# Quantum Field Theory in Curved Space-Time - Material for the year 2019-2020

## Primary tabs

Quantum Field Theory (MT), General Relativity I

(MT). General Relativity II and Advanced Quantum Field Theory will be

helpful but not essential.

### Assessment type:

- No formal assessment; homework completion requirement.

16 lectures

Areas: PT, Astro.

This course builds on both the first courses in quantum field theory and general relativity. The second course in GR and a course on differential geometry will be helpful, but are not essential. It will focus on

classical aspects of fields in curved space-time, global structure and black hole thermodynamics and then on quantum fields on curved backgrounds.

Please also submit your homework for Quantum Field Theory in Curved Space-Time via the assignments tab.

Students will be able to formulate classical and quantum field theories in curved space-time including an understanding of global features.

Non-interacting fields in curved space-time: Lagrangians, coupling to gravity, spinors in curved space-time, global hyperbolicity, asymptotic structure, conformal properties. Black hole thermodynamics. Canonical

formulation.

Quantization, choice of vacuum. Quantum fields in Anti de Sitter space. Quantum fields in an expanding universe. Unruh effect. Casimir effect. Hawking radiation.

The section on global structure, spinors and classical field theory on curved space-time follows the following texts:

Gibbons/Hawking/Townsend, Black Holes lecture notes, arxiv:9707012.

Hawking & Ellis, The large scale structure of Space-time, 1971 CUP.

Penrose & Rindler, Spinors & Space-time, Vols 1 & 2, CUP, 1984 & 1986.

Birrell & Davis, Quantum field theory in curved space-time, CUP.

Ford, Quantum Field theory in Curved space-time, arxiv:9707062.

Jacobson, Introduction to quantum fields in curved space-time and the

Hawking effect, arxiv:0308048.

Mukhanov and Winitzki, Introduction to quantum fields on classical backgrounds.

R Wald, QFT in Curved Space-time and Black Hole Thermodynamics, Univ Chicago Press, 1994, ISBN 0226-87027-8.