Self-Similar Random Processes and Infinite-Dimensional Configuration Spaces

We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary representations of the diffeomorphism group, which are important to nonrelativistic quantum statistical physics and to the quantum theory of extended objects in d-dimensional Euclidean space. Special attention is given to measurable structure and topology underlying measures on generalized configuration spaces obtained from self-similar random processes (both for d = 1 and d > 1), which describe infinite point configurations having accumulation points

On the Fock space for nonrelativistic anyon fields and braided tensor products

We realize the physical N-anyon Hilbert spaces, introduced previously via unitary representations of the group of diffeomorphisms of the plane, as N-fold braided-symmetric tensor products of the 1-particle Hilbert space. This perspective provides a convenient Fock space construction for nonrelativistic anyon quantum fields along the more usual lines of boson and fermion fields, but in a braided category. We see how essential physical information is thus encoded. In particular we show how the algebraic structure of our anyonic Fock space leads to a natural anyonic exclusion principle related to intermediate occupation number statistics, and obtain the partition function for an idealised gas of fixed anyonic vortices.Comment: Added some references, more explicit formulae for the discrete case and remark on partition function. 25 pages latex, no figure

Some Variations on Maxwell's Equations

In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized Yang-Mills equations), and a linear modification motivated by the coupling of the electromagnetic potential with a certain nonlinear Schroedinger equation. In the final section, revisiting an old idea of Lorentz, we write Maxwell's equations for a theory in which the electrostatic force of repulsion between like charges differs fundamentally in magnitude from the electrostatic force of attraction between unlike charges. We elaborate on Lorentz' description by means of electric and magnetic field strengths, whose governing equations separate into two fully relativistic Maxwell systems--one describing ordinary electromagnetism, and the other describing a universally attractive or repulsive long-range force. If such a force cannot be ruled out {\it a priori} by known physical principles, its magnitude should be determined or bounded experimentally. Were it to exist, interesting possibilities go beyond Lorentz' early conjecture of a relation to (Newtonian) gravity.Comment: 26 pages, submitted to a volume in preparation to honor Gerard Emch v. 2: discussion revised, factors of 4\pi corrected in some equation

Energy Spectrum of Anyons in a Magnetic Field

For the many-anyon system in external magnetic field, we derive the energy spectrum as an exact solution of the quantum eigenvalue problem with particular topological constraints. Our results agree with the numerical spectra recently obtained for the 3- and the 4-anyon systems.Comment: 11 pages in Plain LaTeX (plus 4 figures available on request), DFPD 92/TH/4

On the virial coefficients of nonabelian anyons

We study a system of nonabelian anyons in the lowest Landau level of a strong magnetic field. Using diagrammatic techniques, we prove that the virial coefficients do not depend on the statistics parameter. This is true for all representations of all nonabelian groups for the statistics of the particles and relies solely on the fact that the effective statistical interaction is a traceless operator.Comment: 9 pages, 3 eps figure

Open Circuit Potential Shifts of Activated Carbon in Aqueous Solutions During Chemical and Adsorption Interactions

Interaction of certain inorganic and organic compounds with activated carbon and the effect of such interaction on open circuit potential of activated carbon were studied. Open circuit potential shifts were observed for an overwhelming majority of the substances and brands of activated carbons investigated. Both negative and positive potential shifts were observed. It was shown that open circuit potential shifts for organic substances depend on degree of coverage of the activated carbon surface. Whereas adsorption of investigated organic compound on activated carbon led to positive potential shifts, desorption of adsorbates from the activated carbon surface led to potential shifts in the opposite direction. Furthermore, time dependencies of open circuit potential shifts were similar for different carbon brands. The magnitude of the shifts depended on the adsorbate, adsorption activity of the adsorbent, and the steric configuration of potential-determinative pores and adsorbate molecules

A Topological String: The Rasetti-Regge Lagrangian, Topological Quantum Field Theory, and Vortices in Quantum Fluids

The kinetic part of the Rasetti-Regge action I_{RR} for vortex lines is studied and links to string theory are made. It is shown that both I_{RR} and the Polyakov string action I_{Pol} can be constructed with the same field X^mu. Unlike I_{NG}, however, I_{RR} describes a Schwarz-type topological quantum field theory. Using generators of classical Lie algebras, I_{RR} is generalized to higher dimensions. In all dimensions, the momentum 1-form P constructed from the canonical momentum for the vortex belongs to the first cohomology class H^1(M,R^m) of the worldsheet M swept-out by the vortex line. The dynamics of the vortex line thus depend directly on the topology of M. For a vortex ring, the equations of motion reduce to the Serret-Frenet equations in R^3, and in higher dimensions they reduce to the Maurer-Cartan equations for so(m).Comment: To appear in Journal of Physics

Quantum chaos, random matrix theory, and statistical mechanics in two dimensions - a unified approach

We present a theory where the statistical mechanics for dilute ideal gases can be derived from random matrix approach. We show the connection of this approach with Srednicki approach which connects Berry conjecture with statistical mechanics. We further establish a link between Berry conjecture and random matrix theory, thus providing a unified edifice for quantum chaos, random matrix theory, and statistical mechanics. In the course of arguing for these connections, we observe sum rules associated with the outstanding counting problem in the theory of braid groups. We are able to show that the presented approach leads to the second law of thermodynamics.Comment: 23 pages, TeX typ