# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1706.03527