Probing Wigner Rotations for Any Group

TL;DR

This paper investigates Wigner rotations across various symmetry groups, linking them to Thomas precession through Berry connections, and derives formulas for state transformations, broadening understanding of relativistic spin effects.

Contribution

It introduces a general framework connecting Wigner rotations with Berry holonomies for arbitrary semi-direct product groups, extending prior specific cases.

Findings

Established a universal link between Wigner rotations and Thomas precession.

Derived a formula for infinitesimal state transformations in Lie algebra terms.

Connected Wigner rotations to Berry phase holonomies on momentum orbits.

Abstract

Wigner rotations are transformations that affect spinning particles and cause the observable phenomenon of Thomas precession. Here we study these rotations for arbitrary symmetry groups with a semi-direct product structure. In particular we establish a general link between Wigner rotations and Thomas precession by relating the latter to the holonomies of a certain Berry connection on a momentum orbit. Along the way we derive a formula for infinitesimal, Lie-algebraic transformations of one-particle states.