Introduction to Statistical Field Theory

Written for advanced undergraduate and beginning graduate students, this textbook provides a concise introduction to statistical field theory.

Edouard Brézin (Author)

9780521193030, Cambridge University Press

Hardback, published 22 July 2010

176 pages, 28 b/w illus.
25.4 x 17.9 x 1.3 cm, 0.5 kg

'… the author 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.' Nenad Manojlovic, Zentralblatt MATH

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.

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.

Subject Areas: Mathematical physics [PHU], Statistical physics [PHS]