Quantum Field Theory in Curved Spacetime

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Some familiarity with both quantum field theory in flat space and general relativity will be assumed. 


This course introduces the novelties of quantization in curved backgrounds. It will build intuition from simple examples in quantum mechanics. Then we introduce more sophisticated setups, like quantum fields in background electromagnetic and gravitational fields. Some important results will be the derivation of the Schwinger effect, Hawking radiation, and quantization of fields in maximally symmetric curved backgrounds. There will be special emphasis in applications of this framework to calculate the statistics of primordial fluctuations in cosmology. We will discuss the computation of primordial correlation functions within de Sitter space and inflationary cosmology, both from bulk perturbation theory as well as self-consistency "bootstrap" requirements.

Educational aims

The student will, at the end of the course, be able to properly quantize and compute simple observables (correlation functions of weakly coupled theories) of quantum fields in curved backgrounds. These tools are useful in many different contexts: in cosmology, in particle physics, and in quantum gravity. This course will emphasize applications in cosmology. The first half of the course will give the student sufficient background to utilize the methods of quantum field theory in curved space in other contexts as well.

Bibliographical references

Mukhanov and Winitzki, Introduction to Quantum Effects in Gravity, CUP

Birrell and Davies, Quantum Fields in Curved Space, CUP

Parker and Toms, Quantum Field Theory in Curved Spacetime, CUP

I will complement the references above with preprints and papers freely available on the arXiv website.