Symanzik-Becchi-Rouet-Stora lessons on renormalizable models with broken symmetry: the case of Lorentz violation

TL;DR

This paper revisits the renormalization of models with broken Lorentz symmetry using algebraic methods, emphasizing the necessity of including all counter terms consistent with locality and power-counting as per Symanzik's principle.

Contribution

It applies the algebraic perturbative approach to Lorentz-violating models, clarifying the role of counter terms and extending Symanzik's lessons to these theories.

Findings

Confirmed the necessity of including all symmetry-allowed counter terms.

Clarified the application of Symanzik's aphorism in Lorentz-violating models.

Provided a systematic algebraic framework for renormalization in these theories.

Abstract

In this paper, we revisit the issue intensively studied in recent years on the generation of terms by radiative corrections in models with broken Lorentz symmetry. The algebraic perturbative method of handling the problem of renormalization of the theories with Lorentz symmetry breaking, is used. We hope to make clear the Symanzik's aphorism: "{\it Whether you like it or not, you have to include in the lagrangian all counter terms consistent with locality and power-counting, unless otherwise constrained by Ward identities.}"