The momentum operators corresponding to a localized massless particle

TL;DR

This paper uses group theory to show that a localized massless particle has only two possible momentum operators, which are explicitly identified as self-adjoint operators.

Contribution

It introduces a group theoretical approach to determine the limited set of momentum operators for localized massless particles.

Findings

Only two momentum operators are possible for localized massless particles.

The two momentum operators are explicitly constructed as self-adjoint operators.

The approach clarifies the mathematical structure of localization in massless quantum particles.

Abstract

In this article we propose, using a purely group theoretical argument, that if a massless particle is localized, then there are only two momentum operator s corresponding to the localized state. We explicitly determine these self-adjoint operators.