Kinemaitcs in spatially flat FLRW spacetimes

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. Cotȃescu, 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.

Quantum theory of redshift in de Sitter expanding universe

“…[11] we neglected the problem of this phase which is solved here for the first time. This guarantees the correct flat limit as in the case of the rest frame vacua we defined recently for the massive Dirac [20], Klein-Gordon [21] and Proca [22] showing that only these vacua assure correct flat limits [23].…”