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

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

Manifest covariance and the Hamiltonian approach to mass gap in (2+1)-dimensional Yang-Mills theory

In earlier work we have given a Hamiltonian analysis of Yang-Mills theory in (2+1) dimensions showing how a mass gap could arise. In this paper, generalizing and covariantizing from the mass term in the Hamiltonian analysis, we obtain two manifestly covariant and gauge-invariant mass terms which can be used in a resummation of standard perturbation theory to study properties of the mass gap.Comment: Sections 1, 4 modified, part of section 2 moved to appendix, 19 pages, LaTe

Hard Thermal Loops, Gauged WZNW Action and the Energy of Hot Quark-Gluon Plasma

The generating functional for hard thermal loops in QCD is rewritten in terms of a gauged WZNW action by introducing an auxiliary field. This shows in a simple way that the contribution of hard thermal loops to the energy of the quark-gluon plasma is positive.Comment: 9 pages, CU-TP 60

Constant magnetic field and 2d non-commutative inverted oscillator

We consider a two-dimensional non-commutative inverted oscillator in the presence of a constant magnetic field, coupled to the system in a ``symplectic'' and ``Poisson'' way. We show that it has a discrete energy spectrum for some value of the magnetic field.Comment: 7 pages, LaTeX file, no figures, PACS number: 03.65.-

Edges and Diffractive Effects in Casimir Energies

The prototypical Casimir effect arises when a scalar field is confined between parallel Dirichlet boundaries. We study corrections to this when the boundaries themselves have apertures and edges. We consider several geometries: a single plate with a slit in it, perpendicular plates separated by a gap, and two parallel plates, one of which has a long slit of large width, related to the case of one plate being semi-infinite. We develop a general formalism for studying such problems, based on the wavefunctional for the field in the gap between the plates. This formalism leads to a lower dimensional theory defined on the open regions of the plates or boundaries. The Casimir energy is then given in terms of the determinant of the nonlocal differential operator which defines the lower dimensional theory. We develop perturbative methods for computing these determinants. Our results are in good agreement with known results based on Monte Carlo simulations. The method is well suited to isolating the diffractive contributions to the Casimir energy.Comment: 32 pages, LaTeX, 9 figures. v2: additional discussion of renormalization procedure, version to appear in PRD. v3: corrected a sign error in (70

Noncommutative gravity: fuzzy sphere and others

Gravity on noncommutative analogues of compact spaces can give a finite mode truncation of ordinary commutative gravity. We obtain the actions for gravity on the noncommutative two-sphere and on the noncommutative ${\bf CP}^2$ in terms of finite dimensional $(N\times N)$-matrices. The commutative large $N$ limit is also discussed.Comment: LaTeX, 13 pages, section on CP^2 added + minor change

Chern-Simons Theory and the Quark-Gluon Plasma

The generating functional for hard thermal loops in QCD is important in setting up a resummed perturbation theory, so that all terms of a given order in the coupling constant can be consistently taken into account. It is also the functional which leads to a gauge invariant description of Debye screening and plasma waves in the quark-gluon plasma. We have recently shown that this functional is closely related to the eikonal for a Chern-Simons gauge theory. In this paper, this relationship is explored and explained in more detail, along with some generalizations.Comment: 28 pages (4 Feynman diagrams not included, available upon request