Quantum Field Theory And Statistical Mechanics

Author : Andreas Wipf
Publisher : Springer Nature
Page : 568 pages
File Size : 53,7 Mb
Release : 2021-10-25
Category : Science
ISBN : 9783030832636

Get Book

Statistical Approach to Quantum Field Theory by Andreas Wipf Pdf

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 : A.N. Vasiliev
Publisher : CRC Press
Page : 336 pages
File Size : 52,7 Mb
Release : 1998-07-28
Category : Science
ISBN : 9056990357

Get Book

Functional Methods in Quantum Field Theory and Statistical Physics by A.N. Vasiliev Pdf

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 : A. A. Abrikosov,L. P. Gorkov,I. E. Dzyaloshinski
Publisher : Courier Corporation
Page : 384 pages
File Size : 48,5 Mb
Release : 2012-05-04
Category : Science
ISBN : 9780486140155

Get Book

Methods of Quantum Field Theory in Statistical Physics by A. A. Abrikosov,L. P. Gorkov,I. E. Dzyaloshinski Pdf

This comprehensive introduction to the many-body theory was written by three renowned physicists and acclaimed by American Scientist as "a classic text on field theoretic methods in statistical physics."

Author : Alekseĭ Alekseevich Abrikosov
Publisher : Unknown
Page : 376 pages
File Size : 52,9 Mb
Release : 1963
Category : Low temperature research
ISBN : UOM:39015001329716

Get Book

Methods of Quantum Field Theory in Statistical Physics by Alekseĭ Alekseevich Abrikosov Pdf

Author : Edouard Brezin,Spenta R Wadia
Publisher : World Scientific
Page : 1149 pages
File Size : 53,7 Mb
Release : 1993-08-31
Category : Science
ISBN : 9789814506632

Get Book

The Large N Expansion In Quantum Field Theory And Statistical Physics by Edouard Brezin,Spenta R Wadia Pdf

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.

Author : James Glimm,Arthur Jaffe
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461251583

Get Book

Quantum Field Theory and Statistical Mechanics by James Glimm,Arthur Jaffe Pdf

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 : Dr. Gérard G. Emch
Publisher : Courier Corporation
Page : 352 pages
File Size : 50,8 Mb
Release : 2014-08-04
Category : Science
ISBN : 9780486151717

Get Book

Algebraic Methods in Statistical Mechanics and Quantum Field Theory by Dr. Gérard G. Emch Pdf

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 : E. Seiler
Publisher : Springer
Page : 195 pages
File Size : 40,9 Mb
Release : 2014-03-12
Category : Science
ISBN : 3662135191

Get Book

Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics by E. Seiler Pdf

Author : A.N. Vasiliev
Publisher : Routledge
Page : 320 pages
File Size : 51,8 Mb
Release : 2019-01-22
Category : Science
ISBN : 9781351446815

Get Book

Functional Methods in Quantum Field Theory and Statistical Physics by A.N. Vasiliev Pdf

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, quant

Author : Ivo Sachs,Siddhartha Sen,James Sexton
Publisher : Cambridge University Press
Page : 347 pages
File Size : 48,6 Mb
Release : 2006-05-11
Category : Science
ISBN : 9781139452465

Get Book

Elements of Statistical Mechanics by Ivo Sachs,Siddhartha Sen,James Sexton Pdf

This 2006 textbook provides a concise introduction to the key concepts and tools of statistical mechanics. It also covers advanced topics such as non-relativistic quantum field theory and numerical methods. After introducing classical analytical techniques, such as cluster expansion and Landau theory, the authors present important numerical methods with applications to magnetic systems, Lennard-Jones fluids and biophysics. Quantum statistical mechanics is discussed in detail and applied to Bose-Einstein condensation and topics in astrophysics and cosmology. In order to describe emergent phenomena in interacting quantum systems, canonical non-relativistic quantum field theory is introduced and then reformulated in terms of Feynman integrals. Combining the authors' many years' experience of teaching courses in this area, this textbook is ideal for advanced undergraduate and graduate students in physics, chemistry and mathematics.

