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Author : G. Mussardo
Publisher : Oxford University Press
Page : 778 pages
File Size : 47,7 Mb
Release : 2010
Category : Science
ISBN : 9780199547586
A thorough and pedagogical introduction to phase transitions and exactly solved models in statistical physics and quantum field theory.
Author : Moritz Helias,David Dahmen
Publisher : Springer Nature
Page : 203 pages
File Size : 51,8 Mb
Release : 2020-08-20
Category : Science
ISBN : 9783030464448
This book presents a self-contained introduction to techniques from field theory applied to stochastic and collective dynamics in neuronal networks. These powerful analytical techniques, which are well established in other fields of physics, are the basis of current developments and offer solutions to pressing open problems in theoretical neuroscience and also machine learning. They enable a systematic and quantitative understanding of the dynamics in recurrent and stochastic neuronal networks. This book is intended for physicists, mathematicians, and computer scientists and it is designed for self-study by researchers who want to enter the field or as the main text for a one semester course at advanced undergraduate or graduate level. The theoretical concepts presented in this book are systematically developed from the very beginning, which only requires basic knowledge of analysis and linear algebra.
Author : Edouard Brézin
Publisher : Cambridge University Press
Page : 177 pages
File Size : 50,5 Mb
Release : 2010-07-22
Category : Science
ISBN : 9781139490146
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.
Author : Andreas Wipf
Publisher : Springer Nature
Page : 568 pages
File Size : 51,5 Mb
Release : 2021-10-25
Category : Science
ISBN : 9783030832636
This new expanded second edition has been totally revised and corrected. The reader finds two complete new chapters. One covers the exact solution of the finite temperature Schwinger model with periodic boundary conditions. This simple model supports instanton solutions – similarly as QCD – and allows for a detailed discussion of topological sectors in gauge theories, the anomaly-induced breaking of chiral symmetry and the intriguing role of fermionic zero modes. The other new chapter is devoted to interacting fermions at finite fermion density and finite temperature. Such low-dimensional models are used to describe long-energy properties of Dirac-type materials in condensed matter physics. The large-N solutions of the Gross-Neveu, Nambu-Jona-Lasinio and Thirring models are presented in great detail, where N denotes the number of fermion flavors. Towards the end of the book corrections to the large-N solution and simulation results of a finite number of fermion flavors are presented. Further problems are added at the end of each chapter in order to guide the reader to a deeper understanding of the presented topics. This book is meant for advanced students and young researchers who want to acquire the necessary tools and experience to produce research results in the statistical approach to Quantum Field Theory.
Author : Mehran Kardar
Publisher : Cambridge University Press
Page : 376 pages
File Size : 53,5 Mb
Release : 2007-06-07
Category : Science
ISBN : 052187341X
Textbook on statistical field theories for advanced graduate courses in statistical physics.
Author : Giorgio Parisi
Publisher : Westview Press
Page : 366 pages
File Size : 46,5 Mb
Release : 1998-11-26
Category : Science
ISBN : 0738200514
Specifically written to introduce researchers and advanced students to the modern developments in statistical mechanics and field theory, this book's leitmotiv is functional integration and its application to different areas of physics. The book acts as both an introduction to and a lucid overview of the major problems in statistical field theory.
Author : Claude Itzykson,Jean-Michel Drouffe
Publisher : Cambridge University Press
Page : 440 pages
File Size : 49,9 Mb
Release : 1991-03-29
Category : Science
ISBN : 0521408059
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.
Author : Dr. Gérard G. Emch
Publisher : Courier Corporation
Page : 352 pages
File Size : 51,9 Mb
Release : 2014-08-04
Category : Science
ISBN : 9780486151717
This systematic algebraic approach offers a careful formulation of the problems' physical motivations as well as self-contained descriptions of the mathematical methods for arriving at solutions. 1972 edition.
