This book provides a gentle introduction to the physics of quantized fields and many-body physics. Based on courses taught at the University of Illinois, it concentrates on the basic conceptual issues that many students find difficult. It also emphasizes the physical and visualizable aspects of the subject. While the text is intended for students with a wide range of interests, many of the examples are drawn from condensed matter physics because of the tangible character of such systems.
The first part of the book uses the Hamiltonian operator language of traditional quantum mechanics to treat simple field theories and related topics, such as the Klein-Gordon equation, the Dirac equation, quantum electrodynamics, Fermi gases and liquids, and Bose condensates. The Feynman path integral is introduced in the second half, where it is seen as an efficient generator of the Feynman rules and Ward identities. It is indispensable for understanding non-perturbative phenomena as well as the connection between renormalization and critical phenomena.