Functional Integral Approach to the N-Flavor Schwinger Model

TL;DR

This paper analyzes the N-flavor Schwinger model using path integrals, revealing the structure of its conserved currents, mass spectrum, confinement properties, and vacuum sectors, with implications for understanding non-abelian gauge theories.

Contribution

It provides a detailed path integral analysis of the N-flavor Schwinger model, identifying conserved currents, mass spectrum relations, and the structure of vacuum sectors and confinement.

Findings

Mass spectrum follows a Witten-Veneziano type formula.

Confinement occurs only between charges that are multiples of ±Ne.

The theory decomposes into clustering theta vacua.

Abstract

We study massless QED_2 with N flavors using path integrals. We identify the sector that is generated by the N^2 classically conserved vector currents. One of them (the U(1) current) creates a massive particle, while the others create massless ones. We show that the mass spectrum obeys a Witten-Veneziano type formula. Two theorems on n-point functions clarify the structure of the Hilbert space. Evaluation of the Fredenhagen-Marcu order parameter indicates that a confining force exists only between charges that are integer multiples of +/- Ne, whereas charges that are nonzero mod(N) screen their confining forces and lead to non-vacuum sectors. Finally we identify operators that violate clustering, and decompose the theory into clustering theta vacua.