Commuting and Noncommuting Coordinates in Deformed Special Relativity

TL;DR

This paper explores how commuting and noncommuting space-time coordinates behave in deformed special relativity, deriving their algebra, invariants, and field theories, and introducing deformed plane waves as a novel feature.

Contribution

It provides a comprehensive analysis of coordinate structures and field theories in deformed special relativity, including the novel use of deformed plane waves.

Findings

Derived space-time algebra and invariants for deformed coordinates

Established transformation behaviors in momentum space

Introduced deformed plane waves as a new feature

Abstract

Commuting and noncommuting space-time coordinates in a class of deformed special relativity theories are investigated. Their momentum space representation, transformation behaviour, space-time algebra, invariants and the corresponding field theories are derived. Several coordinates require as a novel feature the introduction of deformed plane waves.