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

Abstract

As a sequel to our previous work [1], 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 transforma- tions. 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 ob- tained for Klein-Gordon field. Moreover, the energy-momentum also satisfies geodesic equation, a feature justifying its measurability. As in [1], though the mathematics is carried out in terms of conformal coordi- nates 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.

Keywords

• Quantization
• Dirac field
• de Sitter