March 19 - June 1, 2010
Lectures: Friday: 09:00 - 11:00
Seminar: Thursday: 16:00 - 17:00
ESI, Schrödinger lecture hall

 
Abstract:
In this series of lectures, I will describe the theory of quantized fields on curved spacetime backgrounds. The two main topics of the course are (a) the physical effects that this theory is able to describe and (b) the mathematical foundations of this formalism. In (a) I will describe in some detail the Hawking Effect (black hole radiance), the Unruh effect, the generation of primordial fluctuations in the context of Early Universe cosmology, including--time permitting--the effects of nonlinearities which give rise to the much talked about "Non-Gaussianities'' in the CMB spectrum. In part (b) I am going to describe in detail the formalism that is necessary in order to describe composite quantum fields ("Wick powers"), and the prescription for constructing an interacting (non-linear) quantum field theory from an underlying linear one. This discussion will include mathematical topics such as renormalization procedure, and the necessary tools from microlocal analysis. I will also discuss in detail recent developments concerning the "Operator Product Expansion" in interacting quantum field theory models, the underlying algebraic and cohomological structures, and its calculation in renormalized perturbation theory. I will finish off the course with some fundamental, model independent physical theorems in QFT on curved spacetimes that can be proven with the help of this construction, namely the Parity-Time-Charge theorem, and spin-statistics theorem.

The course is aimed at students with an interest in quantum aspects of relativity, and QFT. A knowledge of quantum mechanics/special relativity is assumed, and it is also to have a basic knowledge in QFT on Minkowski spacetime. The level of presenation can be adapted if necessary to the demands of the audience.