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

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

Resource Letter VWCPF-1: Van der Waals and Casimir-Polder forces

This Resource Letter provides a guide to the literature on van der Waals and Casimir-Polder forces. Journal articles, books, and other documents are cited on the following topics: van der Waals forces, retarded dispersion forces or Casimir-Polder forces between atoms or molecules, Casimir-Polder forces between a molecule and a dielectric or conducting body, the summation of Casimir-Polder forces as leading to the Casimir and Lifshitz forces between conducting and dielectric bodies, Casimir friction, applications to nanotechnology, the nature of the quantum vacuum, and experimental tests of the theory of Casimir and Casimir-Polder and van der Waals forces.Comment: 37 pages, no figures. This resource letter is intended to provide selected references to guide undergraduate students and people new to the field into the subject of CP and Casimir forces. References are not intended to be complete. This is substantially enlarged and revised versio

Finite-element quantum field theory

An alternative approach to lattice gauge theory has been under development for the past decade. It is based on discretizing the operator Heisenberg equations of motion in such a way as to preserve the canonical commutation relations at each lattice site. It is now known how to formulate a non-Abelian gauge theory within this framework. The formulation appears to be free of fermion doubling. Since the theory is unitary, a time-development operator (Hamiltonian) can be constructed.Comment: Talk presented at LATTICE96(theoretical developments), 3 pages, LATEX, uses espcrc2.st

Schwinger's Approach to Einstein's Gravity and Beyond

Julian Schwinger (1918--1994), founder of renormalized quantum electrodynamics, was arguably the leading theoretical physicist of the second half of the 20th century. Thus it is not surprising that he made contributions to gravity theory as well. His students made major impacts on the still uncompleted program of constructing a quantum theory of gravity. Schwinger himself had no doubt of the validity of general relativity, although he preferred a particle-physics viewpoint based on gravitons and the associated fields, and not the geometrical picture of curved spacetime. This note provides a brief summary of his contributions and attitudes toward the subject of gravity.Comment: 6 pages, no figures; revised version has changed title, clarifications, and additional reference

Using tracked mobile sensors to make maps of environmental effects

We present a study the results of a study of environmental carbon monoxide pollution that has uses a set of tracked, mobile pollution sensors. The motivating concept is that we will be able to map pollution and other properties of the real world a fine scale if we can deploy a large set of sensors with members of the general public who would carry them as they go about their normal everyday activities. To prove the viability of this concept we have to demonstrate that data gathered in an ad-hoc manner is reliable enough in order to allow us to build interesting geo-temporal maps. We present a trial using a small number of global positioning system-tracked CO sensors. From analysis of raw GPS logs we find some well-known spatial and temporal properties of CO. Further, by processing the GPS logs we can find fine-grained variations in pollution readings such as when crossing roads. We then discuss the space of possibilities that may be enabled by tracking sensors around the urban environment – both in getting at personal experience of properties of the environment and in making summative maps to predict future conditions. Although we present a study of CO, the techniques will be applicable to other environmental properties such as radio signal strength, noise, weather and so on