No point-localized photon states

TL;DR

This paper critically examines claims of point-localized photon states, proving their impossibility using standard quantum mechanics and highlighting issues with non-standard scalar products used in prior claims.

Contribution

It provides a proof of the impossibility of point-localized photon states and critiques previous claims based on non-standard scalar products.

Findings

Point-localized photon states are impossible under standard quantum mechanics.

Claims of such states rely on non-standard scalar products.

Previous proofs lack satisfaction of all Newton-Wigner criteria.

Abstract

The aim of this paper is to critically examine claims that it is possible to construct point-localized state vectors for the photon. We supply a brief proof of the impossibility of this. Then it is found that the authors making these claims use a non-standard scalar product, not equal to the quantum-mechanical one. This alternative scalar product is found to be proportional to a Dirac delta function in position for the state vectors they use, but the remaining elements of the proof, namely satisfying all three Newton-Wigner criteria, are lacking.