A Generally Covariant Theory of Quantized Real Klein-Gordon Field in de Sitter Spacetime
Abstract
We propose in this paper a quantization scheme for the real Klein-Gordon field in de Sitter spacetime.
Our scheme is generally covariant with the help of vierbein, which is necessary usually for the spinor
field in curved spacetime. We first present a Hamiltonian structure and then quantize the field following
the standard approach. For the free field, the time-dependent quantized Hamiltonian is diagonalized by
Bogliubov transformation, and the eigenstates at each instant are interpreted as the observed particle states
at that instant. The interpretation is supported by the known cosmological redshift formula and the on-
shell condition of 4-momentum for a free field. Though 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 states, such as vacuum states in particular, are
time-dependent and vacuum states at one time evolve into nonvacuum states at later times. The formalism
of perturbation is provided with en extended Dirac picture.
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