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.

'… a concise but clear introduction to this now-classic material. … a magisterial introduction to the subject … an excellent example of what such lectures should be: fast-paced, succinct and clear … an excellent concise treatment of the modern theory of phase transitions and the renormalisation group by an expert in the field.'

Source: Contemporary Physics

‘… 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 Source: Zentralblatt MATH