Local one particle approximation of the current commutators

The spectral functions of the current commutators matrix elements between vacuum and one particle boson states are calculated in a local one particle approximation. In the equal time limit, the restrictions imposed by the current algebra commutation relations without operator Schwinger terms are systematically discussed. It is found, that in this approximation, and when one of the currents is conserved, the PCAC and vector meson dominance models cannot be considered simultaneously. The comparison of the results with experiment gives preference to the first of the two models.     

A causal approximation scheme for the commutator of the axial vector-currents

An approximation scheme which fulfils the causality condition is used to compute the matrix elements of the commutator of two axial-vector currents between one proton state. The commutator sum rule is supposed to be saturated by taking into account the nucleon, theN ^*(3/2, 3/2) resonance, and the partially disconnected pion-proton intermediate states. For the axial current form factors pion pole formulas are assumed. It is shown that only the subtraction constants are relevant for the equal time limit of the commutator and so the equivalence with similar earlier methods is proven.     

Current algebra results for theB - D systems

Using the equal time commutation relations for the components of the vector and axialvector currents and keeping single particle states we obtain relations for the weak form factors for theB - D systems. In the heavy quark effective theory (HQET) limit these relations determine the Isgur-Wise function.     

Particles vs. events: The concatenated structure of world lines in relativistic quantum mechanics

The dynamical equations of relativistic quantum mechanics prescribe the motion of wave packets for sets of events which trace out the world lines of the interacting particles. Electromagnetic theory suggests thatparticle world line densities be constructed from concatenation of event wave packets. These sequences are realized in terms of conserved probability currents. We show that these conserved currents provide a consistent particle and antiparticle interpretation for the asymptotic states in scattering processes. The relation between current conservation and unitarity is used to establish relations between pair production and annihilation amplitudes and scattering. The discrete symmetriesC, T, P are studied and it is shown that no Dirac sea (for fermions where such a construction is possible, or bosons where it is not) is required for consistency of the theory. These currents, furthermore, represent the discrete symmetries in a way consistent with their interpretation as particle currents.This work was supported in part by the Binational Science Foundation (BSF), Jerusalem, Israel. A preliminary report was given at the Conference on Statistical Mechanics and Irreversible Processes, San Antonio, Texas, March 14–17, 1982.The first two authors dedicate this paper to the memory of their friend and colleague, Yeshiahu (Ishi) Lavie, who died in the service of the Israel Defense Forces, January 2, 1983.     

A direct variational method for non-conservative system stability

Hamilton's principle is applied to analyze the problem of the stability of equilibrium of a discrete, holonomic, and scleronomic mechanical system under conservative and non-conservative (position and/or velocity dependent) forces. At the stability limit, the vanishing of the second order terms (in the deviations from equilibrium) of the total action change functional leads to the condition that the matrix of a certain quadratic form be singular; this yields the eigenvalue (frequency-load) curve. The flutter loads follow by setting the frequency derivative of the determinant of this matrix equal to zero; the energetic interpretation of this latter is also given. When the non-conservative forces go to zero it is shown that one recovers the well-known discrete conservative system stability criterion. An application follows, and finally in an Appendix various relevant time-integral equalities are summarized and interpreted.     

Force,momentum and topology of a moving magnetic domain

The following general relations involving force, momentum and topological winding number of a translating magnetic domain are derived from the Landau—Lifshifz equation in a context appropriate to bubbles: The gyrotropic force tending to deflect a steadily moving domain is proportional to a mean winding number linear in Bloch-point coordinates. The time derivative of the canonical momentum for a domain of integer winding number is equal to the total force, which must include gyrotropic and dissipative terms. A new contour integral expresses the momentum in the limit of vanishing wall thickness. Approximate equations of quasi-steady domain motion are cast into a form resembling Hamiltion's equations for a particle. Discussion centers on applications to gradientless propagation, bubble saturation velocity, and the Blochline model of inertial effects, and on general limitations of the theory.     

