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

TL;DR

This paper explores how certain Lorentz-violating theories, including very special relativity, affect particle interactions and dynamics, extending classical non-interaction theorems to these frameworks.

Contribution

It generalizes non-interaction theorems to systems with Lorentz violation and analyzes particle dynamics under various symmetry subgroups.

Findings

Lorentz-violating systems can still exhibit constrained interactions.

Extensions of non-interaction theorems to very special relativity.

Analysis of multiparticle systems under Galilei and anisotropic symmetries.

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 Poincar\'e 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.