Topics in Quantum Field Theory in Curved Space

TL;DR

This paper reviews key topics in Quantum Field Theory in Curved Space, including particle creation, regularization techniques, and quantum corrections, with a focus on mathematical rigor and implications for cosmological singularities.

Contribution

It provides a rigorous mathematical treatment of particle production, regularization, and quantum corrections in curved spacetime, clarifying previous empirical approaches.

Findings

Mathematically rigorous particle production analysis

Reproduction and clarification of regularization results

Quantum corrections suggesting singularity avoidance

Abstract

In these lectures we consider some topics of Quantum Field Theory in Curved Space. In the first one particle creation in curved space is studied from a mathematical point of view, especially, particle production at a given time using the so called "instantaneous diagonalization method". Particle production by strong electromagnetic fields (Schwinger's effect) and particle production by moving mirrors simulating black hole collapse are also studied. In the second lecture we calculate the re-normalized two-point function using the adiabatic regularization. The conformally and minimally coupled cases are considered for a scalar massive and massless field. We reproduce previous results in a rigorous mathematical form and clarify some empirical approximations and bounds. The re-normalized stress tensor is also calculated in several situations. Finally, in last lecture quantum correction due to a massless fields conformally coupled with gravity are considered in order to study the avoidance of singularities that appear in the flat Friedmann-Robertson-Walker (FRW) model.