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Quantum and Statistical Field Theory

Quantum and Statistical Field Theory PDF Author: Michel Le Bellac
Publisher: Oxford University Press
ISBN:
Category : Science
Languages : en
Pages : 592

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Book Description
As a fundamental branch of theoretical physics, quantum field theory has led, in the last 20 years, to spectacular progress in our understanding of phase transitions and elementary particles. This textbook emphasizes the underlying unity of the concepts and methods used in both domains, and presents in clear language topics such as the perturbative expansion, Feynman diagrams, renormalization, and the renormalization group. It contains detailed applications of critical phenomena to condensed matter physics, such as the calculation of critical exponents and a discussion of the XY model. Applications to particle physics include quantum electrodynamics and chromodynamics, electroweak interactions, and lattice gauge theories. The book is based on courses given over several years on statistical mechanics and field theory, and is written at graduate level. It attempts to guide the reader through a somewhat difficult and sometimes intricate subject in as clear a manner as possible, leading to a level of understanding where more advanced textbooks and research articles will be accessible. The only textbook covering the subject at this level, the work is thus an ideal guide for graduate and postgraduate students in physics, researchers in quantum and statistical field theory, and those from other fields of physics seeking an introduction to quantum field theory. A large number of problems are given to test the reader's grasp of the ideas.

Quantum Field Theory and Statistical Mechanics

Quantum Field Theory and Statistical Mechanics PDF Author: James Glimm
Publisher: Springer Science & Business Media
ISBN: 1461251583
Category : Science
Languages : en
Pages : 418

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Book Description
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.

Quantum and Statistical Field Theory

Quantum and Statistical Field Theory PDF Author: Michel Le Bellac
Publisher: Oxford University Press
ISBN:
Category : Science
Languages : en
Pages : 592

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Book Description
As a fundamental branch of theoretical physics, quantum field theory has led, in the last 20 years, to spectacular progress in our understanding of phase transitions and elementary particles. This textbook emphasizes the underlying unity of the concepts and methods used in both domains, and presents in clear language topics such as the perturbative expansion, Feynman diagrams, renormalization, and the renormalization group. It contains detailed applications of critical phenomena to condensed matter physics, such as the calculation of critical exponents and a discussion of the XY model. Applications to particle physics include quantum electrodynamics and chromodynamics, electroweak interactions, and lattice gauge theories. The book is based on courses given over several years on statistical mechanics and field theory, and is written at graduate level. It attempts to guide the reader through a somewhat difficult and sometimes intricate subject in as clear a manner as possible, leading to a level of understanding where more advanced textbooks and research articles will be accessible. The only textbook covering the subject at this level, the work is thus an ideal guide for graduate and postgraduate students in physics, researchers in quantum and statistical field theory, and those from other fields of physics seeking an introduction to quantum field theory. A large number of problems are given to test the reader's grasp of the ideas.

Statistical Field Theory

Statistical Field Theory PDF Author: Giuseppe Mussardo
Publisher: Oxford Graduate Texts
ISBN: 019878810X
Category :
Languages : en
Pages : 1024

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Book Description
Fundamental concepts of phase transitions, such as order parameters, spontaneous symmetry breaking, scaling transformations, conformal symmetry and anomalous dimensions, have deeply changed the modern vision of many areas of physics, leading to remarkable developments in statistical mechanics, elementary particle theory, condensed matter physics and string theory. This self-contained book provides a thorough introduction to the fascinating world of phase transitions and frontier topics of exactly solved models in statistical mechanics and quantum field theory, such as renormalization groups, conformal models, quantum integrable systems, duality, elastic S-matrices, thermodynamic Bethe ansatz and form factor theory. The clear discussion of physical principles is accompanied by a detailed analysis of several branches of mathematics distinguished for their elegance and beauty, including infinite dimensional algebras, conformal mappings, integral equations and modular functions. Besides advanced research themes, the book also covers many basic topics in statistical mechanics, quantum field theory and theoretical physics. Each argument is discussed in great detail while providing overall coherent understanding of physical phenomena. Mathematical background is made available in supplements at the end of each chapter, when appropriate. The chapters include problems of different levels of difficulty. Advanced undergraduate and graduate students will find this book a rich and challenging source for improving their skills and for attaining a comprehensive understanding of the many facets of the subject.

