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
Center of Applied Space Technology and Microgravity (ZARM)

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)