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

  • Sze-Shiang Feng Physics Department, Florida A & M University, Tallahassee, FL 32307, USA
  • Mogus Mochena Physics Department, Florida A & M University, Tallahassee, FL 32307, USA
Keywords: Quantization, Dirac field, de Sitter


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.