High-speed Contraction of Transverse Rotations to Gauge Transformations

TL;DR

This paper applies Inonu-Wigner contraction to Lorentz group symmetries, revealing how high-speed boosts relate to gauge transformations and helicity in electromagnetic theory.

Contribution

It demonstrates how contraction of Lorentz group symmetries at high velocities naturally leads to gauge transformations and helicity, providing a geometric understanding of these phenomena.

Findings

Boosted O(3) symmetry contracts to Euclidean and cylindrical groups.

Cylindrical component corresponds to helicity and gauge degrees of freedom.

Translation along the cylindrical axis induces gauge transformations.

Abstract

The Inonu-Wigner contraction is applied to special relativity and the little groups of the Lorentz group. If the O(3) symmetry group for massive particle is boosted to an infinite-momentum frame, it becomes contracted to a combination of the cylindrical group and the two-dimensional Euclidean group. The Euclidean component becomes the Lorentz condition applicable to the electromagnetic four-potential, and the cylindrical component leads to the helicity and gauge degrees of freedom. The rotation around the cylindrical axis corresponds to the helicity, while the translation parallel to the axis on the cylindrical surface leads to a gauge transformation.