Petrov-type III gravitational fields within the Robinson–Trautman family of metrics, possess movable critical points, that is, they do not exhibit the Painlevé property.
Bounds for the exact matrix elements for radiation processes in hydrogenic atoms. II
Authors: Moses Harry E. , Prosser Reese T.
Published: July 2002

In recent articles [H. E. Moses and R. T. Prosser, ‘‘Exact matrix elements for radiation processes in hydrogenic atoms,’’ J. Math. Phys. 33, 1878–1886 (1992); ‘‘Bounds for the Appell Function F2’’] the authors have obtained uniform bounds for the exact matrix elements for elementary radiation processes involving the ground state in both nonrelativistic and relativistic hydrogenic atoms. Here these results are extended to obtain uniform bounds for the exact matrix elements involving other stationary states of these atoms. These results will be used in a sequel to bound the exact interaction operator in a study of radiation processes involving the hydrogen atom.
A no-go theorem for a Lie-consistent q-Campbell–Baker–Hausdorff expansion
Authors: Katriel Jacob , Solomon Allan I.
Published: July 2002

Lie consistency is defined for commutator expansions and it is shown that while a weakly Lie-consistent q-Campbell–Baker–Hausdorff expansion for a product of two M-type (but not P-type) q exponentials can be formulated, a strongly Lie-consistent expansion only exists for the undeformed case, q=1.
Quantization of a classical system on a coadjoint orbit of the Poincaré group in 1+1 dimensions
Authors: Ali S. Twareque , Mueller Ute A.
Published: July 2002

The connection is investigated between quantization by means of coherent states and geometric quantization, when the base manifold is a coadjoint orbit, and hence a homogeneous space, of the (1+1)-dimensional Poincaré group. Coherent states of the Poincaré group stem from a representation that is square-integrable modulo closed subgroup, and so they depend on a measurable section on the given homogeneous space. For each section that leads to a tight frame, a geometric prequantization is constructed, i.e., a Hermitian line bundle with metric connection. Conditions are given under which the two forms associated to the connection and to the coadjoint orbit structure of the base manifold coincide.
Phase-space dynamics and Hermite polynomials of two variables and two indices
Authors: Dattoli G. , Lorenzutta S. , Maino G. , Torre A.
Published: July 2002

The theory of Hermite polynomials of two variables and two indices is discussed herein. Within the context of phase-space formulation of classical and quantum mechanics, they play the same role as conventional Hermite polynomials in ordinary quantum mechanics. Finally their extension to m variables and m indices is analyzed.
Overcoming dissipative distortions by a waveform restorer and designer
Authors: Foong S. K.
Published: July 2002

Dissipation causes distortions in wave propagations. A new scheme for restoring such distorted waveforms based on a generalized Kac’s method of solving wave equation with dissipation is proposed. From only the component parts of the wave received over time at a point in space, and without the knowledge of them at other points, the wave that would have been received at the point in the absence of dissipation is then restored. The new scheme can be adapted to function as a waveform designer for designing the to-be-transmitted waveform such that the distorted distorted-waveform to be received becomes the intended one. The details of such a mathematical construction of the waveform restorer and designer are given.
Failure of universality in noncompact lattice field theories
Authors: Gallivan T. E. , Kapulkin Arie
Published: July 2002

The nonuniversal behavior of two noncompact nonlinear sigma models is described. When these theories are defined on a lattice, the behavior of the order parameter (magnetization) near the critical point is sensitive to the details of the lattice definition. This is counter to experience and to expectations based on the ideas of universality.
Time displaced interactions: Classical dynamics and path integral quantization
Authors: Schulman L. S.
Published: July 2002

The path integral was created to quantize systems whose dynamics are nonlocal in time and for which a Hamiltonian formulation could not be found. In this article we quantize a linear oscillator with an interaction that depends on the oscillator’s position at past and future times. The central issue is the classical boundary value problem for such an oscillator. Because two-time functional boundary conditions are used to implement the quantization, we take up related questions, such as causality in this context, and the general issue of stability for forward and inward data specifications.
Semiclassical eigenvalues and shape problems on surfaces of revolution
Authors: Gurarie David
Published: July 2002

