Introduction to the Pinch Technique

TL;DR

This paper introduces the pinch technique, demonstrating its equivalence with the background field method at one-loop level in QCD, and reviews its absorptive form, serving as an educational overview.

Contribution

It provides a concise introduction and comparison of the pinch technique and background field method, including one-loop calculations and absorptive aspects.

Findings

Proves equivalence between pinch technique and background field method at one-loop level.

Provides explicit one-loop calculations for QCD Green's functions.

Reviews the absorptive pinch technique and its applications.

Abstract

These notes are a short introduction to the pinch technique. We present the one-loop calculations for basic QCD Green's functions. The equivalence between the pinch technique and the background field method is explicitly shown at the one-loop level. We review the absorptive pinch technique in the last sections. These lectures are a compilation of relevant papers on this subject and are prepared for the third Modave Summer School in Mathematical Physics.