A Generally Covariant Theory of Quantized Dirac Field in de Sitter Spacetime

Abstract

As a sequel to our previous work\cite{Feng2020}, we propose in this paper a quantization scheme for Dirac field in de Sitter spacetime. Our scheme is covariant under both general transformations and Lorentz transformations. We first present a Hamiltonian structure, then quantize the field following the standard approach of constrained systems. For the free field, the time-dependent quantized Hamiltonian is diagonalized by Bogliubov transformation and the eigen-states at each instant are interpreted as the observed particle states at that instant. The measurable energy-momentum of observed particle/antiparticles are the same as obtained for Klein-Gordon field. Moreover, the energy-momentum also satisfies geodesic equation, a feature justifying its measurability. As in \cite{Feng2020}, though the mathematics is carried out in terms of conformal coordinates for the sake of convenience, the whole theory can be transformed into any other coordinates based on general covariance. It is concluded that particle/antiparticle states, such as vacuum states in particular are time-dependent and vacuum states at one time evolves into non-vacuum states at later times. Formalism of perturbational calculation is provided with an extended Dirac picture.