Behaviour of quantum fields in curved spacetime

Abstract

It is believed that all physical fields should be described at fundamental level by the general framework of quantum field theory. But we do not have any successfull theory of quantum gravity, which describes the gravity in the quantum domain. Therefore, to study the influence of the gravitational field on quantum phenomena we quantize the matter fields in the usual way while the gravitational field is treated as the fixed background. Classically gravity is described by the theory of general relativity as the curvature of spacetime. So in order to understand the quantum aspect of gravity one is lead to the subject of quantum field theory in background curved spacetime, which is the subject of this work. In curved spacetime, in general, we do not have any preferred set of basis modes. Even our very notion of particle and vacuum is not very well defined, they depend on the set of modes (in other words they are observerdependent). Theory predicts some interesting phenomenon eg. Casimir effect, Unruh effect. We see that the frequency modes get modified in the presence of boundary or in presence of non-trivial geometry of spacetime. Vacuum is the most simple yet most bizzare. The Casimir effect is regarded as one of the most striking manifestations of vacuum fluctuations in quantum field theory. The Casimir stress for spherical shell turns out to be repulsive with certain constraints, which can be related to the expansion of the universe.