A Generally Covariant Theory of Quantized Real Klein-Gordon Field in de Sitter Spacetime

TL;DR

This paper develops a generally covariant quantization scheme for the real Klein-Gordon field in de Sitter spacetime, incorporating vierbein formalism and analyzing time-dependent particle states and vacuum evolution.

Contribution

It introduces a covariant quantization approach for scalar fields in curved spacetime using vierbeins, with a Hamiltonian structure and Bogliubov transformations for particle interpretation.

Findings

Time-dependent particle states in de Sitter spacetime.

Vacuum states evolve into non-vacuum states over time.

The formalism aligns with cosmological red-shift and on-shell momentum conditions.

Abstract

We propose in this paper a quantization scheme for real Klein-Gordon field in de Sitter spacetime. Our scheme is generally covariant with the help of vierbein, which is necessary usually for spinor field in curved spacetime. We first present a Hamiltonian structure, then quantize the field following the standard approach. 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 interpretation is supported by the known cosmological red-shift formula and the on-shell condition of 4-momentum for a free field. Though the mathematics is carried out in term 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 evolves into non-vacuum states at later times. Formalism of perturbational is provided with an extended Dirac picture.