Mark Kac [‘‘Can one hear the shape of drums?’’ Am. Math. Monthly 73, 1–23 (1966)] asked if the shape of a region Ω⊆Rn could be determined from its sound (spectrum of the Laplacian ΔΩ). He proved the conjecture for special classes of domains, including polygons and balls in Rn. Similar problems could be raised in other geometric contexts, including ‘‘shape of metric’’ for Laplacians on manifolds or ‘‘shape of potential’’ for Schrödinger operators HV=Δ+V. The latter two problems for surfaces of revolution Σ are addressed. An explicit reconstruction procedure will be outlined that leads from the joint spectrum of H=Δ or Δ+V and the angular momentum algebra so(n) to the ‘‘shape of Σ’’ and ‘‘V,’’ respectively. The metric result applies to generic surfaces of revolution, while the Schrödinger result allows all zonal (axisymmetric) potentials V on Σ. So the work extends the Kac’s ‘‘n-ball’’ result as well as the n-sphere ‘‘zonal Schrödinger theory’’ [D. Gurarie, (a) ‘‘Averaging methods in spectral theory of Schrödinger operators,’’ Maximal Principles and Eigenvalues Problems in Differential Equations, Pitman Research Notes Vol. 175, edited by P. W. Schaefer (Pitman, New York, 1980), pp. 167–77; (b) ‘‘Inverse spectral problem for the two-sphere Schrödinger operators with zonal potential,’’ Lett. Math. Phys. 16, 313–323 (1990); (c) ‘‘Zonal Schrödinger operators on the n-sphere: Inverse spectral problem and rigidity,’’ Commun. Math. Phys. 131, 571–603 (1990)].
A noncommutative geometric model with horizontal family symmetry
Authors: Hanlon B. E. , Joshi G. C.
Published: July 2002

The important role of multiple fermionic families in noncommutative geometry is investigated by introducing a horizontal symmetry into the model building scheme. It is demonstrated that this can be done consistently.
Price’s bound on the structure factor: Derivation and comparison with some exact results
Authors: Lee M. Howard
Published: July 2002

Some years ago, P. J. Price obtained an important (but not well recognized) bound on the structure factor in the ground state. A more general version is derived by means of sum rules, showing a limitation imposed on by the f sum rule. The condition for merging of the bound with the structure factor turns out to be the existence of a single branch in the excitation spectrum. Price’s bound is tested in exactly solvable many-body models, most of which are models for Fermi particles, some not satisfying the f sum rule. This analysis sheds light on the structure factors of these models. Also, Price’s bound is compared with other bounds obtained by convexity theory. Finally, by formulating it in terms of a moment, the existence of Price’s bound in a wider class of models is established.
Lazutkin coordinates and invariant curves for outer billiards
Authors: Amiran Edoh Y.
Published: July 2002

The outer billiard ball map (OBM) is defined from and to the exterior of a domain, Ω, in the plane as taking a point, q, to another point, q1, when the line segment with endpoints q and q1 is tangent to the boundary, ∂Ω (with a chosen orientation), and the point of tangency with the boundary divides the segment in half. Let C be an invariant circle for the OBM on Ω, with ∂Ω smooth with positive curvature. After computing the loss of derivatives between ∂Ω and C, it is shown via KAM theory that in this setting the OBM has uncountably many invariant circles in any neighborhood of the boundary. One is also led to an infinitesimal obstruction for the evolution property, an obstruction which, among closed smooth convex curves, is only removed for ellipses.
Hamiltonian structure and integrability of the stationary Kuramoto–Sivashinsky equation
Authors: Bouquet S.
Published: July 2002

