bluuebunny/crossref_metadata_2025 huggingface dataset:
Complete sets of functions for perturbations of Robertson Walker cosmologies
Authors: Kalnins E. G. , Miller W.
Published: July 2002

Crucial to a knowledge of the perturbations of Robertson Walker cosmological models is a knowledge of complete sets of functions with which to expand such perturbations. For the open Robertson Walker cosmology, this question will be completely answered. In addition, some observations will be made concerning explicit solution by separation of variables of wave equations for spin s in a Riemannan space having an infinitesmal line element of which the Robertson Walker models are a special case.
A new identity for some six-j symbols
Authors: Ginocchio Joseph N.
Published: July 2002

A new sum rule is derived for the six-j symbol in which four of the angular momenta are equal. This sum rule differs from other sum rules in that the six-j symbol is not weighted by 2L+1 where L is the angular momentum being summed over.
Vector states on orthoposets and extremality
Authors: Tkadlec Josef
Published: July 2002

Vector states on orthoposets and quantum logics are analyzed. These states are characterized and the sphere-valued states are shown to be orthogonally scattered in the sense of Jajte and Paszkiewicz [Studia Math. 63, 229 (1978)] and Mayet [Ph. D. thesis, Univ. Claude Benard, Lyon, France, 1987]. The relation between the sphere-valued states and extremal (=pure) states is investigated. It will be shown that for the strictly convex spaces the sphere-valued states are always extremal whereas the reverse inclusion is valid only for special types of orthoposets (Propositions 3.4 and 3.6). Finally, extensions of vector states from Boolean subalgebras are considered. A positive result for normed linear spaces, which have a predual (Theorem 5.1), is obtained.
The inverse problem of central, spin-orbit and L2-dependent potentials
Authors: Richardson P. A. , Hooshyar M. A.
Published: July 2002

A method for constructing central, spin-orbit, and L2-dependent potentials from the dependence of phase shifts on the angular momentum for spin-1/2 particles is presented. It is shown that if one of the three potentials is already known, the other two potentials can be constructed from the phase shifts given for one value of energy and for all angular momenta. If none of the potentials is known, it is found that the data from one experiment are inadequate to specify all three potentials, so a method for constructing the three potentials from the data given by two experiments performed at different scattering energies is presented. It is shown that the three potentials can be constructed from such data provided certain arbitrary parameters are correctly chosen. As an interesting by-product, a closed-form expression for a sum of Bessel functions is obtained. This function has played an important role in the inverse scattering theory for spin-orbit potentials.
Characterization of semidirect sum Lie algebras
Authors: Antoniou Ioannis E. , Misra Baidyanath
Published: July 2002

Semidirect sum Lie algebras 𝒜■𝒳 may be characterized by the type of the representation the invariant subalgebra 𝒳 provides for the Lie algebra 𝒜. The method is of particular interest when the invariant subalgebra 𝒳 is infinite dimensional and allows one to compare such algebras provided the representations of the algebra 𝒜 are known. In this way two infinite semidirect sum Lie algebras of the Lorentz algebra, namely the relativistic internal time algebra and the Bondi–Metzner–Sachs algebra, are characterized. Furthermore some minor errors of the commutation relations of the Bondi–Metzner–Sachs algebra have been corrected.
Nonlinear reactor multigroup neutron transport system: Existence and stability problems
Authors: Chen Gen-Shun , Leung Anthony W.
Published: July 2002

This article considers a system of nonlinear transport equations describing multigroup neutron fission and scattering, coupled with temperature feedback. Various possibilities of temperature feedbacks are studied. Existence, together with upper and lower bounds of solutions are considered. Sufficient conditions for stability and instability are given for various feedbacks.
Derivation of the coordinate system that separates the Bethe–Salpeter equation for the Wick–Cutkosky model
Authors: Mainland G. Bruce , Parson L. Alayne
Published: July 2002

Differential equations for an orthogonal transformation that separates the Bethe–Salpeter equation for the Wick–Cutkosky model will be derived and then solved. Although the transformation in which the Wick–Cutkosky model separates is already known, the systematic procedure presented for deriving the transformation may be useful for determining orthogonal transformations that would permit the separation of other Bethe–Salpeter equations.
The conserved quantities and symmetries of the two-dimensional Toda lattice hierarchy
Authors: Kajiwara Kenji , Satsuma Junkichi
Published: July 2002

The conserved quantities and symmetries of the soliton equations included in the 2DTL (two-dimensional Toda lattice) hierarchy are considered by means of the theory of the τ function. A typical example is presented for the 2DTL equation that is the simplest nontrivial equation in the hierarchy. Then, by applying suitable reductions, the cases of the Toda lattice equation and the sine-Gordon equation are discussed.
Quantum degeneracy and classical perturbation theory
Authors: Caliceti Emanuela
Published: July 2002

The degenerate Rayleigh–Schrödinger perturbation theory for the eigenvalues of the class of Schrödinger operators S(Ε)=S0+ΕV, where S0 is the Laplace–Beltrami operator on the one-dimensional torus T1 and V is an analytic potential (perturbed rotator) is explicitly constructed by means of the algorithm of the classical, resonant Birkhoff normal form. As a consequence, the (degenerate) quantum perturbation theory tends to the classical one in the classical limit.
Unitary spin crystals with broken symmetry eigenvectors and spin wave-mediated interactions
Authors: Blood F. A.
Published: July 2002

