Interaction anomalies and one-particle dynamics in very special relativity theories

TL;DR

The paper addresses whether nontrivial interactions can coexist with restricted relativity groups when Lorentz invariance is broken, focusing on Very Special Relativity (VSR) and related Galilei subgroups. It uses world-line conditions to realize symmetry generators on the tangent bundle, derives anomaly-cancellation constraints for static, very special, anisotropic, and homogeneous subgroups, and extracts explicit forms of accelerations $A^{(a)}_l(v,x)$ compatible with each symmetry. The main finding is that single-particle Poincaré symmetry generally enforces free motion ($A_l=0$), while certain subgroups admit nontrivial interactions (e.g., static and VSR Galilei cases) and that the structure of allowed dynamics depends on whether boosts act on time. The results clarify how restricted symmetry groups shape classical multi-particle dynamics in LIV scenarios and provide a systematic classification of permissible interactions under various subalgebras, relevant to LIV phenomenology and foundational questions about no-interaction theorems.

Abstract

It is well known that relativistic invariance introduce strong constraints in the interactions of classical particles. We generalize the non-interaction theorems for Lorentz violating systems which still preserve a subgroup of Poincaré symmetry. In particular we analize the case of very special relativity introduced by Cohen and Glashow. We also extend the analysis for Galilei invariant multiparticle systems and for some anisotropic systems which are still invariant under some maximal subgroups of Galilei group.