MiS Preprint Repository

These notes provide an introduction to quantum field theory in curved space-times, starting from the beginning but leading to some areas of current research. Topics covered include: globally hyperbolic spacetimes, canonical quantization, Euclidean Green functions, the Unruh effect, gravitational particle production, algebraic quantization, the Hadamard and microlocal spectrum conditions, and quantum energy inequalities.

Table of Contents:

1. Introduction, scope and literature
2. Manifolds, covariant derivatives and all that
3. The classical Klein–Gordon field
4. Canonical quantization of the Klein–Gordon field
5. Algebraic approach to quantization
6. Microlocal analysis and the Hadamard condition
7. Closing remarks and additional literature