Generalizations of the Heisenberg spin Hamiltonian, Σσi⋅σj are considered. Particles are grouped into molecules and the σ’s are replaced by the generators τj of the unitary group U(n). Exact eigenvectors are found. A ‘‘vacuum’’ state is given whose U(5) symmetry ‘‘spontaneously’’ breaks for a certain range of potentials. Spin waves superimposed on this vacuum are used to mediate interactions.
The matrix representation of SO7 in an (SU2)3 basis
Authors: Pan Feng
Published: July 2002

Vector coherent state (VCS) theory is applied to SO7 in an (SU2)3 basis. Some reduced matrix elements of the tensor operator that forms part of the SO7 algebra are derived by using the K-matrix technique.
The extension theory and the opening in semitransparent surface
Authors: Popov I. Yu.
Published: July 2002

The model of zero width slits based on the operator’s extension theory for the wave scattering by a semitransparent surface with small aperture is constructed.
Topological gravity in a three-dimensional metric-affine space–time
Authors: Tresguerres Romualdo
Published: July 2002

The topological gauge model of gravity in three dimensions is extended to a metric-affine space–time with nonvanishing torsion and nonmetricity and signature (−++). We find an exact vacuum solution the connection of which includes a Weyl 1-form field.
Invariance transformations of the class y″=F(x)y
n of differential equations
Authors: Herlt E. , Stephani H.
Published: July 2002

Using a systematic search for symmetries of differential equations, transformations are found that leave equations of the type y″=F(x)yn form-invariant, in particular, in the case n=2. Given the (general) solution in case of a function F, these transformations can be used for constructing the (general) solution for a class of related functions F̃.
Continuum theory of microstretch liquid crystals
Authors: Eringen A. Cemal
Published: July 2002

A continuum theory is proposed for liquid crystals whose molecular elements can expand and contract, in addition to undergoing translations and rotations. This is the microstretch continuum theory, generalizing microplar theory of liquid crystals. Constitutive equations are developed for arbitrarily shaped molecular elements. Thermodynamical restrictions are studied. The theory is then specialized for breathing rodlike liquid crystals. Equilibrium configuration for the microstretch motion is studied.
Two-dimensional dynamical system associated with Abel’s nonlinear differential equation
Authors: Matsuno Y.
Published: July 2002

A two-dimensional dynamical system is proposed that is described by a pair of nonlinear ordinary differential equations(ODEs) with a complex parameter. It reduces to Abel’s nonlinear ODE of the first kind by an appropriate transformation. Using this fact the properties of solutions are investigated in detail with the aid of numerical computations. It is found that various types of bifurcation phenomena occur depending on the values of the parameter. In particular, the solution is shown to blow up in finite time under certain conditions. In order to visualize the behaviors of dynamical motions the trajectories of solutions are depicted in the plane. Finally, a discussion is made on some generalizations of the proposed system.
Integrability and singularity structure of predator-prey system
Authors: Sachdev P. L. , Ramanan Sharadha
Published: July 2002

The ‘‘extended’’ ARS (Ablowitz, Ramani, and Segur) algorithm is introduced to characterize a dynamical system as Painlevé or otherwise; to that end, it is required that the formal series—the Laurent series, logarithmic, algebraic psi series about a movable singularity—are shown to converge in the deleted neighborhood of the singularity. The determinations thus obtained are compared with those following from the α method of Painlevé. An attempt is made to relate the structure of solutions about a movable singularity with that of first integrals (when they exist). All these ideas are illustrated by a comprehensive analysis of the general two-dimensional predator-prey system.
Translation normalizers of Euclidean groups. II. Systematic calculation
Authors: Kopský Vojtěch
Published: July 2002

A method of calculation of translation normalizers is described which can be used in any dimension and which consists in three steps: (i) In the first step is determined the continuous part of the normalizer, which is a linear envelope of a stability space of the point group and of the continuous part of translation subgroup of the Euclidean group in question. (ii) In the second step are determined translation normalizers of irreducible components. (iii) And finally there is a theorem which gives an upper and lower limit for the translation normalizer of a reducible arithmetic class in terms of normalizers of its irreducible components. A check of coset representatives in resolution of the upper limit with respect to the lower limit concludes the calculation. The method is used to derive a table of translation normalizers of discrete, continuous, and semicontinous Euclidean groups up to three dimensions; all these groups are of interest in material physics. The consideration of translation normalizers is preceded by an extension and amendment of concepts used in crystallography which aim to specify the groups for which the tables are finally given.
Raising and lowering operators for U
q
(gl(n))
Authors: Links J. , Gould M. D.
Published: July 2002

A set of raising and lowering operators are constructed for Uq(gl(n)). Being Hermitian conjugates of one another, they are easily normalized and allow us to express arbitrary Gelfand–Tzetlin basis states as a product of lowering operators acting on the maximal weight state.
Casimir energy for open membranes
Authors: Zaikov R. P. , Zlatev S. I.
Published: July 2002

