Wigner rotation and Euler angle parametrization

TL;DR

This paper introduces a simplified decomposition of Lorentz transformations in (2+1)-dimensional Minkowski space, making the analysis of Wigner rotations more straightforward and enhancing physical understanding.

Contribution

It presents a novel Euler angle parametrization for Lorentz transformations in (2+1)D Minkowski space, simplifying the mathematics of Wigner rotations.

Findings

Decomposition simplifies Wigner rotation calculations

Mathematical framework becomes more accessible

Physical interpretation is clarified

Abstract

Analogous to the famous Euler angle parametrization in three-dimensional Euclidean space, a reflection-free Lorentz transformation in (2+1)-dimensional Minkowski space can be decomposed into three simple parts. Applying this decomposition to the Wigner rotation problem, we are able to show the related mathematics becomes much simpler and the physical meanings more comprehensible and enlightening.