In this article, the stationary Kuramoto–Sivashinsky (KS) equation is studied. It is shown, first, that this equation can be transformed into a one-dimensional Hamiltonian system describing the motion of a particle in a time-dependent potential. Second, working with this formalism and coming back, then, to the initial KS equation, a subset of initial conditions is derived for which the corresponding solutions u(x) will behave like the dominant pole 120/(x−x0)3, deduced from the Painlevé analysis, and will explode in a finite ‘‘time.’’ Finally, special attention is given to the well-known Kuramoto–Tsuzuki solution and it is shown that provided the independent variable x is initialized in a specified domain, this solution explodes also like 120/(x−x0)3.
Lorentzian three-metrics with degenerate Ricci tensors
Authors: McManus Des J.
Published: July 2002

A classification of Lorentzian three-metrics whose Ricci tensor satisfies Rij=λ1gij+λ2vivj with λ1 and λ2(≠0) constant where vivi=κ(=0 or ±1) is given. An explicit coordinate representation is given for all the metrics that admit a G4 group as their maximal isometry group. Those metrics that admit a G3 as their maximal isometry group belong to either Bianchi class VI0, or VII0, or VIII, or IX when κ ≠ 0, and to either Bianchi class III, or IV, or VI0, VIh, or VIII when κ=0. An explicit coordinate representation is given for all the inhomogeneous solutions in the case κ ≠ 0.
Parametric manifolds. II. Intrinsic approach
Authors: Boersma Stuart , Dray Tevian
Published: July 2002

A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) one-form field. Such a manifold admits natural generalizations of Lie differentiation, exterior differentiation, and covariant differentiation, all based on a nonstandard action of vector fields on functions. There is a new geometric object, called the deficiency, which behaves much like torsion, and which measures whether a parametric manifold can be viewed as a one-parameter family of orthogonal hypersurfaces.
Generalized q-exponentials related to orthogonal quantum groups and Fourier transformations of noncommutative spaces
Authors: Schirrmacher Arne
Published: July 2002

Essential prerequisites for the study of q-deformed physics are particle states in position and momentum representation. In order to relate x and p space by Fourier transformations the appropriate q-exponential series related to orthogonal quantum symmetries is constructed. It turns out to be a new q-special function giving rise to q-plane wave solutions that transform with a noncommutative phase under translations.
The double-well splitting of the low energy levels for the Schrödinger operator of discrete φ4-models on tori
Authors: Dobrokhotov Sergei Yu. , Kolokol’tsov Vassili N.
Published: July 2002

The formula is obtained for the asymptotics of the splitting of the first two eigenvalues of the Schrödinger operator that stands for the discrete multidimensional φ4-model on tori. The behavior of the main term is investigated in the limit of the large number of particles.
Symplectic symmetry of Hubbard model and η pairing
Authors: Sun C. C. , Li B. F. , Li Z. S.
Published: July 2002

By means of symplectic group Sp(2M), the symplectic symmetry of the Hubbard model and the η pairing are investigated to approach the eigenstates which have the largest spin multiplicities. The behavior of the off-diagonal long-range order of these eigenstates is examined by the criterion proposed by Yang and the energy diagram of the corresponding eigenvalues is elucidated by the η pairing mechanism. A basis set which is expressible in terms of η and ηa pairings is proposed.
Similarity solutions for the type D fluid plates in 5-D flat space
Authors: Gupta Y. K. , Sharma J. R.
Published: July 2002

All the similarity solutions, describing the Petrov-type D, plane symmetric perfect fluid distributions of imbedding class one, have been derived by using the Lie continuous point group similarity transformation method.
An equivalence proof of the background gauge field quantization and the conventional one
Authors: Tinebra Fabrizio
Published: July 2002

The background gauge field quantization is a convenient tool for studying weakly interacting gauge and matter fields or analyzing anomalous current conservation in fermionic structures. This method is from the mid 1970’s, but it is only today that it received renewed interest for investigating nonperturbative evolution equations in Yang–Mills theory, as well as gauge field effective action formulations. We reviewed, to start with, the general formulation and assumptions about this method, and we pointed out some critical observations concerning it. In particular, we focus on some of the most common equivalence proofs presently known in the literature. We attempted to give a most convincing demonstration of this equivalence as it stands between the background gauge field scattering operator and the conventional one. The result shown here clearly indicates these methods are indeed physically equivalent. In proving that, we neglected all the infrared problems afflicting the pure Yang–Mills gauge theory; as a matter of fact, they appear to be a parallel, but nonintersecting problem with respect to the present one, i.e., to prove the equivalence.
Qualitative analysis of causal cosmological models
Authors: Méndez Vicenç , Triginer Josep
Published: July 2002

