Renormalization Group

Scaling and self-similarity ideas and methods in theoretical physics have coalesced into renormalization-group methods. This book analyzes some of the most important applications: the critical-point theory in classical standard mechanics, the scalar quantum field theories in two and three space-time dimensions, and Tomonaga's theory of the ground state of one-dimensional Fermi systems. The dimension dependence is discussed, together with the related existence of anomalies. The theory of Bose condensation at zero temperature in three space dimensions is also considered. Attention throughout is focused on results that can in principle be formally established from a mathematical point of view.