The light-cone gauge without prescriptions

TL;DR

This paper proposes an approach to handle unphysical singularities in light-cone gauge Feynman integrals by using the negative dimensional integration method, avoiding traditional prescriptions.

Contribution

It introduces a prescription-free method for solving light-cone gauge integrals based on negative dimensional integration, emphasizing causality.

Findings

Avoids the use of prescriptions in light-cone gauge integrals

Utilizes negative dimensional integration to handle singularities

Provides a more elegant and potentially simpler computational approach

Abstract

Feynman integrals in the physical light-cone gauge are harder to solve than their covariant counterparts. The difficulty is associated with the presence of unphysical singularities due to the inherent residual gauge freedom in the intermediate boson propagators constrained within this gauge choice. In order to circumvent these non-physical singularities, the headlong approach has always been to call for mathematical devices --- prescriptions --- some successful ones and others not so much so. A more elegant approach is to consider the propagator from its physical point of view, that is, an object obeying basic principles such as causality. Once this fact is realized and carefully taken into account, the crutch of prescriptions can be avoided altogether. An alternative third approach, which for practical computations could dispense with prescriptions as well as prescinding the necessity of careful stepwise watching out of causality would be of great advantage. And this third option is realizable within the context of negative dimensions, or as it has been coined, negative dimensional integration method, NDIM for short.