The Path Integral for 1+1-dimensional QCD

TL;DR

This paper derives a gauge-invariant path integral formulation for 1+1-dimensional QCD, addressing gauge fixing and avoiding infinities from gauge redundancies, thus providing a new approach to quantization.

Contribution

It introduces a novel path integral expression for 1+1D QCD using gauge-invariant variables and a Faddeev-Popov like method to handle gauge redundancies.

Findings

Derived a path integral for 1+1D QCD from canonical quantization.

Formulated gauge fixing in terms of gauge-invariant curvilinear variables.

Avoided infinities associated with gauge equivalent configurations.

Abstract

We derive a path integral expression for the transition amplitude in 1+1-dimensional QCD starting from canonically quantized QCD. Gauge fixing after quantization leads to a formulation in terms of gauge invariant but curvilinear variables. Remainders of the curved space are Jacobians, an effective potential, and sign factors just as for the problem of a particle in a box. Based on this result we derive a Faddeev-Popov like expression for the transition amplitude avoiding standard infinities that are caused by integrations over gauge equivalent configurations.