Transformations of coordinates and Hamiltonian formalism in deformed Special Relativity

TL;DR

This paper explores how coordinate transformations and Hamiltonian formalism are modified in deformed special relativity theories with two invariant scales, emphasizing the role of noncommuting spacetime coordinates for covariance.

Contribution

It introduces a framework for understanding transformations in deformed special relativity using noncanonical Poisson brackets and noncommuting coordinates.

Findings

Simple transformation formulas derived under covariance requirements

Noncommuting spacetime coordinates are essential in the formalism

Framework applicable to theories with two observer-independent scales

Abstract

We investigate the transformation laws of coordinates in generalizations of special relativity with two observer-independent scales. The request of covariance leads to simple formulas if one assumes noncanonical Poisson brackets, corresponding to noncommuting spacetime coordinates.