The Einstein’s field equations of Friedmann–Robertson–Walker universes filled with a dissipative fluid described by both the truncated and non-truncated causal transport equations are analyzed using techniques from dynamical systems theory. The equations of state, as well as the phase space, are different from those used in the recent literature. In the de Sitter expansion both the hydrodynamic approximation and the non-thermalizing condition can be fulfilled simultaneously. For Λ=0 these expansions turn out to be stable provided a certain parameter of the fluid is lower than 1/2. The more general case Λ≳0 is studied in detail as well.
A solvable N-body problem in the plane. I
Authors: Calogero F.
Published: July 2002

We introduce and discuss an n-body problem in the plane, characterized by equations of motion of Newtonian type, r⃗̈j=∑k=1nF⃗jk, j=1,..,n, with given ‘‘forces’’ F⃗jk having the following characteristics: F⃗jk depends only on r⃗j,r⃗k,r⃗̇j,r⃗̇k (i.e., only ‘‘one-body’’  and  ‘‘two-body’’  forces  are  present);  F⃗jk behaves as a (two-dimensional) vector under rotations in the plane (i.e., the model is ‘‘rotation-invariant’’); for j=k,F⃗jk is linear in r⃗j and r⃗̇j; for j≠k, F⃗jk=|r⃗j−r⃗k|−2f⃗jk with f⃗jk a homogeneous polynomial of third degree in r⃗j,r⃗k,r⃗̇j,r⃗̇k (hence F⃗jk is homogeneous of degree one in r⃗j,r⃗k,r⃗̇j,r⃗̇k); F⃗jk contains linearly 8 arbitrary (‘‘coupling’’) constants. The n-body problem is solvable for arbitrary n and for arbitrary values of the 8 coupling constants; its solutions display a rich phenomenology. If the 8 coupling constants are suitably restricted, the model is translation-invariant, and/or Hamiltonian; of course, when it is Hamiltonian, it is integrable; indeed in some case a Hamiltonian function can be explicitly displayed, as well as the corresponding Lax pair.
Motion of strings in the plane: A solvable model. I
Authors: Calogero F.
Published: July 2002

By taking appropriately the n→∞ limit of a (recently introduced) eight-parameter family of solvable (classical, nonrelativistic) n-body problems in the plane, a solvable eight-parameter family of models is introduced, each of which describes the motion in the plane of a string (possibly composed of several pieces). In this paper the equations of motion which characterize these models are displayed, the technique to “solve” them is outlined, and special solutions are exhibited (for certain models, quite explicitly). A more detailed analysis of the phenomenology of the string motions entailed by these models is postponed to future papers.
Euclidean two-dimensional gravity with torsion
Authors: Katanaev M. O.
Published: July 2002

Two-dimensional gravity with torsion is considered assuming Euclidean signature of the metric. A general solution of the Euler–Lagrange equations is found in the conformal gauge. Extremals and geodesics are found and analyzed. All global Euclidean solutions are explicitly constructed and classified. Besides the constant curvature Riemann surfaces of arbitrary genus there are a large number of compact and noncompact surfaces of nonconstant curvature and non-trivial torsion possessing conical singularities. The relation between Lorentz and Euclidean global solutions is analyzed.
The universal anomalies and condition for anomaly-free high-order Virasoro algebra
Authors: Zha Chao-zheng , Zhao Wei-zhong
Published: July 2002

We construct the anomalous Ward identity for high-order Virasoro gravity and give the general calculation to obtain the anomaly-free condition.
Bifurcation behavior of the generalized Lorenz equations at large rotation numbers
Authors: Zhou Cangtao , Lai C. H. , Yu M. Y.
Published: July 2002

