Quantum gauge fields and flat connections in 2-dimensional BF theory

The 2-dimensional BF theory is both a gauge theory and a topological Poisson $\sigma$-model corresponding to a linear Poisson bracket. In \cite{To1}, Torossian discovered a connection which governs correlation functions of the BF theory with sources for the $B$-field. This connection is flat, and it is a close relative of the KZ connection in the WZW model. In this paper, we show that flatness of the Torossian connection follows from (properly regularized) quantum equations of motion of the BF theory.Comment: 12 pages, 8 figure

Second-quantization picture of the edge currents in the fractional quantum Hall effect

We study the quantum theory of two-dimensional electrons in a magnetic field and an electric field generated by a homogeneous background. The dynamics separates into a microscopic and macroscopic mode. The latter is a circular Hall current which is described by a chiral quantum field theory. It is shown how in this second quantized picture a Laughlin-type wave function emerges.Comment: 12 pages, 1 figure, LaTeX; comments on the particle density and the charge added, the figure improve

High-TcT_c superconductivity by phase cloning

We consider a BCS-type model in the spin formalism and argue that the structure of the interaction provides a mechanism for control over directions of the spin \vect S other than $S_z$, which is being controlled via the conventional chemical potential. We also find the conditions for the appearance of a high-$T_c$ superconducting phase.Comment: 11 pages, 5 figures v3: section 2 edite

Dirac Variables and Zero Modes of Gauss Constraint in Finite-Volume Two-Dimensional QED

The finite-volume QED$_{1+1}$ is formulated in terms of Dirac variables by an explicit solution of the Gauss constraint with possible nontrivial boundary conditions taken into account. The intrinsic nontrivial topology of the gauge group is thus revealed together with its zero-mode residual dynamics. Topologically nontrivial gauge transformations generate collective excitations of the gauge field above Coleman's ground state, that are completely decoupled from local dynamics, the latter being equivalent to a free massive scalar field theory.Comment: 13 pages, LaTe