Covariant Techniques in Quantum Field Theory

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.

• Introduction and generalities.- The background field approach in quantum field theory.-  The one loop effective action.- Divergences out of Schwinger-DeWitt coefficients.- A One-loop divergences in first order Einstein-Hilbert gravity.