Author : V.N. Popov
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 50,9 Mb
Release : 2001-11-30
Category : Science
ISBN : 1402003072

Get Book

Functional Integrals in Quantum Field Theory and Statistical Physics by V.N. Popov Pdf

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 : 438 pages
File Size : 52,7 Mb
Release : 1985-01-01
Category : Science
ISBN : 0817632719

Get Book

Collected Papers Vol.1: Quantum Field Theory and Statistical Mechanics by James Glimm,Arthur Jaffe Pdf

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 Critical point dominance in quantum field models. . . . . . . . . . . . . . . . . . . . 326 q>,' quantum field model in the single-phase regions: Differentiability of the mass and bounds on critical exponents. . . . 341 Remark on the existence of q>:. . . • . . . . • . . . . • . . . . . . . . • . • . . . . . . . . . . • . 345 On the approach to the critical point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 Critical exponents and elementary particles. . . . . . . . . . . . . . . . . . . . . . . . . . 362 V Particle Structure Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 The entropy principle for vertex functions in quantum field models. . . . . 372 Three-particle structure of q>4 interactions and the scaling limit . . . . . . . . . 397 Two and three body equations in quantum field models. . . . . . . . . . . . . . . 409 Particles and scaling for lattice fields and Ising models. . . . . . . . . . . . . . . . 437 The resummation of one particle lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450 VI Bounds on Coupling Constants Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 Absolute bounds on vertices and couplings. . . . . . . . . . . . . . . . . . . . . . . . . . 480 The coupling constant in a q>4 field theory. . . . . . . . . . . . . . . . . . . . . . . . . . . 491 VII Confinement and Instantons Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 Instantons in a U(I) lattice gauge theory: A coulomb dipole gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 Charges, vortices and confinement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516 ix VIII Reflection Positivity Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531 A note on reflection positivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532 x Introduction 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.

Author : M. Jimbo,T. Miwa,A. Tsuchiya
Publisher : Elsevier
Page : 682 pages
File Size : 52,8 Mb
Release : 2014-05-19
Category : Science
ISBN : 9781483295251

Get Book

Integrable Systems in Quantum Field Theory and Statistical Mechanics by M. Jimbo,T. Miwa,A. Tsuchiya Pdf

Integrable Sys Quantum Field Theory

Author : Stephen L. Adler
Publisher : Cambridge University Press
Page : 239 pages
File Size : 48,6 Mb
Release : 2004-08-26
Category : Science
ISBN : 9781139454094

Get Book

Quantum Theory as an Emergent Phenomenon by Stephen L. Adler Pdf

Quantum mechanics is our most successful physical theory. However, it raises conceptual issues that have perplexed physicists and philosophers of science for decades. This 2004 book develops an approach, based on the proposal that quantum theory is not a complete, final theory, but is in fact an emergent phenomenon arising from a deeper level of dynamics. The dynamics at this deeper level are taken to be an extension of classical dynamics to non-commuting matrix variables, with cyclic permutation inside a trace used as the basic calculational tool. With plausible assumptions, quantum theory is shown to emerge as the statistical thermodynamics of this underlying theory, with the canonical commutation/anticommutation relations derived from a generalized equipartition theorem. Brownian motion corrections to this thermodynamics are argued to lead to state vector reduction and to the probabilistic interpretation of quantum theory, making contact with phenomenological proposals for stochastic modifications to Schrödinger dynamics.

Author : G. Mussardo
Publisher : Oxford University Press
Page : 778 pages
File Size : 40,9 Mb
Release : 2010
Category : Science
ISBN : 9780199547586

Get Book

Statistical Field Theory by G. Mussardo Pdf

A thorough and pedagogical introduction to phase transitions and exactly solved models in statistical physics and quantum field theory.