Conserved spin operator of Dirac's theory in spatially flat FLRW spacetimes

TL;DR

This paper introduces new conserved spin and orbital angular momentum operators for Dirac particles in spatially flat FLRW spacetimes, generalizing previous flat spacetime results and ensuring their form is consistent across different cosmological models.

Contribution

It proposes novel conserved spin and orbital angular momentum operators in FLRW spacetimes, extending Pryce's spin operator to curved cosmological backgrounds.

Findings

New conserved spin operator defined and studied in active mode.

Orbital angular momentum operator derived using a Wigner-inspired method.

Operators have the same form across various FLRW geometries.

Abstract

New conserved spin and orbital angular momentum operators of Dirac's theory on spatially flat FLRW spacetimes are proposed generalizing thus recent results concerning the role of Pryce's spin operator in the flat case [I. I. Cot\u aescu, Eur. Phys. J. C (2022) 82:1073]. These operators split the conserved total angular momentum generating the new spin and orbital symmetries that form the rotations of the isometry groups. The new spin operator is defined and studied in active mode with the help of a suitable spectral representation giving its Fourier transfor. Moreover, in the same manner is defined the operator of the fermion polarization. The orbital angular momentum is derived in passive mode using a new method, inspired by Wigner's theory of induced representations, but working properly only for global rotations. In this approach the quantization is performed finding that the one-particle spin and orbital angular momentum operators have the same form in any FLRW spacetime regardless their concrete geometries given by various scale factors.