The bifurcation structure and periodic orbits of the Lorenz–Stenflo equations at large rotation numbers are given. It is shown that rotation can lead to a much richer dynamical behavior than that of the original Lorenz system and can be used to control or modify the latter’s chaos behavior. Orbits with new topology arising from the merging and splitting of different periodic windows are observed. Abrupt changes in the one-dimensional map are pointed out and studied in terms of the interaction of the interior and exterior boundaries.
Renormalized path integral in quantum mechanics
Authors: Henderson R. J. , Rajeev S. G.
Published: July 2002

We obtain direct, finite, formulations of a renormalized quantum mechanical system with no reference to ultraviolet cutoffs and running coupling constants, in both the Hamiltonian and path integral pictures. The path integral description requires a modification to the Wiener measure on continuous paths that describes an unusual diffusion process wherein colliding particles occasionally stick together for a random interval of time before going their separate ways.
Representations of Sp(6,R) and SU(3) carried by homogeneous polynomials
Authors: Rangarajan Govindan
Published: July 2002

In this paper, we study representations of Sp(6,↛) and SU(3) carried by homogeneous polynomials of phase-space variables in six dimensions. These representations are very important for the study of symplectic integration techniques for Hamiltonian systems. We obtain irreducible representations for Sp(6,↛) and SU(3) and explicit expressions for states within SU(3) representations in terms of phase-space variables.
Comment on: Diffusion through a slab
Authors: Gieseler U. D. J. , Kirk J. G.
Published: July 2002

Mahan [J. Math. Phys. 36, 6758 (1995)] has calculated the transmission coefficient and angular distribution of particles which enter a thick slab at normal incidence and which diffuse in the slab with linear anisotropic, non-absorbing, scattering. Using orthogonality relations derived by McCormick and Kuščer [J. Math. Phys. 6, 1939 (1965); 7, 2036 (1966)] for the eigenfunctions of the problem, this calculation is generalized to a boundary condition with particle input at arbitrary angles. It is also shown how to use the orthogonality relations to relax in a simple way the restriction to a thick slab.
On a coupled Kuramoto–Sivashinsky and Ginzburg–Landau-type model for the Marangoni convection
Authors: Duan Jinqiao , Bu Charles , Gao Hongjun , Taboada Mario
Published: July 2002

The surface tension driven Marangoni convection is an interesting pattern formation system. The “primitive” governing equations are too complicated to be investigated analytically. In this paper, the authors consider a simplified model for this system. This simplified model is in the form of coupled Kuramoto-Sivashinsky and Ginzburg-Landau type partial differential equations. The authors prove the existence and uniqueness of global solutions of this simplified mathematical model under the condition that the Marangoni number Ma>Mac+k/25, where Mac is the critical Marangoni number at which the trivial stationary state becomes linearly unstable, and k is a positive constant related to other system parameters. The authors use the contraction mapping principle in the proof. This work sets the foundation for further study of this model.
Differential Hopf algebra structure of the quantum standard complex
Authors: Drabant Bernhard
Published: July 2002

We are investigating the quantum standard complex (K(q,g),d) of the quantum enveloping algebra Uq(g) for Lie algebras 𝔤 associated with the root systems, An, Bn, Cn, and Dn. It is a quantum version of the standard Koszul complex associated to a Lie algebra as applied for instance in the BRS quantization procedure in connection with spin representations. Using techniques from the theory of braided monoidal categories we obtain a differential Hopf algebra structure on the complex (K(q,g),d).
Irregular Uq
(sl(3)) representations at roots of unity via Gel’fand–(Weyl)–Zetlin basis
Authors: Dobrev V. K. , Truini P.
Published: July 2002