The static potential for a membrane with a fixed smooth boundary is considered in the semiclassical approximation and in the leading order of the 1/D expansion for a circular membrane.
Curvature invariants for Kantowski–Sachs metrics with source: A conformally invariant scalar field
Authors: Lake Kayll
Published: July 2002

Xanthopoulos and Zannias have solved the coupled Einstein conformally invariant massless scalar field equations under the assumption that the metric admits a four-parameter group of isometries with spacelike generators when the three-parameter subgroup of isometries acts on two-dimensional surfaces of positive, negative, and zero curvature. In this paper all known independent second order curvature invariants of these metrics are constructed in order to discuss the scalar curvature singularities. The plane metrics are, except for a subset of measure zero, singular free.
Oscillating thin shells in Weyl space
Authors: Wood W. R. , Feoli A. , Papini G.
Published: July 2002

An exact spherically symmetric thin shell solution to the Einstein equations is obtained in the Weyl–Dirac theory with an oscillating scalar field. Boundary conditions are chosen such that the conformal invariance is broken in the interior space and the bubble has a scalar-field-induced surface stress-energy tensor that causes the thin shell to oscillate.
Addendum to ‘‘Conservation laws of the quantized Davey–Stewartson I system in (2+1) dimensions’’ [J. Math. Phys. 3
4, 1063 (1993)]
Authors: Pang Gen-Di , Zhao Bao-Heng
Published: July 2002

The main formulas of the previous article are rewritten in a new and simple form. From the new form, the relation between the conservation laws of the quantized Davey–Stewartson I (DSI) system in (2+1) dimensions and that of the related systems in (1+1) dimensions can be very clearly seen. References and notations are the same.
Dynamical algebraic approach and invariants for time-dependent Hamiltonian systems in two dimensions
Authors: Kaushal R. S. , Mishra S. C.
Published: July 2002

Dynamical invariants for time-dependent (TD) oscillator systems in two dimensions are derived. The applications of the dynamical algebraic approach known already for one-dimensional TD systems [R. S. Kaushal and H. J. Korsch, J. Math. Phys. 22, 1904 (1981)] are now carried out to two-dimensional TD systems. A possible generalization of Ermakov systems to higher dimensions is discussed.
New deformed boson algebra
Authors: Chung Won-Sang
Published: July 2002

In this article the new deformed boson algebra is proposed and the nonlinear shift operator for the algebra is obtained.
Note on Maxwell’s equations in relativistically rotating frames
Authors: Kichenassamy S. , Krikorian R. A.
Published: July 2002

It is shown that the relativistic rotation transformation of Trocheris and Takeno restores the full Lorentz covariance of electrodynamics, lost in previous investigations using the Galilean rotation transformation along with the Frenet–Serret tetrad associated to the world line of a rotating observer of velocity v=ωΛr; it also recovers, at the approximation of small velocities, the results of the anholonomic approach corresponding to the use of the ‘‘instantaneous’’ Lorentz transformation of Galilean velocity v=ωr (in domains restricted by r<c/ω).
A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope
Authors: Dowker J. S.
Published: July 2002

A derivation of the Cesàro–Fedorov relation from the Selberg trace formula on an orbifolded 2-sphere is elaborated and extended to higher dimensions using the known heat-kernel coefficients for manifolds with piecewise-smooth boundaries. Several results are obtained that relate the coefficients, bi, in the Shephard–Todd polynomial to the geometry of the fundamental domain. For the 3-sphere, it is shown that b4 is given by the ratio of the volume of the fundamental tetrahedron to its Schläfli reciprocal.
Deformation of the exterior algebra and the GLq(r, C)
Authors: El Hassouni A. , Hassouni Y. , Zakkari M.
Published: July 2002

The deformation of the associative algebra of exterior forms is performed. This operation leads to a Yang–Baxter equation. Its relation with the braid group Bn−1 is analyzed. The correspondence of this deformation with the GLq(r,C) algebra is developed.
A new lattice formulation of the continuum
Authors: Friedberg R. , Lee T. D. , Pang Y.
Published: July 2002

A new lattice formulation of the continuum is presented, which can be applied to quantum or classical field theories in any space–time dimension. The method is illustrated with an application to relativistic nontopological solitons. This approach also provides an effective means of removing the spurious lattice fermion degenerate solutions for the Dirac equation.
*-structures on braided spaces
Authors: Majid S.
Published: July 2002

*-structures on quantum and braided spaces of the type defined via an R-matrix are studied. These include q-Minkowski and q-Euclidean spaces as additive braided groups. The duality between the *-braided groups of vectors and covectors is proved and some first applications to braided geometry are made.
On the construction of free fields in relativistic quantum mechanics
Authors: Grigore D. R.
Published: July 2002

A general discussion of the construction of free fields based on Weinberg anszatz is provided and various applications appearing in the literature are considered.
Operator analysis of nonrenormalizable multicomponent ultralocal field models
Authors: Zhu Chengjun , Klauder John R.
Published: July 2002

