Group of boost and rotation transformations with two observer-independent scales

TL;DR

This paper analyzes the structure of deformed Lorentz transformations with two observer-independent scales, developing a technique to verify their group properties and examining combinations of rotations and boosts.

Contribution

It introduces a method for analyzing deformed Lorentz transformations with two scales and confirms their group structure for combined rotations and boosts.

Findings

Transformations form a mathematical group

Technique for analyzing combined rotations and boosts

Explicit verification of group properties

Abstract

I examine the structure of the deformed Lorentz transformations in one of the recently-proposed schemes with two observer-independent scales. I develop a technique for the analysis of general combinations of rotations and deformed boosts. In particular, I verify explicitly that the transformations form group.