Introduction to Quantum Field Theory with Applications to Quantum Gravity

Abstract

This book focuses on quantum field theory and its application to gravitational physics, in both semiclassical and full quantum frameworks, with special attention paid to renormalization, gauge theories and, especially, effective action formalism. Part I provides both conceptual and technical introductions to quantum field theory, starting from elements of group theory, through classical fields, up to effective action formalism in general gauge theories. Compared to other books on this topic, this book describes the general formalism of renormalization in more detail and pays more attention to gauge theories. Part II discusses basic aspects of quantum field theory in curved spacetime and perturbative quantum gravity. More than half of this part is written with a full exposition of details, including well-explained examples with simple calculations. All chapters include exercises, which range from very simple ones to those requiring small original investigations. The material in the second part was selected on the basis of the “must-know” principle: while detailed expositions are provided for relatively simple techniques and calculations, it is expected that the interested reader will be able to learn more advanced issues independently after learning the basic material and working through the exercises provided. In some cases, when more complicated subjects were discussed, the book only provides references for the original publications, where the reader can find the full details of the calculations used.