Fermion current algebras and Schwinger terms in (3+1)-dimensions

We derive an ODE for the macroscopic evolution of a tagged particle in models such as asymmetric simple exclusions and zero range processes. The right-hand side of the ODE is discontinuous and its solutions are understood in the Filippov sense. We establish the uniqueness of the ODE, and explore its relationship with the hydrodynamic equation of the particle density.Research partially supported by National Science Foundation grant DMS-9208490.     

Hilbert space cocycles as representations of (3 + 1)-d current algebras

It is proposed that instead of normal representations, one should look at cocycles of group extensions valued in certain groups of unitary operators acting in a Hilbert space (e.g. the Fock space of chiral fermions), when dealing with groups associated to current algebras in gauge theories in 3 + 1 spacetime dimensions. The appropriate cocycle is evaluated in the case of the group of smooth maps from the physical three-space to a compact Lie group.The cocyclic representation of a componentX of the current is obtained through two regularizations, (1) a conjugation by a background potential dependent unitary operatorh _A, (2) by a subtraction-h _A ^-1 _xhA, where _x is a derivative along a gauge orbit. It is only the total operatorh _A ^-1 Xh _A -h _A ^-1 _xhA which is quantizable in the Fock space using the usual normal ordering subtraction.Supported by the Alexander von Humboldt Foundation     

Current algebras ind+1-dimensions and determinant bundles over infinite-dimensional Grassmannians

We extend the methods of Pressley and Segal for constructing cocycle representations of the restricted general linear group in infinite-dimensions to the case of a larger linear group modeled by Schatten classes of rank 1p<. An essential ingredient is the generalization of the determinant line bundle over an infinite-dimensional Grassmannian to the case of an arbitrary Schatten rank,p1. The results are used to obtain highest weight representations of current algebras (with the operator Schwinger terms) ind+1-dimensions when the space dimensiond is any odd number.This work is supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069     

Elasticity,factorization and S-matrices in (1+1)-dimensions

The hypothesis of vanishing particle-production, non-vanishing backward scattering and a factorisation condition on the S-matrix allow an infinite arbitrariness in the two-particle scattering amplitudes. The general form is explicitly obtained.     

Gravitational collapse of phantom fluid in (2 + 1)-dimensions

In this paper, we solve Einsteins’ field equations for a circularly symmetric anisotropic fluid, with kinematic self-similarity of the first kind, in (2 + 1)-dimensional spacetimes. Considering the case where the radial pressure vanishes, we show that there exists a solution that represents the gravitational collapse of an anisotropic fluid, and the collapse will finally form a black hole, even if the fluid is constituted by phantom energy.     

Deformation of current algebras in 3+1 dimensions

It was shown in an earlier paper that there is an Abelian extension of the general linear algebra gl ₂, that contains the current algebra with anomaly in 3+1 dimensions. We construct a three-parameter family of deformations of . For certain choices of the deformation parameters, we can construct unitary representations. We also construct highest-weight nonunitary representations for all choices of the parameters.This work was supported in part by U.S. Department of Energy Contract No. DE-AC02-76ER13065.     

Constrained quantization of a topologically massive gauge theory in (2+1)-dimensions

We present a canonical quantization for a gauge field theory in a (2+1) dimensional space-time in both Dirac brackets and Schwinger action principle formalisms.     

Electrohydrodynamic wave-packet collapse and soliton instability for dielectric fluids in (2 + 1)-dimensions

In this paper we introduce a modified lattice Boltzmann model (LBM) with the capability of mimicking a fluid system with dynamic heterogeneities. The physical system is modeled as a one-dimensional fluid, interacting with finite-lifetime moving obstacles. Fluid motion is described by a lattice Boltzmann equation and obstacles are randomly distributed semi-permeable barriers which constrain the motion of the fluid particles. After a lifetime delay, obstacles move to new random positions. It is found that the non-linearly coupled dynamics of the fluid and obstacles produces heterogeneous patterns in fluid density and non-exponential relaxation of two-time autocorrelation function.Received: 19 March 2004, Published online: 29 June 2004PACS: 47.11. + j Computational methods in fluid dynamics - 05.70.Ln Nonequilibrium and irreversible thermodynamics     

Electrohydrodynamic wave-packet collapse and soliton instability for dielectric fluids in (2 + 1)-dimensions

A weakly nonlinear theory of wave propagation in two superposed dielectric fluids in the presence of a horizontal electric field is investigated using the multiple scales method in (2 + 1)-dimensions. The equation governing the evolution of the amplitude of the progressive waves is obtained in the form of a two-dimensional nonlinear Schrödinger equation. We convert this equation for the evolution of wave packets in (2 + 1)-dimensions, using the function transformation method, into an exponentional and a Sinh-Gordon equation, and obtain classes of soliton solutions for both the elliptic and hyperbolic cases. The phenomenon of nonlinear focusing or collapse is also studied. We show that the collapse is direction-dependent, and is more pronounced at critical wavenumbers, and dielectric constant ratio as well as the density ratio. The applied electric field was found to enhance the collapsing for critical values of these parameters. The modulational instability for the corresponding one-dimensional nonlinear Schrödinger equation is discussed for both the travelling and standing waves cases. It is shown, for travelling waves, that the governing evolution equation admits solitary wave solutions with variable wave amplitude and speed. For the standing wave, it is found that the evolution equation for the temporal and spatial modulation of the amplitude and phase of wave propagation can be used to show that the monochromatic waves are stable, and to determine the amplitude dependence of the cutoff frequencies.Received: 23 November 2003, Published online: 15 March 2004PACS: 47.20.-k Hydrodynamic stability - 52.35.Sb Solitons; BGK modes - 42.65.Jx Beam trapping, self-focusing and defocusing; self-phase modulation - 47.65. + a Magnetohydrodynamics and electrohydrodynamicsM.F. El-Sayed: Permanent address: Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt     