A nontrivial, nonperturbative quantum field theory of O(N)-invariant multicomponent, nonrenormalizable ultralocal models is developed along lines presented earlier for single-component models. The additional, nonclassical, repulsive potential that is always present in the solution of the single-component case becomes indefinite, and may even vanish in the multicomponent case. The disappearance of the nonclassical and singular potential does not mean a return to a conventional quantum field theory, and the operator solution of multicomponent ultralocal fields remains noncanonical. Nontrivial, i.e., non-Gaussian, results hold for any number N of components, and suitable nontrivial behavior persists, even in the infinite-component (N=∞) case as well.
Path integral for spinning particle in magnetic field via bosonic coherent states
Authors: Boudjedaa T. , Bounames A. , Chetouani L. , Hammann T. F. , Nouicer Kh.
Published: July 2002

Using the coherent states representation and the Schwinger boson model, the propagator of a spinning particle in interaction with an arbitrary magnetic field is derived in the framework of the path integral formalism. To show the relevance of the formalism to some applications, the Green function of spinning particle s=1/2 in special configuration of magnetic field is calculated. The transition amplitude and Berry’s phase for an arbitrary spin and time dependent magnetic field are deduced. The case of half integer spin is also considered.
A variational proof of the Thomas effect
Authors: Coutinho F. A. B. , Perez J. Fernando , Wreszinski Walter F.
Published: July 2002

A simple variational proof of the Thomas effect is provided, which shows clearly why it is related to the Efimov effect. The proof is also valid in the case of three equal masses a generalization needed in the briefly commented application to triviality of (λφ4)d in the nonrelativistic limit.
Further uses of the quantum mechanical path integral in quantum field theory
Authors: McKeon D. G. C. , Wong C.
Published: July 2002

It has been shown how matrix elements of the form 〈x‖exp(−iHt)‖y〉 which arise when using operator regularization to do perturbative calculations in quantum field theory can be evaluated using the quantum mechanical path integral (QMPI). This technique has the advantage of eliminating loop momentum integrals and algebraically complicated vertices in gauge theories. A similar (but distinct) approach of Polyakov and Strassler has been applied to one loop processes with external vector particles and is related to the string based methods of Bern and Kosower. In this article, several features of the QMPI technique are examined. First, it is demonstrated how the path ordering in the QMPI can be handled by considering a model of three interacting scalar fields, each with a distinct mass. Next, it is shown how the QMPI can be used when the external wave function is not a plane wave field. The particular case of having an exponentially damped wave function is considered. Next, a discussion of the difference between the approach of Polyakov and Strassler and that employed here is given. Finally, it is demonstrated how the QMPI can be used to considerably simplify calculations in quantum gravity.
Gauge invariance and second class constraints in three-dimensional linearized massive gravity
Authors: Arias Pío José , Stephany Jorge
Published: July 2002

A recently introduced approach for the dynamical analysis and quantization of field theoretical models with second class constraints is illustrated in the context of linearized gravity in 3D. The canonical structures of the intermediate and the self-dual models linearized gravity in 3D are discussed in detail. It is shown that the first order self-dual model whose constraints are all second class may be regarded as a gauge fixed version of the second order gauge invariant intermediate model. In particular it is shown how to construct the gauge invariant Hamiltonian of the intermediate model starting from the Hamiltonian of the self-dual model. The relation with the topologically massive linearized gravity is also discussed.
An exact spinor solution in Kantowski–Sachs cosmology
Authors: Krori K. D. , Goswami A. K. , Purkayastha Anuradha Das
Published: July 2002

An exact spinor solution in inflationary Kantowski–Sachs cosmology is presented in this paper.
The quantum two-dimensional Poincaré group from quantum group contraction
Authors: Zaugg Philippe
Published: July 2002

A new derivation of the algebra of functions on the two-dimensional Euclidean Poincaré group is proposed. It is based on a contraction of the Hopf algebra Fun(SOq(3)), where the deformation parameter q is sent to one. In this geometric construction, the action of Fun(SOq(3)) on the noncommutative Euclidean space is a key ingredient.
Abstract carrier space formalism for the irreducible tensor operators of compact quantum group algebras
Authors: Cornwell J. F.
Published: July 2002

Defining conditions for irreducible tensor operators associated with the unitary irreducible corepresentations of compact quantum group algebras are deduced within the framework of the abstract carrier space formalism. It is shown that there are two types of irreducible tensor operator, which may be called ‘ordinary’ and ‘twisted’. The consistency of the definitions is demonstrated, and various consequences are deduced, including generalizations of the Wigner–Eckart theorem for both the ordinary and twisted operators. Examples of irreducible tensor operators for the standard deformation of the function algebra of the compact Lie group SU(2) are described to demonstrate the applicability of the new definitions.
Abstract space–times and their Lorentz groups
Authors: Smith Jonathan D. H. , Ungar Abraham A.
Published: July 2002

It has recently been discovered [A. A. Ungar, Am. J. Phys. 59, 824 (1991); 60, 815 (1992)] that the set R3c={v∈R3 : ∥v∥<c} of all relativistically admissible velocities in Euclidean three-space R3, with a binary operation ⊕ given by relativistic velocity addition, forms a gyrogroup (R3c,⊕). The gyrogroup (R3c,⊕) reduces to the group (R3,+) in the limit c→∞, + being the prerelativistic velocity addition (that is, the ordinary vector addition in the Euclidean three-space R3). The binary operation ⊕ in R3c is gyroassociative and gyrocommutative, as opposed to the binary operation + in R3 which is associative and commutative. In this article we extend the study of gyrogroups into that of Lorentz groups. In particular, we find that a gyrogroup must be equipped with a cocycle form in order to be extendible into a Lorentz group. We thus study gyrogroups that are equipped with a cocycle form, and their resulting Lorentz groups. Interestingly, the cocycle form needed for the extension of gyrogroups into Lorentz groups involves a cocycle identity which is known to be useful in various branches of mathematics [B. R. Ebanks and C. T. Ng, Aequat. Math. 46, 76 (1993)].
Squeezing Bogoliubov transformations on the infinite mode CCR-algebra
Authors: Honegger Reinhard , Rieckers Alfred
Published: July 2002

