Propagators with the Mandelstam-Leibbrandt Prescription in the Light-Cone Gauge

TL;DR

This paper investigates the behavior of propagators in the light-cone gauge with the Mandelstam-Leibbrandt prescription, revealing issues like logarithmic growth and coordinate-dependent mass, and suggests fixing residual gauge freedoms to address these problems.

Contribution

It demonstrates the unphysical behaviors of propagators in this gauge and proposes fixing residual gauge invariances to eliminate these issues.

Findings

Feynman propagator exhibits logarithmic growth at large t;

Retarded propagator develops a coordinate-dependent mass;

Fixing residual gauge invariance can remove unphysical behaviors.

Abstract

We show that the Feynman propagator in the light-cone gauge with the Mandelstam-Leibbrandt prescription has a logarithmic growth for large $\tilde{n}\cdot x$ which is related to the presence of a residual gauge invariance. Furthermore, we show that the retarded propagator for the $\tilde{n}\cdot A$ component of the gauge field develops a coordinate dependent mass which is inversely proportional to the magnitude of the transverse coordinate. We argue that this unphysical behavior may be eliminated by fixing the residual gauge degrees of freedom.