Acceleration of Convergence to Equilibrium in Markov Chains by Breaking Detailed Balance

We analyse and interpret the effects of breaking detailed balance on the convergence to equilibrium of conservative interacting particle systems and their hydrodynamic scaling limits. For finite systems of interacting particles, we review existing results showing that irreversible processes converge faster to their steady state than reversible ones. We show how this behaviour appears in the hydrodynamic limit of such processes, as described by macroscopic fluctuation theory, and we provide a quantitative expression for the acceleration of convergence in this setting. We give a geometrical interpretation of this acceleration, in terms of currents that are antisymmetric under time-reversal and orthogonal to the free energy gradient, which act to drive the system away from states where (reversible) gradient-descent dynamics result in slow convergence to equilibrium.     

Gibbsian Stationary Non-equilibrium States

We study the structure of stationary non-equilibrium states for interacting particle systems from a microscopic viewpoint. In particular we discuss two different discrete geometric constructions. We apply both of them to determine non reversible transition rates corresponding to a fixed invariant measure. The first one uses the equivalence of this problem with the construction of divergence free flows on the transition graph. Since divergence free flows are characterized by cyclic decompositions we can generate families of models from elementary cycles on the configuration space. The second construction is a functional discrete Hodge decomposition for translational covariant discrete vector fields. According to this, for example, the instantaneous current of any interacting particle system on a finite torus can be canonically decomposed in a gradient part, a circulation term and an harmonic component. All the three components are associated with functions on the configuration space. This decomposition is unique and constructive. The stationary condition can be interpreted as an orthogonality condition with respect to an harmonic discrete vector field and we use this decomposition to construct models having a fixed invariant measure.     

Conserved currents and symmetry transformations in local scattering theory

The relation between conserved currents and symmetries of theS-matrix is investigated within the framework of Wightman field theory. Assuming a complete particle interpretation with no massless particles, it is shown that every conserved current yields a self-adjoint charge operator which acts additively onn-particle states and commutes with theS-matrix. For currents satisfying current algebra relations of a groupG, the corresponding charges generate a unitary representation ofG.     

Information recovery from black holes

We argue that if black hole entropy arises from a finite number of underlying quantum states, then any particular such state can be identified from infinity. The finite density of states implies a discrete energy spectrum, and, in general, such spectra are non-degenerate except as determined by symmetries. Therefore, knowledge of the precise energy, and of other commuting conserved charges, determines the quantum state. In a gravitating theory, all conserved charges including the energy are given by boundary terms that can be measured at infinity. Thus, within any theory of quantum gravity, no information can be lost in black holes with a finite number of states. However, identifying the state of a black hole from infinity requires measurements with Planck scale precision. Hence observers with insufficient resolution will experience information loss. First Award in the 2006 Essay Competition of the Gravity Research Foundation.     

Hexagonal discrete Boltzmann models with and without rest particles

We consider seven different hexagonal discrete Boltzmann models corresponding to one, two, three, and five hexagons with or without rest particles. In the microscopic collisions the number of particles associated with a given speed is not necessarily conserved, except for two models without rest particles. We compare different behaviors for the macroscopic quantities between models with and without rest particles and when the number of velocities (or hexagons) increases. We study similarity waves with two asymptotic states and consider two classes of solutions at one asymptotic state: either isotropic (densities associated with the same speed are equal) or anisotropic. Two macroscopic quantities seem useful for such studies: internal energy and mass ratio across the asymptotic states, which satisfy a relation deduced from continuous theory. Here we report results for the isotropic solutions, whoch only exist, for both models, in the subdomains where the propagation speed is larger than some well-defined value. Outside these subdomains, modifications occur when the rest particle desity becomes large. For both models we find a monotonic internal energy and subdomains with a mass ratio equal to the one in continuous theory.     

How to extract QCD baryons from a lattice theory with staggered fermions

The explicit form of the correlation function for the most general local baryon operators is obtained for staggered fermions, in the center of mass. From the discrete symmetries of the action, it is shown that all operators couple to spin-$\text{1}\text{2}$ states only. The whole physical information coming from any numerical simulation, including parity assignments, can be extracted from only one real function of the lattice time. All other correlation functions which can be measured vanish in the limit of large samples of gauge configurations, which may be used as a measure of the statistical significance of data.     

