Renormalization of Lorentz violating theories
Damiano Anselmi, Milenko Halat
TL;DR
This work classifies unitary, renormalizable Lorentz-violating quantum field theories built from scalars and fermions by introducing higher-space-derivative terms to improve UV behavior. A weighted power-counting framework is developed to control divergences while ensuring that renormalization does not generate higher time derivatives, preserving unitarity. The authors derive the weighted trace anomaly, study RG flows for representative models, and extend the formalism to nonrelativistic theories and multi-subspace spacetime splittings. The results suggest Lorentz-violating, Lifshitz-type theories can serve as UV completions or effective descriptions with finite, controllable couplings, with potential relevance to quantum gravity, condensed matter, and beyond. These constructions pave the way for incorporating gauge fields and gravity in future work, and for exploring weighted conformal structures in high-energy physics.
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.