Statistical Field Theory

From Brownian Motion to Renormalization and Lattice Gauge Theory
Erscheinungsjahr 1991
ISBN: 978-0-521-40805-9
Verlag: Cambridge University Press

Buch, Englisch, 419 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 691 g

Reihe: Cambridge Monographs on Mathematical Physics

Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory. Volume 2: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. This two-volume work provides a comprehensive and timely survey of the application of the methods of quantum field theory to statistical physics, a very active and fruitful area of modern research. The first volume provides a pedagogical introduction to the subject, discussing Brownian motion, its anticommutative counterpart in the guise of Onsager's solution to the two-dimensional Ising model, the mean field or Landau approximation, scaling ideas exemplified by the Kosterlitz-Thouless theory for the XY transition, the continuous renormalization group applied to the standard phi-to the fourth theory (the simplest typical case) and lattice gauge theory as a pathway to the understanding of quark confinement in quantum chromodynamics. The second volume covers more diverse topics, including strong coupling expansions and their analysis, Monte Carlo simulations, two-dimensional conformal field theory, and simple disordered systems. The book concludes with a chapter on random geometry and the Polyakov model of random surfaces which illustrates the relations between string theory and statistical physics. The two volumes that make up this work will be useful to theoretical physicists and applied mathematicians who are interested in the exciting developments which have resulted from the synthesis of field theory and statistical physics.

Autoren/Hrsg.

Itzykson, Claude

Drouffe, Jean-Michel

Fachgebiete

• Naturwissenschaften Physik Angewandte Physik Soziophysik, Wirtschaftsphysik
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme

Inhaltsverzeichnis

1. From Brownian motion to Euclidean fields; 2. Grassmannian integrals and two-dimensional Ising models; 3. Spontaneous symmetry breaking; 4. Scaling transformations and the XY-model; 5. Continuous field theory and the renormalization group; 6. Lattice gauge fields.