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

TL;DR

This paper explores quantum field theory in curved spacetime, focusing on the particle concept and Hamiltonian formalism, with applications to black holes and cosmology, highlighting conceptual and mathematical challenges.

Contribution

It provides a detailed Hamiltonian formulation of quantum field theory in static curved spacetimes and discusses issues related to the particle notion in such contexts.

Findings

Hamiltonian formalism developed for static spacetimes

Insights into particle concept in curved spacetime

Application to black hole physics and cosmological redshift

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.