Generalized Triply Special Relativity models and their classical limit

TL;DR

This paper generalizes Triply Special Relativity models, explores their algebraic structures, and examines their classical limits through Poisson brackets, contributing to the understanding of noncommutative geometries in curved spacetime.

Contribution

It introduces a generalized framework for Triply Special Relativity and constructs its realizations on phase space, analyzing the classical limit with Poisson brackets.

Findings

Constructed realizations of generalized models on phase space

Analyzed the classical limit using Poisson brackets

Preserved Lorentz invariance in the generalized models

Abstract

Triply Special Relativity is a deformation of Special Relativity based on three fundamental parameters, that describes a noncommutative geometry on a curved spacetime, preserving the Lorentz invariance and the principle of relativity. Its symmetries are generated by a 14-parameter nonlinear algebra. In this paper, we discuss a generalization of the original model and construct its realizations on a canonical phase space. We also investigate in more detail its classical limit, obtained by replacing the commutators by Poisson brackets.