Statistical Field Theory: Volume 2, Strong Coupling, Monte Carlo Methods, Conformal Field Theory and Random Systems

Statistical Field Theory: Volume 2, Strong Coupling, Monte Carlo Methods, Conformal Field Theory and Random Systems
Author: Claude Itzykson
Publisher: Cambridge University Press
Total Pages: 440
Release: 1991-03-29
Genre: Mathematics
ISBN: 9780521408066

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.

Statistical Field Theory: Volume 1, From Brownian Motion to Renormalization and Lattice Gauge Theory

Statistical Field Theory: Volume 1, From Brownian Motion to Renormalization and Lattice Gauge Theory
Author: Claude Itzykson
Publisher: Cambridge University Press
Total Pages: 440
Release: 1991-03-29
Genre: Science
ISBN: 9780521408059

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.

Twistor Geometry and Field Theory

Twistor Geometry and Field Theory
Author: R. S. Ward
Publisher: Cambridge University Press
Total Pages: 534
Release: 1990
Genre: Mathematics
ISBN: 9780521422680

Deals with the twistor treatment of certain linear and non-linear partial differential equations. The description in terms of twistors involves algebraic and differential geometry, and several complex variables.

The Theory and Applications of Instanton Calculations

The Theory and Applications of Instanton Calculations
Author: Manu Paranjape
Publisher: Cambridge University Press
Total Pages: 325
Release: 2017-11-16
Genre: Science
ISBN: 110854763X

Instantons, or pseudoparticles, are solutions to the equations of motion in classical field theories on a Euclidean spacetime. Instantons are found everywhere in quantum theories as they have many applications in quantum tunnelling. Diverse physical phenomena may be described through quantum tunnelling, for example: the Josephson effect, the decay of meta-stable nuclear states, band formation in tight binding models of crystalline solids, the structure of the gauge theory vacuum, confinement in 2+1 dimensions, and the decay of superheated or supercooled phases. Drawing inspiration from Sidney Coleman's Erice lectures, this volume provides an accessible, detailed introduction to instanton methods, with many applications, making it a valuable resource for graduate students in many areas of physics, from condensed matter, particle and nuclear physics, to string theory.

Introduction to Classical Integrable Systems

Introduction to Classical Integrable Systems
Author: Olivier Babelon
Publisher: Cambridge University Press
Total Pages: 622
Release: 2003-04-17
Genre: Mathematics
ISBN: 9780521822671

This book provides a thorough introduction to the theory of classical integrable systems, discussing the various approaches to the subject and explaining their interrelations. The book begins by introducing the central ideas of the theory of integrable systems, based on Lax representations, loop groups and Riemann surfaces. These ideas are then illustrated with detailed studies of model systems. The connection between isomonodromic deformation and integrability is discussed, and integrable field theories are covered in detail. The KP, KdV and Toda hierarchies are explained using the notion of Grassmannian, vertex operators and pseudo-differential operators. A chapter is devoted to the inverse scattering method and three complementary chapters cover the necessary mathematical tools from symplectic geometry, Riemann surfaces and Lie algebras. The book contains many worked examples and is suitable for use as a textbook on graduate courses. It also provides a comprehensive reference for researchers already working in the field.

Supersymmetry, Supergravity, and Unification

Supersymmetry, Supergravity, and Unification
Author: Pran Nath
Publisher: Cambridge University Press
Total Pages: 539
Release: 2017
Genre: Science
ISBN: 0521197023

This book offers a comprehensive discussion of developments at the interface of particle physics, supergravity, and cosmology, for graduates and researchers.

Inflation and String Theory

Inflation and String Theory
Author: Daniel Baumann
Publisher: Cambridge University Press
Total Pages: 395
Release: 2015-04-23
Genre: Science
ISBN: 1107089697

This accessible volume provides a modern treatment of the cosmological and string-theoretic background necessary to understand inflation in string theory.

Noether Symmetries in Theories of Gravity

Noether Symmetries in Theories of Gravity
Author: Francesco Bajardi
Publisher: Cambridge University Press
Total Pages: 451
Release: 2022-11-30
Genre: Science
ISBN: 1009208748

This volume summarizes the many modified theories of gravity and shows how to select physically viable models using symmetry principles.