Generalized commutation relations and Non linear momenta theories, a close relationship

TL;DR

This paper explores the connection between generalized commutation relations and nonlinear momenta theories, revealing a new algebraic structure and analyzing its unique features within the context of DSR theories.

Contribution

It establishes a close relationship between generalized commutation relations and nonlinear momenta, introducing a new algebra with distinct properties.

Findings

Identifies a close relationship between generalized commutation relations and nonlinear momenta.

Introduces a new algebra with unique features derived from this relationship.

Analyzes the implications of this algebra within DSR theories.

Abstract

A revision of generalized commutation relations is performed, besides a description of Non linear momenta realization included in some DSR theories. It is shown that these propositions are closely related, specially we focus on Magueijo Smolin momenta and Kempf et al. and L.N. Chang generalized commutators. Due to this, a new algebra arises with its own features that is also analyzed.