Notes on Quantum Field Theory in Curved Spacetime: Problems Relating to the Concept of Particles and Hamiltonian Formalism

Abstract: The aim of these notes is to elucidate some aspects of quantum field theory in curved spacetime, especially those relating to the notion of particles. A selection of issues relevant to wave-particle duality is given. The case of a generic curved spacetime is outlined. A Hamiltonian formulation of quantum field theory in curved spacetime is elaborated for a preferred reference frame with a separated space metric (a static spacetime and a reductive synchronous reference frame). Applications: (1) Black hole. (2) The universe; the cosmological redshift is obtained in the context of quantum field theory.