Author : A.N. Vasiliev
Publisher : CRC Press
Page : 336 pages
File Size : 54,8 Mb
Release : 1998-07-28
Category : Science
ISBN : 9056990357
Providing a systematic introduction to the techniques which are fundamental to quantum field theory, this book pays special attention to the use of these techniques in a wide variety of areas, including ordinary quantum mechanics, quantum mechanics in the second-quantized formulation, relativistic quantum field theory, Euclidean field theory, quantum statistics at finite temperature, and the classical statistics of nonideal gas and spin systems. The extended chapter on variational methods and functional Legendre transformations contains completely original material.
Author : Michel Le Bellac
Publisher : Unknown
Page : 0 pages
File Size : 46,6 Mb
Release : 2023
Category : Quantum field theory
ISBN : 138302653X
A presentation of the concepts and methods of quantum field theory that have been so successful over the past 20 years in treating the theory of second order phase transitions and elementary particle physics. It emphasizes the underlying unity of the subject and details various applications.
Author : Philippe Francesco,Pierre Mathieu,David Senechal
Publisher : Springer Science & Business Media
Page : 908 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461222569
Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles. The treatment is self-contained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algebras. The many exercises, with a wide spectrum of difficulty and subjects, complement and in many cases extend the text. The text is thus not only an excellent tool for classroom teaching but also for individual study. Intended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics. It will prepare the reader for original research in this very active field of theoretical and mathematical physics.
Author : V.N. Popov
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 41,5 Mb
Release : 2001-11-30
Category : Science
ISBN : 1402003072
Functional integration is one of the most powerful methods of contempo rary theoretical physics, enabling us to simplify, accelerate, and make clearer the process of the theoretician's analytical work. Interest in this method and the endeavour to master it creatively grows incessantly. This book presents a study of the application of functional integration methods to a wide range of contemporary theoretical physics problems. The concept of a functional integral is introduced as a method of quantizing finite-dimensional mechanical systems, as an alternative to ordinary quantum mechanics. The problems of systems quantization with constraints and the manifolds quantization are presented here for the first time in a monograph. The application of the functional integration methods to systems with an infinite number of degrees of freedom allows one to uniquely introduce and formulate the diagram perturbation theory in quantum field theory and statistical physics. This approach is significantly simpler than the widely accepted method using an operator approach.
Author : James Glimm,Arthur Jaffe
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461251583
This volume contains a selection of expository articles on quantum field theory and statistical mechanics by James Glimm and Arthur Jaffe. They include a solution of the original interacting quantum field equations and a description of the physics which these equations contain. Quantum fields were proposed in the late 1920s as the natural framework which combines quantum theory with relativ ity. They have survived ever since. The mathematical description for quantum theory starts with a Hilbert space H of state vectors. Quantum fields are linear operators on this space, which satisfy nonlinear wave equations of fundamental physics, including coupled Dirac, Max well and Yang-Mills equations. The field operators are restricted to satisfy a "locality" requirement that they commute (or anti-commute in the case of fer mions) at space-like separated points. This condition is compatible with finite propagation speed, and hence with special relativity. Asymptotically, these fields converge for large time to linear fields describing free particles. Using these ideas a scattering theory had been developed, based on the existence of local quantum fields.
Author : John Cardy
Publisher : Cambridge University Press
Page : 264 pages
File Size : 41,8 Mb
Release : 1996-04-26
Category : Science
ISBN : 0521499593
This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. It begins with a brief review of phase transitions in simple systems, then goes on to introduce the core ideas of the renormalisation group.
Author : Edouard Brezin,Spenta R Wadia
Publisher : World Scientific
Page : 1149 pages
File Size : 40,6 Mb
Release : 1993-08-31
Category : Science
ISBN : 9789814506632
This book contains an edited comprehensive collection of reprints on the subject of the large N limit as applied to a wide spectrum of problems in quantum field theory and statistical mechanics. The topics include (1) Spin Systems; (2) Large N Limit of Gauge Theories; (3) Two-Dimensional QCD; (4) Exact Results on Planar Perturbation Series and the Nature of the 1/N Series; (5) Schwinger-Dyson Equations Approach; (6) QCD Phenomenological Lagrangians and the Large N Limit; (7) Other Approaches to Large N: Eguchi-Kawai Model, Collective Fields and Numerical Methods; (8) Matrix Models; (9) Two-Dimensional Gravity and String Theory.