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.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Letters in High Energy Physics (LHEP) is an open access journal published by Andromeda Publishing and Education Services. The articles in LHEP are distributed according to the terms of the creative commons license CC-BY 4.0. Under the terms of this license, copyright is retained by the author while use, distribution and reproduction in any medium are permitted provided proper credit is given to original authors and sources.
Terms of Submission
By submitting an article for publication in LHEP, the submitting author asserts that:
1. The article presents original contributions by the author(s) which have not been published previously in a peer-reviewed medium and are not subject to copyright protection.
2. The co-authors of the article, if any, as well as any institution whose approval is required, agree to the publication of the article in LHEP.