The Pinch Technique at Two Loops

TL;DR

This paper extends the pinch technique to two loops, ensuring gauge-independence, gauge-invariance, unitarity, and analyticity of the $S$-matrix are maintained in higher-order calculations.

Contribution

It provides a rigorous generalization of the pinch technique algorithm to two-loop order, preserving fundamental properties of quantum field theory.

Findings

Successful extension of the pinch technique to two loops.

Maintains gauge-independence and unitarity at two loops.

Ensures analyticity of the $S$-matrix in higher-order calculations.

Abstract

It is shown that the fundamental properties of gauge-independence, gauge-invariance, unitarity, and analyticity of the $S$-matrix lead to the unambiguous generalization of the pinch technique algorithm to two loops.