Spectral Functions in QFT

Abstract: We present a pedagogical exposition of some applications of functional methods in quantum field theory: we use heat-kernel and zeta-function techniques to study the Casimir effect, the pair production in strong electric fields, quantum fields at finite temperature and beta-functions for a self-interacting scalar field, QED and pure Yang-Mills theories. The more recent application to the UV/IR mixing phenomenon in noncommutative theories is also discussed in this framework.