Statistical Approach to Quantum Field Theory
Statistical Approach to Quantum Field Theory

Author: Andreas Wipf

Publisher: Springer Nature

Published: 2021-10-25

Total Pages: 568

ISBN-13: 3030832635

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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.

Functional Methods in Quantum Field Theory and Statistical Physics
Functional Methods in Quantum Field Theory and Statistical Physics

Author: A.N. Vasiliev

Publisher: CRC Press

Published: 1998-07-28

Total Pages: 336

ISBN-13: 9789056990350

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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.

Algebraic Methods in Statistical Mechanics and Quantum Field Theory
Algebraic Methods in Statistical Mechanics and Quantum Field Theory

Author: Dr. Gérard G. Emch

Publisher: Courier Corporation

Published: 2014-08-04

Total Pages: 336

ISBN-13: 0486151719

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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.

Statistical Field Theory
Statistical Field Theory

Author: G. Mussardo

Publisher: Oxford University Press, USA

Published: 2010

Total Pages: 778

ISBN-13: 0199547580

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

Quantum Field Theory
Quantum Field Theory

Author: Eduardo Fradkin

Publisher: Princeton University Press

Published: 2021-03-23

Total Pages: 760

ISBN-13: 0691189552

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The only graduate-level textbook on quantum field theory that fully integrates perspectives from high-energy, condensed-matter, and statistical physics Quantum field theory was originally developed to describe quantum electrodynamics and other fundamental problems in high-energy physics, but today has become an invaluable conceptual and mathematical framework for addressing problems across physics, including in condensed-matter and statistical physics. With this expansion of applications has come a new and deeper understanding of quantum field theory—yet this perspective is still rarely reflected in teaching and textbooks on the subject. Developed from a year-long graduate course Eduardo Fradkin has taught for years to students of high-energy, condensed-matter, and statistical physics, this comprehensive textbook provides a fully "multicultural" approach to quantum field theory, covering the full breadth of its applications in one volume. Brings together perspectives from high-energy, condensed-matter, and statistical physics in both the main text and exercises Takes students from basic techniques to the frontiers of physics Pays special attention to the relation between measurements and propagators and the computation of cross sections and response functions Focuses on renormalization and the renormalization group, with an emphasis on fixed points, scale invariance, and their role in quantum field theory and phase transitions Other topics include non-perturbative phenomena, anomalies, and conformal invariance Features numerous examples and extensive problem sets Also serves as an invaluable resource for researchers

Statistical Methods in Quantum Optics 1
Statistical Methods in Quantum Optics 1

Author: Howard J. Carmichael

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 384

ISBN-13: 3662038757

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This is the first of a two-volume presentation on current research problems in quantum optics, and will serve as a standard reference in the field for many years to come. The book provides an introduction to the methods of quantum statistical mechanics used in quantum optics and their application to the quantum theories of the single-mode laser and optical bistability. The generalized representations of Drummond and Gardiner are discussed together with the more standard methods for deriving Fokker-Planck equations.

Statistical Structure of Quantum Theory
Statistical Structure of Quantum Theory

Author: Alexander S. Holevo

Publisher: Springer Science & Business Media

Published: 2001-06-20

Total Pages: 189

ISBN-13: 3540420827

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New ideas on the mathematical foundations of quantum mechanics, related to the theory of quantum measurement, as well as the emergence of quantum optics, quantum electronics and optical communications have shown that the statistical structure of quantum mechanics deserves special investigation. In the meantime it has become a mature subject. In this book, the author, himself a leading researcher in this field, surveys the basic principles and results of the theory, concentrating on mathematically precise formulations. Special attention is given to the measurement dynamics. The presentation is pragmatic, concentrating on the ideas and their motivation. For detailed proofs, the readers, researchers and graduate students, are referred to the extensively documented literature.

Statistical Methods in Quantum Optics 2
Statistical Methods in Quantum Optics 2

Author: Howard J. Carmichael

Publisher: Springer Science & Business Media

Published: 2009-04-25

Total Pages: 551

ISBN-13: 3540713204

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This second volume of Howard Carmichael’s work continues the development of the methods used in quantum optics to treat open quantum systems and their fluctuations. Its early chapters build upon the phase-space methods introduced in Volume 1. Written on a level suitable for debut researchers or students in an advanced course in quantum optics, or a course in quantum mechanics or statistical physics that deals with open quantum systems.

Quantum Field Theory Approach to Condensed Matter Physics
Quantum Field Theory Approach to Condensed Matter Physics

Author: Eduardo C. Marino

Publisher: Cambridge University Press

Published: 2017-09-28

Total Pages: 537

ISBN-13: 1108508855

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A balanced combination of introductory and advanced topics provides a new and unique perspective on the quantum field theory approach to condensed matter physics. Beginning with the basics of these subjects, such as static and vibrating lattices, independent and interacting electrons, the functional formulation for fields and different generating functionals and their roles, this book presents a unified viewpoint illustrating the connections and relationships among various physical concepts and mechanisms. Advanced and newer topics bring the book up to date with current developments and include sections on cuprate and pnictide superconductors, graphene, Weyl semimetals, transition metal dichalcogenides and topological insulators. Finally, well-known subjects such as the quantum Hall effect, superconductivity, Mott and Anderson insulators, and the Anderson–Higgs mechanism are examined within a unifying QFT-CMP approach. Presenting new insights on traditional topics, this text allows graduate students and researchers to master the proper theoretical tools required in a variety of condensed matter physics systems.