A detailed analysis of and a general decomposition theorem for in general unbounded symplectic transformations on an arbitrary complex pre-Hilbert space (one–boson test function space) are given. The structure of strongly continuous symplectic groups on such spaces is determined. The connection between quadratic Hamiltonians, Bogoliubov transformations, and symplectic transformations is discussed in the Fock representation, and their relevance for squeezing operations in quantum optics is pointed out. The results for this rather general class of transformations are proved in a self-contained fashion.
Solutions of the Regge equations on some triangulations of CP2
Authors: Hartle James B. , Perjés Zoltan
Published: July 2002

Simplicial geometries are collections of simplices making up a manifold together with an assignment of lengths to the edges that define a metric on that manifold. The simplicial analogs of the Einstein equations are the Regge equations. Solutions to these equations define the semiclassical approximation to simplicial approximations to a sum over geometries in quantum gravity. In this paper, we consider solutions to the Regge equations with a cosmological constant that give Euclidean metrics of high symmetry on a family of triangulations of CP2 presented by Banchoff and Kühnel. This family is characterized by a parameter p. The number of vertices grows larger with increasing p. We exhibit a solution of the Regge equations for p=2 but find no solutions for p=3. This example shows that merely increasing the number of vertices does not ensure a steady approach to a continuum geometry in the Regge calculus.
General static axially symmetric solutions of (2+1)-dimensional Einstein-Maxwell-Dilaton theory
Authors: Park Dahl , Kim Jae Kwan
Published: July 2002

We obtain the general static solutions of the axially symmetric (2+1)-dimensional Einstein-Maxwell-Dilaton theory by dimensionally reducing it to a two-dimensional dilaton gravity theory. The solutions consist of the magnetically charged sector and the electrically charged sector. We illuminate the relationship between the two sectors by pointing out the transformations between them.
An asymptotic limit law with a singularly perturbed drift and a random noise
Authors: Kim Jeong-Hoon
Published: July 2002

An asymptotic stochastic initial value problem with a random microscale superposed upon a deterministic macroscale is considered in this article. We derive and prove a limit theorem for the random problem with a rapidly varying deterministic component. The asymptotic character of the stochastic initial value problem with a small parameter is realized by solving a final value problem of which the infinitesimal generator consists of a singularly perturbed deterministic component and a random fluctuation intensity component. We also give an estimate for the error in the asymptotic approximation in terms of the small parameter. This abstract limit theorem is reduced to a limit theorem for the stochastic processes solving a system of stochastic differential equations. The corresponding infinitesimal generator of the Kolmogorov–Fokker–Planck equation is obtained in an asymptotic form and demonstrates how an effective driving force couples with a zero-mean random perturbation in both drift and diffusion coefficients. Our theorem provides a characterization of random noise for evanescent waves in a layered random medium.
Incorporation of anomalous magnetic moments in the two-body relativistic wave equations of constraint theory
Authors: Jallouli H. , Sazdjian H.
Published: July 2002

Using a Dirac-matrix substitution rule, applied to the electric charge, the anomalous magnetic moments of fermions are incorporated in local form in the two-body relativistic wave equations of constraint theory. The structure of the resulting potential is entirely determined, up to magnetic type form factors, from that of the initial potential describing the mutual interaction in the absence of anomalous magnetic moments. The wave equations are reduced to a single eigenvalue equation in the sectors of pseudoscalar and scalar states (j=0). The requirement of a smooth introduction of the anomalous magnetic moments imposes restrictions on the behavior of the form factors near the origin, in x-space. These conditions are satisfied at the one-loop level of perturbation theory. The nonrelativistic limit of the eigenvalue equation is also studied.
Comment on: Path integral solution of the Schrödinger equation in curvilinear coordinates: A straightforward procedure [J. Math. Phys. 37, 4310–4319 (1996)]
Authors: Wurm Alexander , LaChapelle John
Published: July 2002

The authors comment on the paper by J. LaChapelle, J. Math. Phys. 37, 4310 (1996), and give explicit expressions for the parametrization, its solution, and the Lie derivatives of the Schrödinger equation for the case of n-dimensional spherical coordinates.
Noncommutative geometry with graded differential Lie algebras
Authors: Wulkenhaar Raimar
Published: July 2002

Starting with a Hilbert space endowed with a representation of a unitary Lie algebra and an action of a generalized Dirac operator, we develop a mathematical concept towards gauge field theories. This concept shares common features with the Connes–Lott prescription of noncommutative geometry, differs from that, however, by the implementation of unitary Lie algebras instead of associative  * -algebras. The general scheme is presented in detail and is applied to functions ⊗ matrices.
The modified Newton–Sabatier method for the coupled channel inverse scattering problem with charged particles at fixed energy
Authors: Eberspächer Matthias , Scheid Werner
Published: July 2002

