The purpose of this book is to illustrate some of the most important techniques which are helpful in combinatorial problems when computing quantum effects in covariant theories, like general relativity. In fact, most of the techniques find application also in broader contexts, such as low energy effective (chiral) Lagrangians or even in specific problems in condensed matter. Some of the topics covered are: the background field approach and the heat kernel ideas. The arguments are explained in some detail and the presentation is meant for young researchers and advanced students who are starting working in the field. As prerequisite the reader should have attended a course in quantum field theory including Feynman's path integral. In the Appendix a nontrivial calculation of one-loop divergences in Einstein-Hilbert gravity is explained step-by-step.

Autorentext

Enrique Álvarez is Professor (Emeritus) at the Autonomous University of Madrid (UAM), Spain. He received the PhD in Physics in 1975 working in the group of Lluis Bel. After that, he covered postdoctoral positions in Paris, Harvard and Princeton becoming Professor at UAM in 1989. He had visiting stays at CERN, Bern, Berkeley, Padua and Rome, just to mention few. His research focuses on abelian and non-abelian T-duality in string theory and Kaluza-Klein theories. He is one of the people behind the revival of Einstein's unimodular gravity (1919).

Jesús Anero received the PhD in Physics from the National Distance Education University of Madrid, Spain, in 2012. Since 2016, he has been a scientific collaborator at the Institute of Theoretical Physics in Madrid, working with Prof. Enrique Álvarez. He has coauthored several papers published in peer-reviewed main journals like JCAP, JHEP, Phys. Rev. D, Class. Quant.Grav. He also works with Dr. Carmelo P. Martín at the Complutense University of Madrid, Spain. His main research areas of investigation are quantum gravity and supergravity.