Poincar\'e Covariant k-Minkowski Spacetime

TL;DR

This paper constructs a Poincare' covariant model of k-Minkowski spacetime, demonstrating that doubly special relativity can be realized without deforming Poincare' symmetry, using a Wigner approach.

Contribution

It presents a fully covariant k-Minkowski spacetime model that preserves Poincare' symmetry via a unitary representation, aligning with Wigner's quantum symmetry framework.

Findings

Covariance implemented by a unitary Poincare' representation.

Model realizes doubly special relativity without deforming Poincare' symmetry.

Provides an alternative to the DFR model for quantum spacetime.

Abstract

A fully Poincare' covariant model is constructed out of the k-Minkowski spacetime. Covariance is implemented by a unitary representation of the Poincare' group, and thus complies with the original Wigner approach to quantum symmetries. This provides yet another example (besides the DFR model), where Poincare' covariance is realised a` la Wigner in the presence of two characteristic dimensionful parameters: the light speed and the Planck length. In other words, a Doubly Special Relativity (DSR) framework may well be realised without deforming the meaning of "Poincare covariance".