Baryons in chiral SU(N)—QCD on the light-cone in 1 + 1-dimensions

We demonstrate that using bosonization techniques in 1+1-dimensional QCD in the chiral limit a unique definition of baryons is possible for finiteN _c despite the fact that mesons, baryons and anti-baryons are massless. The definition which is based on the construction of an SU(2)-algebra provides the basis for a new approach to investigate hadronic properties in the strong coupling limit. It is used to study the Fock-state decomposition and structure functions of baryons for various finite values ofN _c . The results are discussed in comparison to similar calculations based on discretized lightcone quantization.     

Universal transverse conductance between quantum Hall regions and (2+1) D bosonization

Using bosonization techniques for (2+1) D systems, we show that the transverse conductance for a system with general current interactions, when measured between perfect Hall regions is not renormalized at low temperatures. Our method extends two results we have recently obtained on low dimensional fermionic systems: on the one hand, the relationship between universality of Landauer conductance and universality of bosonization rules for (1+1) D systems, and on the other hand, the universal character of the bosonized topological current associated to a (2+1) D fermionic system with current interactions.     

Approximate solution of the spin-one Duffin-Kemmer-Petiau (DKP) equation under a non-minimal vector Yukawa potential in (1+1)-dimensions

We solve the Duffin-Kemmer-Petiau (DKP) equation with a non-minimal vector Yukawa potential in (1+1)-dimensional space-time for spin-1 particles. The Nikiforov-Uvarov method is used in the calculations, and the eigenfunctions as well as the energy eigenvalues are obtained in a proper Pekeris-type approximation.     

An exact solution for static scalar fields coupled to gravity in (2+1)-dimensions

We obtain an exact solution for the Einstein’s equations with cosmological constant coupled to a scalar, static particle in static, “spherically” symmetric background in (2+1)-dimensions.     

Localized excitations with and without propagating properties in （2＋1）-dimensions obtained by a mapping approach

By means of an extended mapping approach, a new type of variable-separation excitation is derived with two arbitrary functions in a (2 1)-dimensional modified dispersive water-wave system. Based on the derived variable-separation excitation, abundant nonpropagating and propagating solitons such as dromions, rings, peakons and compactons are revealed by selecting appropriate functions in this paper.     

Nonlinearity of the zigzag graphene nanoribbons with antidots via the f-deformed Dirac oscillator in (2+1)-dimensions

We study the nonlinearity for the zigzag graphene nanoribbons (ZGNRs) with zigzag triangular holes (ZTHs). We show that in the presence of an external uniform magnetic field, a two-dimensional f-deformed Dirac oscillator can be used to describe the dynamics of the electrons in the ZGNRs with ZTHs. It is shown for the first time that the magnetic field direction has effect on the chirality of charge carriers in the ZGNRs punched with triangular holes. We also obtain the Landau-level spectrum in the weak and strong magnetic field regimes. Additionally, we compare Landau-level spectrum of this graphene-based device in the f-deformed scenario and original one. Our results provide a general viewpoint for the development of the zigzag graphene nanoribbons.     

On how the (1+1)-dimensional Dirac equation arises in classical physics

We demonstrate how the (1+1)-dimensional Dirac equation can be derived from the equation for the probability distribution governing a stochastic process when particles are permitted to propagate both backwards and forwards in time. This derivation uses a real transfer matrix and does not require a formal analytic continuation from classical physics. The physical significance of the quantity we interpret as being the wave function is discussed.     

Multi soliton solutions,M-lump waves and mixed soliton-lump solutions to the awada-Kotera equation in (2+1)-dimensions

In this research paper, the well-known simple Hirota’s method is employed to study the (2+1)-dimensional Sawad-Kotera equation. The logarithmic variable transformation is implemented on the proposed problem to construct the bilinear Hirota form. Based on its bilinear representation, the features of multi soliton solutions, M-lump waves, and the mixed 1-M-lump with one-soliton, and two-soliton solutions are explored. For one M-lump solution, the wave motion in the x and y directions are also studied. To better understand the physical phenomena of the gained solutions, three-dimensional graphics and their corresponding surfaces are also presented.     

Ruppeiner Geometry of （2 ＋ 1）-Dimensional Spinning Dilaton Black Hole

In this paper, we study the geometrothermodynamics of (2+1)-dimensional spinning dilaton black hole. We show that the Ruppeiner curvature vanishes, which implies that there exist no phase transitions and thermodynamic interactions. However when the thermodynamics fluctuation is included, the geometry structure is reconsidered. The non-vanishing Ruppeiner curvature is obtained, which means the phase space is non-flat. We also study the phasetransitions and show that it can indeed take place at some points.