Specialist Course HS16:

Introduction to Quantum Field Theory in Curved Spacetime

Prerequisites, Timetable, Outline, Literature, and more ...

Summary and Overview

The main aim of this course is to explain what are (some of) the obstacles that one faces when trying to generalise the standard formalism and procedures of Minkowski space Poincare-covariant QFT to curved spacetimes, and to illustrate the new phenomena that one encounters by some typical and important examples: particle creation by time-dependent gravitational fields, the Unruh effect, and (some elementary aspects of) Hawking black hole radiation and black hole thermodynamics.

Many of the key-issues can already be understood in a purely quantum-mechanical context by studying the Heisenberg picture quantisation of a time-dependent harmonic oscillator, so I will spend some time to discuss the issue of quantisation ambiguities, Bogoliubov transformations, mode creation etc., in this setting. When moving on to field theory, we will consider the simplest possible case of a free Klein-Gordon scalar field (in 1+1 or 3+1 dimensions). The general lesson is that in general in a curved spacetime the notion of vacuum and particles (and the corresponding particle interpretation of QFT) are ambiguous and observer-dependent.

We will then apply these insights to briefly look at the creation of particles in a time-dependent gravitational field, Minkowski space QFT and accelerated observers (the Unruh effect), and scalar fields in the Schwarzschild black hole metric (Hawking radiation).

Time permitting, and if there is sufficient interest, I will add a few remarks either on black hole thermodynamics, the black hole information loss paradox and the recent debate in the literature on ``firewalls'', or on more general (physically and mathematically more satisfactory) approaches to defining and making sense of quantum field theory in curved spacetime backgrounds.



Outline (tentative)

  1. Introduction: Motivation and Overview
  2. Heisenberg Picture Quantum Theory of a (Time-dependent) Harmonic Oscillator
  3. QFT in FRW Cosmological Backgrounds and Particle Production
  4. Developing the Formalism
  5. Rindler Space and the Unruh Effect
  6. Aspects of the Classical Theory of Black Holes
  7. Hawking Radiation
  8. Black Hole Entropy and related Issues (if there is time)