Conserved spin operator of Dirac’s theory in spatially flat FLRW space-times

Abstract

New conserved spin and orbital angular momentum operators of Dirac’s theory on spatially flat FLRW space-times are proposed generalizing thus the recent results concerning the role of Pryce’s spin operator in the flat case (Cotăescu in Eur Phys J C, 82, 1073, 2022). 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 transform. 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.