Quantum Geometry

Quantum Geometry PDF Author: Jan Ambjørn
Publisher: Cambridge University Press
ISBN: 0521461677
Category : Science
Languages : en
Pages : 363

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Book Description
Describes random geometry and applications to strings, quantum gravity, topological field theory and membrane physics.

Statistical Field Theory

Statistical Field Theory PDF Author: G. Mussardo
Publisher: Oxford University Press
ISBN: 0199547580
Category : Science
Languages : en
Pages : 778

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

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 PDF Author: Claude Itzykson
Publisher: Cambridge University Press
ISBN: 9780521408066
Category : Science
Languages : en
Pages : 432

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Book Description
Notes after each chapter.

Methods of Quantum Field Theory in Statistical Physics

Methods of Quantum Field Theory in Statistical Physics PDF Author: A. A. Abrikosov
Publisher: Courier Corporation
ISBN: 0486140156
Category : Science
Languages : en
Pages : 384

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Book Description
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."

Statistical Approach to Quantum Field Theory

Statistical Approach to Quantum Field Theory PDF Author: Andreas Wipf
Publisher: Springer
ISBN: 9783030832629
Category : Science
Languages : en
Pages : 554

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Book Description
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.

Quantum Statistical Field Theory

Quantum Statistical Field Theory PDF Author: Norman J. Morgenstern Horing
Publisher: Oxford University Press
ISBN: 0198791941
Category :
Languages : en
Pages : 448

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Book Description
This book provides an introduction to the methods of coupled quantum statistical field theory and Green's functions. The methods of coupled quantum field theory have played a major role in the extensive development of nonrelativistic quantum many-particle theory and condensed matter physics. This introduction to the subject is intended to facilitate delivery of the material in an easily digestible form to advanced undergraduate physics majors at a relatively early stage of their scientific development. The main mechanism to accomplish this is the early introduction of variational calculus and the Schwinger Action Principle, accompanied by Green's functions. Important achievements of the theory in condensed matter and quantum statistical physics are reviewed in detail to help develop research capability. These include the derivation of coupled field Green's function equations-of-motion for a model electron-hole-phonon system, extensive discussions of retarded, thermodynamic and nonequilibrium Green's functions and their associated spectral representations and approximation procedures. Phenomenology emerging in these discussions include quantum plasma dynamic-nonlocal-screening, plasmons, polaritons, linear electromagnetic response, excitons, polarons, phonons, magnetic Landau quantization, van der Waals interactions, chemisorption, etc. Considerable attention is also given to low dimensional and nanostructured systems, including quantum wells, wires, dots and superlattices, as well as materials having exceptional conduction properties such as Superconductors, Superfluids and Graphene.

Quantum Field Theory, Statistical Mechanics, Quantum Groups And Topology - Proceedings Of The Nato Advanced Research Workshop

Quantum Field Theory, Statistical Mechanics, Quantum Groups And Topology - Proceedings Of The Nato Advanced Research Workshop PDF Author: Curtright Thomas L
Publisher: World Scientific
ISBN: 9814554898
Category :
Languages : en
Pages : 364

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Book Description
The book is an introduction to quantum mechanics at a level suitable for the second year in a European university (junior or senior year in an American college). The matrix formulation of quantum mechanics is emphasized throughout, and the student is introduced to Dirac notation from the start. A number of major examples illustrate the workings of quantum mechanics. Several of these examples are taken from solid state physics, with the purpose of showing that quantum mechanics forms the common basis for understanding atoms, molecules and condensed matter. The book contains an introductory chapter which puts the concepts of quantum mechanics into a historical framework. The solid-state applications discussed in this text include the quantum Hall effect, spin waves, quantum wells and energy bands. Other examples feature the two-dimensional harmonic oscillator, coherent states, two-electron atoms, the ammonia molecule and the chemical bond. A large number of homework problems are included.