A realisation of Lorentz algebra in Lorentz violating theory

TL;DR

This paper demonstrates how Lorentz algebra can be realized in a Lorentz-violating higher derivative theory by restricting field configurations, enabling the construction of a Poincaré invariant symplectic structure.

Contribution

It introduces a method to realize Lorentz algebra in Lorentz-violating theories through background-dependent field restrictions, facilitating Poincaré invariance in the phase space.

Findings

Lorentz algebra can be realized in Lorentz-violating theories.

Restricted fields form a basis for Lorentz algebra realization.

A Poincaré invariant symplectic form can be constructed on the phase space.

Abstract

A Lorentz non-invariant higher derivative effective action in flat spacetime, characterised by a constant vector, can be made invariant under infinitesimal Lorentz transformations by restricting the allowed field configurations. These restricted fields are defined as functions of the background vector in such a way that background dependance of the dynamics of the physical system is no longer manifest. We show here that they also provide a field basis for the realisation of Lorentz algebra and allow the construction of a Poincar\'e invariant symplectic two form on the covariant phase space of the theory.