The modified Newton–Sabatier method was recently developed for inelastic inverse problems for the scattering of neutral particles. In this paper, the method is extended to the solution of the inelastic inverse scattering problem with charged particles. The bases are radial Schrödinger equations coupled by a local potential matrix known from a certain distance on. The inversion procedure starts with the S-matrix fixing the asymptotic wave functions of the charged scattering system. This S-matrix can be transformed to another one for asymptotic constant potentials instead of Coulomb potentials. The new S-matrix belongs to the same inner potential matrix as the original one and is solved by the modified Newton–Sabatier method similar to the case of neutral particles. An application with a given S-matrix, belonging to a coupled square-well potential matrix with an outer Coulomb potential yields good agreement between the inverted potential matrix and the original one.
Thermal conduction before relaxation in slowly rotating fluids
Authors: Herrera L. , Martı́nez J.
Published: July 2002

For slowly rotating fluids, we establish the existence of a critical point similar to the one found for nonrotating systems. As the fluid approaches the critical point, the effective inertial mass of any fluid element decreases, vanishing at that point and changing sign beyond it. This result implies that the first-order perturbative method is not always reliable to study dissipative processes occurring before relaxation. Physical consequences that might follow from this effect are commented on.
Static perfect fluid cylinders
Authors: Nilsson Ulf S. , Uggla Claes , Marklund Mattias
Published: July 2002

The field equations for cylindrically symmetric perfect fluid models with a non-scale invariant equation of state where the energy density is linearly related to the pressure are rewritten as a set of first order coupled ordinary differential equations. Variables are chosen such that the resulting phase space is compact and everywhere regular. The dynamical systems approach, used in the past mainly for scale invariant matter sources, is subsequently used to gain qualitative information about the space of solutions. It leads to a simple way of demonstrating the existence and properties of interior sources for cylindrically symmetric vacuum solutions. The models are shown to exhibit asymptotic scale invariance.
Transformations of strongly causal space–times preserving null geodesics
Authors: Huang Wen-ling
Published: July 2002

Let (M,g) be a strongly causal space–time, dimM⩾3. Let f:M→M be a bijection such that images and pre-images of null geodesics (as point sets) are null geodesics. Then f is a conformal transformation.
Unitary implementations of one-parameter squeezing groups
Authors: Honegger Reinhard , Rieckers Alfred
Published: July 2002

For the case of infinitely many photon (Boson) modes we investigate the unitary implementability of a class of symplectic one-parameter groups (more exactly, of the associated groups of Bogoliubov automorphisms on the CCR algebra) in the Fock representation and in representations of the CCR algebra, which are symplectically related and inequivalent to Fock. Furthermore, the existence of the associated (squeezing) quadratic Hamiltonians is discussed. Finally, applications in the theory of quantization in QED and in the Luttinger model are pointed out.
Enlarged test-function spaces for the global free folia dynamics on the CCR-algebra
Authors: Honegger Reinhard
Published: July 2002

The global free dynamics for the boson field is investigated for the test-function space D(R3) of infinitely differentiable functions with compact support in the position space R3. D(R3) is not invariant with respect to the one-boson dynamics, and thus the free dynamics cannot be formulated in terms of Bogoliubov automorphisms on the CCR-algebra over D(R3). In the Schrödinger picture the free dynamics here is constructed in terms of a group of affine bijections on suitable folia of the CCR-algebra so that the expectations are continuous in time. These folia contain a continuum of disjoint subfolia, namely the squeezed vacuum sectors. Those squeezed vacuum sectors are determined which give rise to covariant dynamical subdescriptions, that is, for which the time evolution of the states satisfies the stronger time-continuity with respect to the norm, and thus in the Heisenberg picture lead to W*-dynamical systems.
Hidden algebras of the (super) Calogero and Sutherland models
Authors: Brink Lars , Turbiner Alexander , Wyllard Niclas
Published: July 2002

We propose to parametrize the configuration space of one-dimensional quantum systems of N identical particles by the elementary symmetric polynomials of bosonic and fermionic coordinates. It is shown that in this parametrization the Hamiltonians of the AN, BCN, BN, CN and DN Calogero and Sutherland models, as well as their supersymmetric generalizations, can be expressed—for arbitrary values of the coupling constants—as quadratic polynomials in the generators of a Borel subalgebra of the Lie algebra gl(N+1) or the Lie superalgebra gl(N+1|N) for the supersymmetric case. These algebras are realized by first order differential operators. This fact establishes the exact solvability of the models according to the general definition given by Turbiner, and implies that the Calogero and Jack–Sutherland polynomials, as well as their supersymmetric generalizations, are related to finite-dimensional irreducible representations of the Lie algebra gl(N+1) and the Lie superalgebra gl(N+1|N).
Similarity and intertwining of Dirac operators
Authors: Willis Barton L.
Published: July 2002

