Optical theorem and effective action: new proofs of old results in QFT

TL;DR

This paper presents simplified proofs of the optical theorem and the effective action in Quantum Field Theory, highlighting their fundamental roles and providing clearer insights into their derivations.

Contribution

It offers new, straightforward proofs of the optical theorem and the effective action, connecting them to pole-ology formalism in QFT.

Findings

Simplified proof of the optical theorem at all orders.

New proof of the effective action as a generating functional.

Clarification of the connection between pole-ology and fundamental QFT results.

Abstract

A new proof of the optical theorem at all orders is presented. Although the theorem is a well-known result in Quantum Field Theory, our proof is interesting because it is particularly simple. Indeed, the theorem is a direct consequence of the pole-ology formalism discussed in Weinberg's Cambridge books. We also discuss a new proof of the standard result concerning the effective action as generating functional of 1PI contributions.