Causal Propagators for Algebraic Gauges

TL;DR

This paper derives causal gluon propagators in algebraic gauges using analytic extension, and applies them to compute one-loop integrals in the three-gluon vertex, confirming consistency with traditional methods.

Contribution

It introduces a method to derive causal propagators in algebraic gauges and demonstrates their application in loop integral calculations.

Findings

Causal gluon propagators are successfully derived for algebraic gauges.

The derived propagators produce results consistent with traditional prescriptions.

Application to three-gluon vertex correction confirms the method's validity.

Abstract

Applying the principle of analytic extension for generalized functions we derive causal propagators for algebraic non-covariant gauges. The so generated manifestly causal gluon propagator in the light-cone gauge is used to evaluate two one-loop Feynman integrals which appear in the computation of the three-gluon vertex correction. The result is in agreement with that obtained through the usual prescriptions.