Lorentz invariant field theory on kappa-Minkowski space

TL;DR

This paper develops a complex scalar field theory on kappa-Minkowski space that preserves Lorentz symmetry by modifying the Lorentz generator action, and explores its conserved charges and quantum structure.

Contribution

It introduces a Lorentz-invariant scalar field theory on kappa-Minkowski space with a modified Lorentz action to prevent symmetry breaking.

Findings

Constructed a Lorentz-invariant scalar field theory on kappa-Minkowski space.

Derived conserved charges for translational and U(1) symmetries.

Analyzed the inner product and Hilbert space structure of the quantum field.

Abstract

It is by now well established that the momentum space dual to the non-commutative $\kappa$-Minkowski space is a submanifold of de Sitter space. It has been noticed recently that field theories built on such momentum space suffer from a subtle form of Lorentz symmetry breaking. Namely, for any negative energy mode the allowed range of rapidities is bounded above. In this paper we construct a complex scalar field theory with a modified action of Lorentz generators which avoids this problem. For such theory we derive conserved charges corresponding to translational and U(1) symmetries. We also discuss in some details the inner product and Hilbert space structure of the $\kappa$-deformed complex quantum field.