# IRMACS Visiting Scholar Lecture Series: "Quantum Gravity and Effective Action"

### Abstract

Quantum field theory developed in elementary particle physics turned out to be one of the most successful physical theories, and its powerful methods found applications in many other areas. However, this theory had troubles to be reconciled with general relativity - Einstein's theory of gravity. Nevertheless, the low energy approximation of quantum field theory in curved spacetime is a viable approach, capable of describing observable phenomena. It is at the center of a renewed interest in semiclassical quantum gravity. Some mathematical tools used include techniques of the heat kernels, functional integrals, and elliptic differential operators on Riemannian manifolds. This talk overviews principles and methods of the effective action - quantum generalization of the classical action describing a physical model. Among potential applications are effects of particle creation from vacuum, both in gauge field and gravity backgrounds, e.g. the Hawking radiation from black holes.