Renormalization of Lorentz violating theories

TL;DR

This paper classifies and analyzes unitary, renormalizable Lorentz-violating quantum field theories with higher spatial derivatives, exploring their renormalization, scale invariance, and anomalies.

Contribution

It introduces a weighted power counting method to ensure renormalizability and classifies Lorentz-violating theories with higher spatial derivatives, including their quantum properties.

Findings

Higher space derivatives improve Feynman diagram behavior.

Renormalization does not generate higher time derivatives.

Weighted scale invariance is anomalous at the quantum level.

Abstract

We classify the unitary, renormalizable, Lorentz violating quantum field theories of interacting scalars and fermions, obtained improving the behavior of Feynman diagrams by means of higher space derivatives. Higher time derivatives are not generated by renormalization. Renormalizability is ensured by a "weighted power counting" criterion. The theories contain a dimensionful parameter, yet a set of models are classically invariant under a weighted scale transformation, which is anomalous at the quantum level. Formulas for the weighted trace anomaly are derived. The renormalization-group properties are studied.