TC3: Quantum Field Theory in Curved Spaces – Overview

Topic overview:

This lecture represents an elementary introduction to the tree-level theory of quantum fields on curved spacetimes. The essential structures relevant for a precise development are introduced at the level of classical mechanics and quantum mechanics. Once the level of presentation is sufficiently abstract, these concepts are lifted to infinite-dimensional Hamiltonian systems with a focus on massive scalar fields. Our approach to the corresponding quantum theory on globally hyperbolic backgrounds consists of two steps: In the first step the algebra of observables is constructed and studied, and in the second step a physical state concept is introduced in accordance with the usual interpretation of quantum systems. Finally the framework is applied to a thorough analysis of the so-called Unruh-effect and Hawking effect. If time permits an outlook beyond tree-level physics will be given.

Moodle:

Most information will be distributed using Moodle in which you log in with your LMU account and use the course password "Wald" following this link:

https://moodle.lmu.de/course/view.php?id=14929

Literature:

• Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics
• Bär et al., Wave equations on Lorentzian manifolds and Quantisation
• Wald, General Relativity
• Schottenloher, Geometrie und Symmetrie in der Physik
• Araki, Mathematical Theory of QFT