On the structure of symmetry generators

In a field theoretic framework we investigate generators of symmetry transformations induced by conserved local, not necessarily translationally covariant currents. Assuming the invariance of the vacuum and a mass gap, it is shown that the generator on one-particle states in general can be any polynomial of the generators of the Poincaré group and the internal symmetries. We give an example showing that the generator, defined as an integral over a conserved current, in spite of leaving the vacuum invariant, need not be self-adjoint.Supported by a DAAD grant     

Dirac equation in metric-affine gravitation theories and superpotentials

We consider a metric-affine gravitational framework in which the dynamical fields are the spin structures, the general linear connections, and the Dirac fermion fields. Using a spin structure and a linear connection on the world manifold, we construct a principal connection on the spinor bundle. By applying general ideas concerning the conservation laws in the Lagrangian approach to field theory, we examine the corresponding conserved currents. The main result is that the currents associated with infinitesimal vertical (internal) transformations of the covariance group are shown to vanish identically. It follows that to every vector field on the world manifold there corresponds a well-defined current, the stress-energymomentum of the fields. It turns out that the fermion fields do not contribute at all to the superpotential terms. Actually the expression we get for the superpotential generalizes the well-known expression obtained by Komar.     

Hydrodynamics and time correlation functions for cellular automata

Hydrodynamic excitations in lattice gas cellular automata are described in terms of equilibrium time correlation functions for the local conserved variables. For large space and time scales the linearized hydrodynamic equations are obtained to Navier-Stokes order. Exact expressions for the associated susceptibilities and transport coefficients are identified in terms of correlation functions. The general form of the time correlation functions for conserved densities in the hydrodynamic limit is given and illustrated by some examples suitable for comparison with computer simulation. The transport coefficients are related to time correlation functions for the conserved fluxes in a way analogous to the Green-Kubo expressions for continuous fluids. The general results are applied for a one-component fluid and several types of binary diffusion. Also discussed are the effects of unphysical slow modes such as staggered particle or momentum densities.     

On Algebraic Integrability of the Deformed Elliptic Calogero-Moser Problem

Abstract

We discuss stationary solutions of the discrete nonlinear Schrödinger equation (DNSE) with a potential of the ? ⁴ type which is generically applicable to several quantum spin, electron and classical lattice systems. We show that there may arise chaotic spatial structures in the form of incommensurate or irregular quantum states. As a first (typical) example we consider a single electron which is strongly coupled with phonons on a 1D chain of atoms — the (Rashba)–Holstein polaron model. In the adiabatic approximation this system is conventionally described by the DNSE. Another relevant example is that of superconducting states in layered superconductors described by the same DNSE. Amongst many other applications the typical example for a classical lattice is a system of coupled nonlinear oscillators. We present the exact energy spectrum of this model in the strong coupling limit and the corresponding wave function. Using this as a starting point we go on to calculate the wave function for moderate coupling and find that the energy eigenvalue of these structures of the wave function is in exquisite agreement with the exact strong coupling result. This procedure allows us to obtain (numerically) exact solutions of the DNSE directly. When applied to our typical example we find that the wave function of an electron on a deformable lattice (and other quantum or classical discrete systems) may exhibit incommensurate and irregular structures. These states are analogous to the periodic, quasiperiodic and chaotic structures found in classical chaotic dynamics.     

Topological anomalies from the path integral measure in superspace

A fully quantum version of the Witten-Olive analysis of the central charge in the N=1 Wess-Zumino model in d=2 with a kink solution is presented by using path integrals in superspace. We regulate the Jacobians with heat kernels in superspace, and obtain all superconformal anomalies as one Jacobian factor. The conserved quantum currents differ from the Noether currents by terms proportional to field equations, and these terms contribute to the anomalies. We identify the particular variation of the superfield which produces the central charge current and its anomaly; it is the variation of the auxiliary field. The quantum supersymmetry algebra which includes the contributions of superconformal anomalies is derived by using the Bjorken-Johnson-Low method instead of semi-classical Dirac brackets. We confirm earlier results that the BPS bound remains saturated at the quantum level due to equal anomalies in the energy and central charge.     

Nonconservation of gauge singlet charge operators in light cone field theories

A light cone gauge theory is considered which possesses one or more conserved currents. It is shown quite generally that the usual associated charge operator is not conserved whenever the current transforms as a vector in Minkowski space. This includes the case of a conserved current which is a singlet under the operations of any group associated with a coupling to a non-abelian gauge field. As one application of this result one infers that there are no conserved flavor charge operators in the light cone formulation of quantum chromodynamics.