Thomas-Wigner rotation as a holonomy for spin- 1/2 particles

authored by
Veiko Palge, Christian Pfeifer
Abstract

The Thomas-Wigner rotation (TWR) results from the fact that a combination of boosts leads to a nontrivial rotation of a physical system. Its origin lies in the structure of the Lorentz group. In this article we discuss the idea that the TWR can be understood in the geometric manner, being caused by the nontrivially curved relativistic momentum space, i.e., the mass shell, seen as a Riemannian manifold. We show explicitly how the TWR for a massive spin-1/2 particle can be calculated as a holonomy of the mass shell. To reach this conclusion we recall how to construct the spin bundle over the mass shell manifold. Interpreting TWR as a holonomy means it belongs to the same family of phenomena as Berry's phase.

Organisation(s)
QuantumFrontiers
External Organisation(s)
University of Tartu
University of Bremen
Type
Article
Journal
Physical Review A
Volume
109
ISSN
2469-9926
Publication date
11.03.2024
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Atomic and Molecular Physics, and Optics
Electronic version(s)
https://doi.org/10.1103/PhysRevA.109.032206 (Access: Unknown)