Trivial Lagrangians in the Causal Approach

TL;DR

This paper proves a non-uniqueness theorem for chronological products in gauge models using cohomological methods, showing how trivial Lagrangians affect perturbative gauge invariance.

Contribution

It introduces a cohomological framework to analyze the impact of trivial Lagrangians on the non-uniqueness of chronological products in gauge theories.

Findings

Non-uniqueness theorem established for chronological products.

Gauge invariance up to order n is preserved under coboundary modifications.

Trivial Lagrangians induce coboundary changes in chronological products.

Abstract

We prove the non-uniqueness theorem for the chronological products of a gauge model. We use a cohomological language where the cochains are chronological products, gauge invariance means a cocycle restriction and coboundaries are expressions producing zero sandwiched between physical states. Suppose that we have gauge invariance up to order n of the perturbation theory and we modify the first-order chronological products by a coboundary (a trivial Lagrangian). Then the chronological products up to order n get modified by a coboundary also.