Space-time origin of gauge symmetry

TL;DR

This paper demonstrates that gauge symmetry in massless particles emerges from parity considerations in the relativistic quantum states of massive particles, linking fundamental symmetries to gauge invariance.

Contribution

It provides a first principles derivation showing gauge symmetry arises from parity-related kinematical conditions in relativistic quantum states.

Findings

Parity determines kinematical conditions for massive particles.

Gauge symmetry emerges in the massless limit.

The origin of gauge symmetry is traced to parity quantum number.

Abstract

In this work I show by a first principles calculation that quantum states describing massive relativistic free spinning particles obey kinematical conditions whose origin can be traced to parity as a good quantum number. These conditions are at the root of the equations of motion and of the constraints satisfied by the corresponding fields. In the massless limit, well defined parity is lost but a symmetry emerges related to arbitrary changes in the unphysical parity components. It is shown that this emergent symmetry is the celebrated gauge symmetry.