Magnetic Field and Curvature Effects on Pair Production I: Scalars and Spinors

The pair production rates for spin-zero and spin-$\frac{1}{2}$ particles are calculated on spaces of the form $M \times {\mathbb R}^{1,1}$ with $M$ corresponding to ${\mathbb R}^2$ (flat), $T^2$ (flat, compactified), $S^2$ (positive curvature) and $H^2$ (negative curvature), with and without a background magnetic field on $M$. The motivation is to elucidate the effects of curvature and background magnetic field. Contrasting effects for positive and negative curvature on the two cases of spin are obtained. For positive curvature, we find enhancement for spin-zero and suppression for spin-$\frac{1}{2}$, with the opposite effect for negative curvature.Comment: 28 pages, 10 figure

Magnetic Field and Curvature Effects on Pair Production II: Vectors and Implications for Chromodynamics

We calculate the pair production rates for spin-$1$ or vector particles on spaces of the form $M \times {\mathbb R}^{1,1}$ with $M$ corresponding to ${\mathbb R}^2$ (flat), $S^2$ (positive curvature) and $H^2$ (negative curvature), with and without a background (chromo)magnetic field on $M$. Beyond highlighting the effects of curvature and background magnetic field, this is particularly interesting since vector particles are known to suffer from the Nielsen-Olesen instability, which can dramatically increase pair production rates. The form of this instability for $S^2$ and $H^2$ is obtained. We also give a brief discussion of how our results relate to ideas about confinement in nonabelian theories.Comment: 24 pages, 9 figure

The Isospin Asymmetry in Anomalous Fluid Dynamics

The dynamics of fluids in which the constituent particles carry nonabelian charges can be described succinctly in terms of group-valued variables via a generalization of the co-adjoint orbit action for particles. This formalism, which is particularly suitable for incorporating anomalies, has previously been used for the chiral magnetic and chiral vorticity effects. Here we consider the similar effect for the isospin which corresponds to an angular asymmetry for neutral pions.Comment: 12 page

Plasmon interactions in the quark-gluon plasma

Yang-Mills theory at finite temperature is rewritten as a theory of plasmons which provides a Hamiltonian framework for perturbation theory with resummation of hard thermal loops.Comment: 12 pages, LaTeX, minor typos corrected, discussion adde

Fuzzy spaces and new random matrix ensembles

We analyze the expectation value of observables in a scalar theory on the fuzzy two sphere, represented as a generalized hermitian matrix model. We calculate explicitly the form of the expectation values in the large-N limit and demonstrate that, for any single kind of field (matrix), the distribution of its eigenvalues is still a Wigner semicircle but with a renormalized radius. For observables involving more than one type of matrix we obtain a new distribution corresponding to correlated Wigner semicircles.Comment: 12 pages, 1 figure; version to appear in Phys. Rev.

Effective Theory of Wilson Lines and Deconfinement

To study the deconfining phase transition at nonzero temperature, I outline the perturbative construction of an effective theory for straight, thermal Wilson lines. Certain large, time dependent gauge transformations play a central role. They imply the existence of interfaces, which can be used to determine the form of the effective theory as a gauged, nonlinear sigma model of adjoint matrices. Especially near the transition, the Wilson line may undergo a Higgs effect. As an adjoint field, this can generate eigenvalue repulsion in the effective theory.Comment: 6 pages, LaTeX. Final, published version. Refs. 7, 39, and 40 added. In Ref. 37, there is an expanded discussion of a "fuzzy" bag mode

Supersymmetry and Mass Gap in 2+1 Dimensions: A Gauge Invariant Hamiltonian Analysis

A Hamiltonian formulation of Yang-Mills-Chern-Simons theories with $0\leq N\leq 4$ supersymmetry in terms of gauge-invariant variables is presented, generalizing earlier work on nonsupersymmetric gauge theories. Special attention is paid to the volume measure of integration (over the gauge orbit space of the fields) which occurs in the inner product for the wave functions and arguments relating it to the renormalization of the Chern-Simons level number and to mass-gaps in the spectrum of the Hamiltonians are presented. The expression for the integration measure is consistent with the absence of mass gap for theories with extended supersymmetry (in the absence of additional matter hypermultiplets and/or Chern-Simons couplings), while for the minimally supersymmetric case, there is a mass-gap, the scale of which is set by a renormalized level number, in agreement with indications from existing literature. The realization of the supersymmetry algebra and the Hamiltonian in terms of the gauge invariant variables is also presented.Comment: 31 pages, References added, typos correcte

Wave Functionals, Hamiltonians and Renormalization Group

We analyze the renormalization of wave functionals and energy eigenvalues in field theory. A discussion of the structure of the renormalization group equation for a general Hamiltonian system is also given.Comment: 14, CCNY-HEP 5/9

Sterols and sterolins in Hypoxis hemerocallidea (African potato)

Commercially available health supplements and herbal remedies containing sterols and sterolins, either from African potato (Hypoxis hemerocallidea) alone, or whether enriched with sterols and sterolins, are claimed to be efficacious in the treatment of a variety of ailments. Sterols and sterolins in African potato are purported to be the relevant constituents that are required for the therapeutic claims of such products. A patent describing the extraction of sterolins from African potato plant material has claimed that approximately 9 mg sterolins can be isolated from 100 g of an enriched aqueous African potato extract. Our analysis of African potato plant material and its sterol and sterolin content, when similarly prepared, shows that the measureable content of sterols and sterolins in African potato is far less than the amounts of these compounds that have been claimed to be necessary for therapeutic benefit. We conclude that therapeutic claims relating to sterol and sterolin content in African potato are unsubstantiated, in view of the extremely low content of such compounds that we have isolated from our plant material, and in products containing African potato, or extracts thereof