Similarity and symmetry of quantum mechanical operators are the basic theoretical means for systematizing quantum dynamics. The classical counterparts of these concepts are canonical transformations and conservation laws. For operators, a concept called intertwining encompasses both similarity and symmetry. In this paper, we construct pairs of Dirac operators with noncentral potentials that are intertwined by multiplication operators.
A note on Tauber’s expanding universe in conformally flat coordinates
Authors: Endean Geoffrey
Published: July 2002

The solutions given by Tauber, based on conformally flat space–time, of Einstein’s field equations for the Friedmann–Robertson–Walker, closed topology, dust model are corrected. The corrected solutions are shown to reduce to the standard textbook solutions obtained directly in Friedmann–Robertson–Walker coordinates, with the parameter identified as a component of the transformation to conformally flat space–time coordinates. The general significance of Tauber’s work and its relationship to more recent papers by Endean on this subject are discussed.
Fluid space–times and conharmonic symmetries
Authors: Abdussattar  , Dwivedi Babita
Published: July 2002

The conharmonic curvature tensor is considered as an invariant of the conharmonic transformation defined by Ishii and the necessary and sufficient conditions for the conharmonic curvature tensor in a perfect fluid space–time to be divergence free has been obtained. Conharmonic motion, conharmonic collineation, and conharmonic curvature collineation are introduced as subcases of conformal motion, conformal collineation, and Weyl conformal collineation, respectively, and relations of conharmonic symmetries with inheriting symmetries are investigated. In the case of an existing conharmonic Killing vector along the flow vector, along the anisotropy vector, and perpendicular to both in an anisotropic fluid space–time it is found that no equation of state is singled out unless the conharmonic Killing vector is also a curvature inheritance vector. Conditions are obtained for the symmetries of the anisotropic fluid space–time admitting a conharmonic Killing vector to be inherited. In the case of a conharmonic symmetric space–time and also in the case of a space–time with a divergence-free conharmonic curvature tensor it is found that if the space–time admits an infinitesimal conharmonic Killing vector then the scalar curvature of the space–time vanishes and the space–time is either conharmonically flat or has four distinct principal null directions.
Full causal bulk-viscous cosmological models
Authors: Mak M. K. , Harko T.
Published: July 2002

New exact solutions of the gravitational field equations for a homogeneous flat Friedmann–Robertson–Walker Universe filled with a causal bulk-viscous fluid with a bulk viscosity coefficient proportional to the Hubble function are obtained in the framework of the full causal Israel–Stewart–Hiscock (ISH) theory. The evolution equation of the Universe is reduced to a first kind Abel-type first-order differential equation and new classes of exact solutions of the field equations are generated from some particular solutions of this equation leading to two classes of general solutions of the Einstein field equations corresponding to particular values of the parameters entering in the physical model. The obtained solutions are represented mathematically in an exact parametric form and are interpreted physically as describing cosmological particle production. The evolution of the temperature, entropy, deceleration parameter, and bulk viscosity coefficient is also considered for each model.
A number of quasiexactly solvable N-body problems
Authors: Khare Avinash , Mandal Bhabani Prasad
Published: July 2002

We present several examples of quasiexactly solvable N-body problems in one, two, and higher dimensions. We study various aspects of these problems in some detail. In particular, we show that in some of these examples the corresponding polynomials form an orthogonal set, and many of their properties are similar to those of the Bender–Dunne polynomials. We also discuss QES problems where the polynomials do not form an orthogonal set.
Large smoke rings with concentrated vorticity
Authors: Marchioro Carlo
Published: July 2002

In this paper we study an incompressible inviscid fluid when the initial vorticity is sharply concentrated in N disjoint regions. This problem has been well studied when a planar symmetry is present, i.e., the fluid moves in R2. In this case we know that, when the diameter σ of each region supporting the vorticity is very small, the time evolution of the fluid is quite well described by a dynamical system with finite degrees of freedom called the “point vortex model.” In particular the connection between this model and the Euler equation has been proved rigorously as σ→0. In the present paper we discuss the “stability” of the point vortex model with respect to a particular small perturbation of the planar symmetry. More precisely we consider a fluid moving in R3 with a cylindrical symmetry without swirl in which each vortex is no longer a straight tube, but a vorticity ring. We prove that large annuli of radii r≈σ−β for any β>0 remain “localized” and hence we obtain the point vortex model as σ→0.
Deformations of global symmetries in the extended antifield formalism
Authors: Brandt Friedemann
Published: July 2002

It is outlined how deformations of field theoretical rigid symmetries can be constructed and classified by cohomological means in the extended antifield formalism. Special attention is devoted to deformations referring only to a subset of the rigid symmetries of a given model and leading to a nontrivial extension of the graded Lie algebra associated with that subset. The method is illustrated for a D=4, N=2 supersymmetric model where the central extension of the supersymmetry algebra emerges via a deformation. Deformations of gauge fixed actions with a BRST symmetry are discussed too and illustrated by the Curci–Ferrari model.
Singularities at the tip of a plane angular sector
Authors: Keller Joseph B.
Published: July 2002

