Comment on `Relativistic wave-particle duality for spinors'

TL;DR

This paper critiques a recent proposal linking relativistic wave-particle duality to Dirac currents, highlighting issues with spin-torsion energy interpretation and rest frame implications, and suggests a possible resolution.

Contribution

It identifies problems in the recent relativistic wave-particle duality proposal and offers a potential way to resolve the identified issues.

Findings

Spin-torsion term should represent negative energy.

The proposed relation implies zero spin-torsion in the fermion's rest frame.

The paper discusses a possible resolution to the identified problems.

Abstract

In a recent paper [1], it has been proposed that relativistic wave-particle duality can be embodied in a relation that shows that the four-velocity of a particle is proportional to the Dirac four-current. In this note we bring out some problems with that idea. In particular, we point out that, in line with existing literature on Einstein-Cartan gravity with torsion, the spin-torsion term should represent negative energy. Moreover, if what is proposed in Eq. (20) of [1] is correct, then the spin torsion term would be zero in the rest frame of the fermion. We suggest a possible resolution of that dilemma.