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

Author: V.N. Popov

Publisher: Springer Science & Business Media

Published: 2001-11-30

Total Pages: 316

ISBN-13: 9781402003073

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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.

Path Integrals in Physics
Path Integrals in Physics

Author: M Chaichian

Publisher: CRC Press

Published: 2001-07-01

Total Pages: 368

ISBN-13: 9780750308021

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The path integral approach has proved extremely useful for the understanding of the most complex problems in quantum field theory, cosmology, and condensed matter physics. Path Integrals in Physics: Volume II, Quantum Field Theory, Statistical Physics and other Modern Applications covers the fundamentals of path integrals, both the Wiener and Feynman types, and their many applications in physics. The book deals with systems that have an infinite number of degrees of freedom. It discusses the general physical background and concepts of the path integral approach used, followed by a detailed presentation of the most typical and important applications as well as problems with either their solutions or hints how to solve them. Each chapter is self-contained and can be considered as an independent textbook. It provides a comprehensive, detailed, and systematic account of the subject suitable for both students and experienced researchers.

Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets
Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets

Author: Hagen Kleinert

Publisher: World Scientific

Published: 2009

Total Pages: 1626

ISBN-13: 9814273570

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Topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern-Simons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect." "The relevance of path integrals to financial markets is discussed, and improvements of the famous Black-Scholes formula for option prices are developed which account for the fact that large market fluctuations occur much more frequently than in Gaussian distributions." --Book Jacket.

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.

Quantum Field Theory
Quantum Field Theory

Author: Kerson Huang

Publisher: John Wiley & Sons

Published: 2008-09-26

Total Pages: 446

ISBN-13: 3527617388

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A unique approach to quantum field theory, with emphasis on the principles of renormalization Quantum field theory is frequently approached from the perspective of particle physics. This book adopts a more general point of view and includes applications of condensed matter physics. Written by a highly respected writer and researcher, it first develops traditional concepts, including Feynman graphs, before moving on to key topics such as functional integrals, statistical mechanics, and Wilson's renormalization group. The connection between the latter and conventional perturbative renormalization is explained. Quantum Field Theory is an exceptional textbook for graduate students familiar with advanced quantum mechanics as well as physicists with an interest in theoretical physics. It features: * Coverage of quantum electrodynamics with practical calculations and a discussion of perturbative renormalization * A discussion of the Feynman path integrals and a host of current subjects, including the physical approach to renormalization, spontaneous symmetry breaking and superfluidity, and topological excitations * Nineteen self-contained chapters with exercises, supplemented with graphs and charts

Path Integral Methods in Quantum Field Theory
Path Integral Methods in Quantum Field Theory

Author: R. J. Rivers

Publisher: Cambridge University Press

Published: 1988-10-27

Total Pages: 356

ISBN-13: 9780521368704

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The applications of functional integral methods introduced in this text for solving a range of problems in quantum field theory will prove useful for students and researchers in theoretical physics and 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.

Quantum Physics
Quantum Physics

Author: James Glimm

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 551

ISBN-13: 1461247284

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Describes fifteen years' work which has led to the construc- tion of solutions to non-linear relativistic local field e- quations in 2 and 3 space-time dimensions. Gives proof of the existence theorem in 2 dimensions and describes many properties of the solutions.

Quantum Field Theory
Quantum Field Theory

Author: Lukong Cornelius Fai

Publisher: CRC Press

Published: 2019-06-20

Total Pages: 595

ISBN-13: 0429589417

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Choice Recommended Title, February 2020 This book explores quantum field theory using the Feynman functional and diagrammatic techniques as foundations to apply Quantum Field Theory to a broad range of topics in physics. This book will be of interest not only to condensed matter physicists but physicists in a range of disciplines as the techniques explored apply to high-energy as well as soft matter physics. Features: Comprehensive and rigorous, yet presents an easy to understand approach Applicable to a wide range of disciplines Accessible to those with little, or basic, mathematical understanding

Path Integrals in Physics
Path Integrals in Physics

Author: M Chaichian

Publisher: CRC Press

Published: 2019-08-30

Total Pages: 336

ISBN-13: 9780367397142

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Path Integrals in Physics: Volume I, Stochastic Processes and Quantum Mechanics presents the fundamentals of path integrals, both the Wiener and Feynman type, and their many applications in physics. Accessible to a broad community of theoretical physicists, the book deals with systems possessing a infinite number of degrees in freedom. It discusses the general physical background and concepts of the path integral approach used, followed by a detailed presentation of the most typical and important applications as well as problems with either their solutions or hints how to solve them. It describes in detail various applications, including systems with Grassmann variables. Each chapter is self-contained and can be considered as an independent textbook. The book provides a comprehensive, detailed, and systematic account of the subject suitable for both students and experienced researchers.