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

TL;DR

This paper reformulates finite-volume 2D QED using Dirac variables, revealing topological gauge features and zero modes, and shows how collective gauge excitations emerge independently of local scalar field dynamics.

Contribution

It provides an explicit solution to the Gauss constraint in finite-volume 2D QED, highlighting the role of topology and zero modes in gauge dynamics.

Findings

Explicit Dirac variable formulation of finite-volume QED2+1

Identification of topological gauge transformations and zero modes

Decoupling of collective gauge excitations from local scalar dynamics

Abstract

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.