Lorentz-violating dilatations in the momentum space and some extensions on non-linear actions of Lorentz algebra-preserving systems

TL;DR

This paper explores extensions of Lorentz-invariant theories with nonlinear momentum space transformations, focusing on deformed dilatations and their algebraic relations, with potential experimental implications for detecting Lorentz violations.

Contribution

It introduces new models of deformed Lorentz symmetries with specific dilatation transformations and analyzes their algebraic structure and potential experimental signatures.

Findings

Two cases of deformed dilatations with spacelike and lightlike preferred directions analyzed.

Algebraic relations linking deformed and usual Lorentz symmetries established.

Potential experimental effects of Lorentz violations identified.

Abstract

We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the corresponding deformed symmetries are presented with particular emphasis on deformed dilatation transformations. The algebraic transformations relating the deformed symmetries with the usual (undeformed) ones are provided in order to preserve the Lorentz algebra. Two distinct cases are considered: a deformed dilatation transformation with a spacelike preferred direction and a very special relativity embedding with a lightlike preferred direction. In both analysis we consider the possibility of introducing quantum deformations of the corresponding symmetries such that the spacetime coordinates can be reconstructed and the particular form of the real space-momentum commutator remains covariant. Eventually feasible experiments, for which Lorentz violating effects here pointed out may be detectable, are suggested.