The Gel’fand–(Weyl)–Zetlin (GWZ) description of the Uq(sl(3)) irregular irreps at roots of unity is explicitly given. Those are irreps fixed by the same parameters as the unitary irreducible representations (UIRs) of SU(3) yet having dimensions smaller than their classical counterparts, the reason being that to obtain an irregular irrep one has to make factorization of an additional submodule. This description is made geometrically transparent by an arrangement of the standard SU(3) GWZ basis in a hexagonal pyramid, which is valid for any q and seems new even for q=1. The pyramid has as a base the standard hexagon which gives the weight space of the UIRs of SU(3) in the plane of third component of isospin Iz and hypercharge Y, while third dimension of this pyramid is related to the isospin I. Algebraically this arrangement is related to a one-to-one correspondence between the abstract GWZ states and monomials in the algebra of raising generators Uq(𝒢+); however, those monomials are not in the standard Poincaré–Birkhoff–Witt (PBW) basis of Uq(𝒢+). The additional factorization corresponds to taking away an upper part of the pyramid, itself being a hexagonal pyramid representing another SU(3) irrep of smaller dimension, which for roots of unity becomes the submodule to be factored out. The technical tool in this factorization is the explicit coincidence of two polynomials: one giving the singular vectors of the Verma modules, the other used in the algebraic description of the pyramid.
Grassmann manifold bosonization of QCD in two dimensions
Authors: Han Kyoung Ho , Shin H. J.
Published: July 2002

Two-dimensional QCD is bosonized to be an integrably deformed Wess–Zumino–Witten model under proper limit. Fermions are identified having indices of the Grassmann manifold. Conditions for integrability are analyzed and their physical meanings are discussed. We also address the nature of the exactly solvable part of the theory and find the infinitely many conserved quantities.
Nonlinear quantization of integrable classical systems
Authors: Scotti Antonio , Ushveridze Alexander
Published: July 2002

It is demonstrated that the so-called “unavoidable quantum anomalies” can be avoided in the framework of a special nonlinear quantization scheme. In this scheme, the quantized Hamiltonians are represented by nonlinear but homogeneous operators in Hilbert space. The nonlinear terms are of the same order as quantum anomalies, and their role is to cancel anomalies. The quantization method proposed is applicable to integrable classical dynamical systems and the result of quantization is again an integrable (but, generally, nonlinear) “quantum” system. A simple example is discussed in detail. Irrespective of the existence of possible physical applications, the method provides a constructive way for extending the notion of quantum integrability to nonlinear spectral problems and gives a practical tool for building completely integrable nonlinear spectral equations in Hilbert space.
Representations of the BRST algebra and unsolvable algebraic problems
Authors: Horuzhy S. S. , Voronin A. V.
Published: July 2002

Complete solution of the decomposition problem for finite-dimensional representations π of the BRST algebra 𝒜 is presented. As shown earlier by the authors [Rev. Math. Phys. 5, 191 (1993)], 𝒜 coincides with the Lie superalgebra l(1,1). It is proved that an arbitrary π either has the decomposition into a direct sum of irreducible and/or indecomposable representations (IR and IDR, respectively) or has the set of indecomposable subrepresentations that does not admit any classification. All the series of IDR are explicitly described, and all the unclassifiable cases are reduced to definite unsolvable algebraic problems. The absence of classification is established by means of a special computer method, which opens a new possibility to search for unsolvable algebraic problems.
Quantum martingale measures and stochastic partial differential equations in Fock space
Authors: Applebaum David
Published: July 2002

A concept of quantum martingale measure is introduced and examples are constructed as quantum stochastic spectral integrals in Fock space. These are then utilized as space–time noise to drive a parabolic stochastic partial differential equation (spde). We establish the existence and uniqueness of the solutions as families of densely defined closable operators in Fock space that are jointly continuous in time and space variables and satisfy a Markov property.
Constrained dynamics for quantum mechanics. I. Restricting a particle to a surface
Authors: Grundling Hendrik , Hurst C. A.
Published: July 2002

We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done, in particular, for the restriction of a quantum particle in Rn to a curved submanifold, and we propose a method of constraining and dynamics adjustment that produces the right Hamiltonian on the submanifold when tested on known examples. This method will be the germ of a “Dirac algorithm for quantum constraints.” We generalize it to the situation where the constraint is a general self-adjoint operator with some additional structures.
Generalized similarity solutions for the type D fluid in five-dimensional flat space
Authors: Bhutani O. P. , Singh K.
Published: July 2002

