Quasi-Local Formulation of Non-Abelian Finite-Element Gauge Theory

Recently it was shown how to formulate the finite-element equations of motion of a non-Abelian gauge theory, by gauging the free lattice difference equations, and simultaneously determining the form of the gauge transformations. In particular, the gauge-covariant field strength was explicitly constructed, locally, in terms of a path ordered product of exponentials (link operators). On the other hand, the Dirac and Yang-Mills equations were nonlocal, involving sums over the entire prior lattice. Earlier, Matsuyama had proposed a local Dirac equation constructed from just the above-mentioned link operators. Here, we show how his scheme, which is closely related to our earlier one, can be implemented for a non-Abelian gauge theory. Although both Dirac and Yang-Mills equations are now local, the field strength is not. The technique is illustrated with a direct calculation of the current anomalies in two and four space-time dimensions. Unfortunately, unlike the original finite-element proposal, this scheme is in general nonunitary.Comment: 19 pages, REVTeX, no figure

Facilitation of transmitter release at squid synapses

Facilitation is shown to decay as a compound exponential with two time constants (T1, T2) at both giant and non-giant synapses in squid steilate ganglia bathed in solutions having low extracellular calcium concentrations ([Ca++]o). Maximum values of facilitation (F~) were significantly larger, and T1 was significantly smaller in giant than non-giant synapses. Decreases in [Ca++]o or increases in [Mn++]o had variable effects on T1 and F1, whereas decreases in temperature increased T~ but had insignificant effects on/'1. The growth of facilitation during short trains of equal interval stimuli was adequately predicted by the linear summation model developed by Mallart and Martin (1967.J. Physiol. (Lond.). 193: 676-694) for frog neuromuscular junctions. This result suggests that the underlying mechanisms of facilitation are similar in squid and other synapses which release many transmitter quanta.This work was supported by National Science Foundation research grant GB-36949, National Research Council (Canada) and Grass Fellowships to Dr. Charlton, and a National Institutes of Health career award (NS-00070) to Dr. Bittner.Neuroscienc

Relativistic Coulomb Resummation in QCD

A relativistic Coulomb-like resummation factor in QCD is suggested, based on the solution of the quasipotential equation.Comment: 4 pages, 2 eps figures, REVTe

Casimir Energies and Pressures for δ\delta-function Potentials

The Casimir energies and pressures for a massless scalar field associated with $\delta$-function potentials in 1+1 and 3+1 dimensions are calculated. For parallel plane surfaces, the results are finite, coincide with the pressures associated with Dirichlet planes in the limit of strong coupling, and for weak coupling do not possess a power-series expansion in 1+1 dimension. The relation between Casimir energies and Casimir pressures is clarified,and the former are shown to involve surface terms. The Casimir energy for a $\delta$-function spherical shell in 3+1 dimensions has an expression that reduces to the familiar result for a Dirichlet shell in the strong-coupling limit. However, the Casimir energy for finite coupling possesses a logarithmic divergence first appearing in third order in the weak-coupling expansion, which seems unremovable. The corresponding energies and pressures for a derivative of a $\delta$-function potential for the same spherical geometry generalizes the TM contributions of electrodynamics. Cancellation of divergences can occur between the TE ($\delta$-function) and TM (derivative of $\delta$-function) Casimir energies. These results clarify recent discussions in the literature.Comment: 16 pages, 1 eps figure, uses REVTeX

COMMODITY POLICY ISSUES FOR THE 1980S

Agricultural and Food Policy,

Energy conditions outside a dielectric ball

We show analytically that the vacuum electromagnetic stress-energy tensor outside a ball with constant dielectric constant and permeability always obeys the weak, null, dominant, and strong energy conditions. There are still no known examples in quantum field theory in which the averaged null energy condition in flat spacetime is violated.Comment: 12 pages, RevTex

Casimir energy, dispersion, and the Lifshitz formula

Despite suggestions to the contrary, we show in this paper that the usual dispersive form of the electromagnetic energy must be used to derive the Lifshitz force between parallel dielectric media. This conclusion follows from the general form of the quantum vacuum energy, which is the basis of the multiple-scattering formalism. As an illustration, we explicitly derive the Lifshitz formula for the interaction between parallel dielectric semispaces, including dispersion, starting from the expression for the total energy of the system. The issues of constancy of the energy between parallel plates and of the observability of electrostrictive forces are briefly addressed.Comment: 11 pages, no figure

Probing the helium-graphite interaction

Two separate lines of investigation have recently converged to produce a highly detailed picture of the behavior of helium atoms physisorbed on graphite basal plane surfaces. Atomic beam scattering experiments on single crystals have yielded accurate values for the binding energies of several· states for both (^4)He and (^3)He, as well as matrix elements of the largest Fourier component of the periodic part of the interaction potential. From these data, a complete three-dimensional description of the potential has been constructed, and the energy band structure of a helium atom moving in this potential calculated. At the same time, accurate thermodynamic measurements were made on submonolayer helium films adsorbed on Grafoil. The binding energy and low-coverage specific heat deduced from these measurements are in excellent agreement with those calculated from the band structures