Knowledge of the renormalization group and field theory is a key part of physics, and is essential in condensed matter and particle physics. Written for advanced undergraduate and beginning graduate students, this textbook provides a concise introduction to this subject. The textbook deals directly with the loop expansion of the free energy, also known as the background field method. This is a powerful method, especially when dealing with symmetries, and statistical mechanics. In focussing on free energy, the author avoids long developments on field theory techniques. The necessity of renormalization then follows.
Edouard Brezin is Honorary Professor of Physics at the Ecole Polytechnique, and Emeritus Professor at the Ecole Normale Superieure (Paris). A former President of the French Academy of Sciences, he is also a Foreign Member of the National Academy of Sciences (USA), the American Academy of Arts and Sciences, the Royal Society, and Academia Europaea.
1. A few well-known basic results; 2. Introduction: order parameters, broken symmetries; 3. Examples of physical situations modelled by the Ising model; 4. A few results about the Ising model; 5. High temperature and low temperature expansions; 6. Some geometric problems related to phase transitions; 7. Phenomenological description of the critical behaviour; 8. Mean field theory; 9. Beyond mean field theory; 10. Introduction to the renormalization group; 11. Renormalization group for the ? 4 theory; 12. Renormalized theory; 13. Goldstone modes; 14. Large n; Index.