The partial differential equation corresponding to the metric function in a five-dimensional flat space describing the perfect fluid distribution has been examined for generalized symmetries via a new approach. It is shown that the approach utilized here has, besides providing generalized symmetries, for some particular values of the parameters involved, yielded new metrics and Petrov type D solutions. Further, for the general case the problem is reduced to the solution of an Abel’s equation of second kind, which obviously generalizes the scope for new metrics and new Petrov type D solutions.
On different integrable systems sharing the same nondynamical r-matrix
Authors: Qiao Zhijun , Strampp Walter
Published: July 2002

In a recent paper [Zhijun Qiao and Ruguang Zhou, Phys. Lett. A 235, 35 (1997)], the amazing fact was reported that a discrete and a continuous integrable system share the same r-matrix with the interesting property of being nondynamical. Now, we present three further pairs of different continuous integrable systems sharing the same r-matrix again being nondynamical. The first pair is the finite-dimensional constrained system (FDCS) of the famous AKNS hierarchy and the Dirac hierarchy; the second pair is the FDCS of the well-known geodesic flows on the ellipsoid and the Heisenberg spin chain hierarchy; and the third pair is the FDCS of one hierarchy studied by Xianguo Geng [Phys. Lett. A 162, 375 (1992)] and another hierarchy proposed by Zhijun Qiao [Phys. Lett. A 192, 316 (1994)]. All those FDCSs possess Lax representations and from the viewpoint of r-matrix can be shown to be completely integrable in Liouville’s sense.
A dynamical symmetry breaking model in Weyl space
Authors: Feoli A. , Wood W. R. , Papini G.
Published: July 2002

The dynamical process following the breaking of Weyl geometry to Riemannian geometry is considered by studying the motion of de Sitter bubbles in a Weyl vacuum. The bubbles are given in terms of an exact, spherically symmetric thin shell solution to the Einstein equations in a Weyl–Dirac theory with a time-dependent scalar field of the form β=f(t)/r. The dynamical solutions obtained lead to a number of possible applications. An important feature of the thin shell model is the manner in which β provides a connection between the interior and exterior geometries since information about the exterior geometry is contained in the boundary conditions for β.
Duality, partial supersymmetry, and arithmetic number theory
Authors: Spector Donald
Published: July 2002

We find examples of duality among quantum theories that are related to arithmetic functions by identifying distinct Hamiltonians that have identical partition functions at suitably related coupling constants or temperatures. We are led to this after first developing the notion of partial supersymmetry, in which some, but not all, of the operators of a theory have superpartners, and using it to construct fermionic and parafermionic thermal partition functions, and to derive some number theoretic identities. In the process, we also find a bosonic analog of the Witten index, and use this, too, to obtain some number theoretic results related to the Riemann zeta function.
Infinite moments of the partition function for random walks in a random potential
Authors: Coyle Lester N.
Published: July 2002

We consider a system of random walks (directed polymers) in a potential which is random in space and time. Investigations into untypical behavior and the inverse of the partition function leads to the result that, regardless of the strength of the potential and in all dimensions, all higher moments of the partition function are unbounded as time goes to infinity. One can interpret this result in a many-body quantum mechanical setting as saying that no matter how small the strength of an attractive potential, in any dimension one can find N (the number of particles) large enough so that there is a bound state.
Infinite and finite Gleason’s theorems and the logic of indeterminacy
Authors: Pitowsky Itamar
Published: July 2002

In the first half of the paper I prove Gleason’s lemma: Every non-negative frame function on the set of rays in R3 is continuous. This is the central and most difficult part of Gleason’s theorem. The proof is a reconstruction of Gleason’s idea in terms of orthogonality graphs. The result is a demonstration that this theorem is actually combinatorial in nature. It depends only on a finite graph structure. In the second half of the paper I use the graph construction to obtain results about probability distributions (non-negative frame functions with weight one) on finite sets of rays. For example, given any two distinct nonorthogonal rays a and b, I construct a finite set of rays Γ that contains them, and has the following property: No probability distribution on Γ assigns both a and b a truth value (probability zero or one) unless they are both false. Thus the principle of indeterminacy turns into a theorem of propositional quantum logic (or partial Boolean algebras).
Yang–Mills field equations for the Coriolis tensor in the n-body problem
Authors: Reinsch Matthias
Published: July 2002

