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 spinorfield in curved spacetime. We first present a Hamiltonian structure and then quantize the field followingthe standard approach. For the free field, the time-dependent quantized Hamiltonian is diagonalized byBogliubov 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 coordinatesbased on general covariance. It is concluded that particle states, such as vacuum states in particular, aretime-dependent and vacuum states at one time evolve into nonvacuum states at later times. The formalismof perturbation is provided with en extended Dirac picture.
Highlights
Is it necessary to pursue a quantum field theory conforming to the principle of general covariance and why another discussion on the same topic? To the first question, the answer seems affirmative
To understand the necessity of quantization of matter fields in curved spacetime, one can consider a basic question: pions in cosmic rays come down to the earth all the way from distant universe, are they quantized particles when pass some region which maybe strongly curved by gravity? The answer is seemingly affirmative, i.e., we should have a complete theory of quantum field theory in curved spacetime
We propose in this paper a quantization scheme for real Klein-Gordon field in de Sitter spacetime
Summary
Is it necessary to pursue a quantum field theory conforming to the principle of general covariance and why another discussion on the same topic? To the first question, the answer seems affirmative. This inevitably entails the difficulty of interpretation of concepts such as particles and vacuum states Observable quantities such as energy and momentum et al are not clearly defined as in conventional Minkowski spacetime quantum field theories. Unlike standard quantum field theory in Minkowski spacetime which are Lorentz invariant, most of these theories are short of either general covariance or important concepts such as Hamiltonian and measurable particle states. Our goals of this paper is of three folds: (i) providing a generally covariant quantum theory of Klein-Gordon field in de Sitter spacetime, in light of the fact that existing theories are short of general covariance either implicitly or explicitly; (ii) providing observable quantities of the field quanta; (ii) providing calculation approaches for scattering matrix; The present paper is arranged as follows.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