Solutions of the Helmholtz and Laplace equations in three dimensions which vanish, or have vanishing normal derivative on an angular sector of opening angle β, are considered. The solutions are required to be functions of distance from the tip of the sector multiplied by functions of the angular coordinates. The angular functions are eigenfunctions of the Laplace–Beltrami operator on the unit sphere, which vanish or have vanishing normal derivative, on a great circle arc of length β. It is shown that the Dirichlet eigenvalues are nondecreasing functions of β, and the Neumann eigenvalues are nonincreasing. Furthermore, each Dirichlet eigenvalue of a sector of angle β is a Neumann eigenvalue of a sector of angle 2π−β and conversely. The eigenvalues for β=0, π, and 2π are found explicitly. These results lead to a qualitative description of the eigenvalues as functions of β. The eigenvalues determine the singular behavior of the solutions at the tip.
Highly localized solutions of the wave equation
Authors: Kiselev Aleksei P. , Perel Maria V.
Published: July 2002

Simple explicit solutions of the linear wave equation in three dimensions are presented which describe wave packets exponentially localized near a point moving with the wave speed. For large values of a certain free parameter these new solutions are localized in Gaussian manner with respect to longitudinal and transverse variables and time. This agrees with considerations by Babich–Ulin and Ralston who have presented an asymptotic description of solutions exhibiting such local behavior. Global estimates and large-time asymptotics of these solutions are given.
Prediction of bubble velocity in a Hele–Shaw cell: Thin film and contact angle effects
Authors: Saffman P. F. , Tanveer S.
Published: July 2002

The effect of the thin film between a bubble of a less viscous fluid and the transverse walls on the velocity of steady propagation of the bubble is explored. The estimates suggest that the film corrections for small capillary number cannot account for the large discrepancy between the experimentally observed [Phys. Fluids 31, 18 (1988)] bubble velocities and the theoretical values based on a simplified theory. However, if the thin film is ignored and it is assumed that the contact angle between the interface and the plate varies at different points of the interface in some prescribed manner, then it is possible to account in a qualitative way for the small bubble velocities in the Kopf-Sill–Homsy experiment.
A k-ε model for turbulent mixing in shock-tube flows induced by Rayleigh–Taylor instability
Authors: Gauthier Serge , Bonnet Michel
Published: July 2002

A k-ε model for turbulent mixing induced by Rayleigh–Taylor instability is described. The classical linear closure relations are supplemented with algebraic relations in order to be valid under strong gradients. Calibrations were made against two shock-tube experiments (Andronov et al. [Sov. Phys. JETP 44, 424 (1976); Sov. Phys. Dokl. 27, 393 (1982)] and Houas et al. [Proceedings of the 15th International Symposium on Shock Waves and Shock Tubes (Stanford U.P., Stanford, CA, 1986)]) using the same set of constants. The new interpretation of the experimental data of Brouillette and Sturtevant [Physica D 37, 248 (1989)], where the mixing length is discriminated from the wall jet, requires a different numerical value for the Rayleigh–Taylor source term coefficient. A detailed physical study is given in both cases. It turns out that the spectrum is narrower in the Brouillette and Sturtevant case than in the Andronov et al. case but the small length scales are of the same magnitude.
Explosive-driven cylindrical imploding shocks
Authors: Matsuo H. , Fujiwara K.
Published: July 2002

Cylindrical imploding shocks are analyzed numerically. The shocks are supposed to be generated by detonating cylindrical explosive shells. Detonations are assumed to be initiated either from the inner or the outer surface of the shells. Explosive shells of different thicknesses are compared. The conversion mechanism of the chemical energy of explosives into gas energy is investigated. In the implosion stage general features of the flow near the shock front are much the same between two different initiations. The same is also true among different explosive thicknesses. However, in the reflection stage after the shock is reflected from the axis, thicker explosives produce higher pressure and temperature near the axis. The difference in the initiation method does not make a very noticeable difference, even in the reflection stage. Shock trajectories, temperatures at the shock front, and evolutions of the pressure at a fixed point are compared between numerical and experimental results. Agreements between the two results are close.
The development of a swirling round laminar jet
Authors: Hwang Wei-Shien , Chwang Allen T.
Published: July 2002

The development of a swirling round laminar jet in an unbounded viscous fluid is investigated in this Brief Communication by applying the unsteady Stokes equations instead of the full Navier–Stokes equations. The solutions corresponding to a constant linear-momentum source, an impulsive linear-momentum source, and constant and impulsive angular-momentum sources are presented. Since the Stokes equations are linear, these results can be superimposed together. For a constant linear-momentum source and a constant angular-momentum source, the present results reduce to the Stokeslet and rotlet solutions, which are the singular solutions of the Stokes equations, respectively, as time approaches infinity. It is also found that the developing flow field due to a linear-momentum source at the initial stage is irrotational and has a dipolelike structure. However, the developing flow field due to an angular-momentum source is immediately rotational and the magnitude of the velocity is exponentially small.
Numerical and experimental results for developing curved channel flow
Authors: Bottaro Alessandro , Matsson O. John E. , Alfredsson P. Henrik
Published: July 2002

Three-dimensional finite-volume simulations of the spatial development of centrifugally unstable flow in a curved channel have been performed, and compared with detailed hot-wire measurements. Both approaches revealed spatially developing streamwise vortex pairs at the concave wall, which gave rise to regions of alternating negative and positive streamwise perturbation velocities. The computational box size was chosen large enough so that the flow was allowed to naturally select the spanwise wave number. The computed velocity field was found to be in excellent agreement with the experimentally determined one.