A Generalization of Gauge Invariance

TL;DR

This paper explores a generalization of gauge invariance within perturbative quantum field theory, focusing on identities involving Wick sub-monomials and proposing conjectures for higher-order cases.

Contribution

It introduces a novel generalization of gauge invariance identities involving Wick sub-monomials, supported by explicit lower-order computations and conjectures for all orders.

Findings

Derived gauge invariance identities involving Wick sub-monomials.

Performed explicit calculations in lower orders of perturbation theory.

Proposed conjectures for the general case at arbitrary orders.

Abstract

We consider perturbative quantum field theory in the causal framework. Gauge invariance is, in this framework, an identity involving chronological products of the interaction Lagrangian; it express the fact that the scattering matrix must leave invariant the sub-space of physical states. We are interested in generalizations of such identity involving Wick sub-monomials of the interaction Lagrangian. The analysis can be performed by direct computation in the lower orders of perturbation theory; guided by these computations we conjecture a generalization for arbitrary orders.