The configuration space of a system of n particles has the structure of a principal fiber bundle under the action of the rotation group. In this paper, identities are derived for the curvature of the natural connection on this bundle. These identities are translated into statements about the Coriolis tensor, the local expression for this curvature on the base space of the bundle. The Coriolis tensor is shown to obey field equations of the Yang–Mills type.
Quantization of a particle in a background Yang–Mills field
Authors: Wu Yihren
Published: July 2002

Two classes of observables defined on the phase space of a particle are quantized, and the effects of the Yang–Mills field are discussed in the context of geometric quantization.
Integrable structure of the new Calogero models
Authors: Karimipour V.
Published: July 2002

We show that the integrability of the dynamical system recently proposed by Calogero and characterized by the Hamiltonian H=∑j,kNpjpk{λ+μ cos[ν(qj−qk)]} is due to a simple algebraic structure. It is shown that this system is canonically equivalent to the classical Heisenberg magnet with long-range interactions. Our method shows clearly how these types of systems can be generalized and provides the mechanism of integrability of a large class of similar systems.
Anti-isospectral transformations, orthogonal polynomials, and quasi-exactly solvable problems
Authors: Khare Avinash , Mandal Bhabani Prasad
Published: July 2002

We consider the double sinh-Gordon potential which is a quasi-exactly solvable problem and show that in this case one has two sets of Bender–Dunne orthogonal polynomials. We study in some detail the various properties of these polynomials and the corresponding quotient polynomials. In particular, we show that the weight functions for these polynomials are not always positive. We also study the orthogonal polynomials of the double sine-Gordon potential which is related to the double sinh-Gordon case by an anti-isospectral transformation. Finally we discover a new quasi-exactly solvable problem by making use of the anti-isospectral transformation.
On a certain formulation of the Einstein equations
Authors: Nurowski Paweł
Published: July 2002

We define a certain differential system on an open set of R6. The system locally defines a Lorentzian four-manifold satisfying the Einstein equations. The converse statement is indicated and its details are postponed to the forthcoming paper.
Stochastic construction of a Feynman path integral representation for Green’s functions in radiative transfer
Authors: Miller Steven D.
Published: July 2002

A construction of a stochastic, Lagrangian path integral representation is presented for classical Green’s functions or propagators for radiative transfer in random scattering medias. As Fermat rays comprising the initial collimated pulse (e.g., from a laser) enter the medium, they evolve into a bundle of random paths or trajectories due to scattering. Stochastically, this can be interpreted as a bundle of randomly evolving Markov trajectories traced out by a gas or ensemble of “Brownian-type” classical point photons undergoing multiple scatterings. The path integral is structurally of the same form as a Wick rotated Euclidean quantum Feynman integral with direct optical analogs of the Hamiltonian and Lagrangian emerging. However, the optical stochastic integral is real and is defined in real time becoming exponentially damped rather than oscillatory. The calculation also constitutes an alternative mathematical derivation of the time dependent diffusion equation from the radiative transfer theory. The limits of the path integral representation give a maximally diffused Gaussian distribution of the heat kernal form (the large scatter limit) and a Beer’s law exponential decay corresponding to the extremal Fermat rays obeying Euler–Lagrange equations (the zero scatter limit). The approach also highlights the direct structural analogs between classical radiative transfer and optical diffusion in real time (t) and ordinary quantum mechanics in Euclidean time (√(−1)t=it).
The monotony criterion for a finite size scaling analysis of phase transitions
Authors: Meyer-Ortmanns Hildegard , Reisz Thomas
Published: July 2002

We propose a new criterion to analyze the order of phase transitions within a finite size scaling analysis. It refers to response functions like order parameter susceptibilities and the specific heat and states different monotony behavior in volume for first- and second-order transitions close to the transition point. The criterion applies to analytical and numerical studies of phase diagrams including tricritical behavior.