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.

Author: R. J. Rivers

Publisher: Cambridge University Press

ISBN: 0521368707

Category: Science

Page: 339

View: 937

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.

Path Integrals in Field Theory paves the way for both more rigorous studies in fundamental mathematical issues as well as for applications in hadron, particle and nuclear physics, thus addressing students in mathematical and theoretical ...

Author: Ulrich Mosel

Publisher: Springer Science & Business Media

ISBN: 3540403825

Category: Science

Page: 213

View: 227

Concise textbook intended as a primer on path integral formalism both in classical and quantum field theories, although emphasis is on the latter. It is ideally suited as an intensive one-semester course, delivering the basics needed by readers to follow developments in field theory. Path Integrals in Field Theory paves the way for both more rigorous studies in fundamental mathematical issues as well as for applications in hadron, particle and nuclear physics, thus addressing students in mathematical and theoretical physics alike. Assuming some background in relativistic quantum theory (but none in field theory), it complements the authors monograph Fields, Symmetries, and Quarks (Springer, 1999).

The book deals with systems that have an infinite number of degrees of freedom.

Author: M Chaichian

Publisher: CRC Press

ISBN: 0750308028

Category: Science

Page: 346

View: 708

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.

The path integral approach brings out this feature most clearly. In this book, the path integral approach is developed in detail completely within the context of quantum mechanics. Subsequently, it is applied to various areas of physics.

Author: Ashok Das

Publisher: World Scientific

ISBN: 9810213972

Category: Science

Page: 399

View: 784

Traditionally, field theory is taught through canonical quantization with a heavy emphasis on high energy physics. However, the techniques of field theory are applicable as well and are extensively used in various other areas of physics such as consdensed matter, nuclear physics and statistical mechanics. The path integral approach brings out this feature most clearly. In this book, the path integral approach is developed in detail completely within the context of quantum mechanics. Subsequently, it is applied to various areas of physics.

Specifically designed to introduce graduate students to the functional integration method in contemporary physics as painlessly as possible, the book concentrates on the conceptual problems inherent in the path integral formalism.

Author: Gert Roepstorff

Publisher: Springer

ISBN: 3540611061

Category: Science

Page: 387

View: 639

Specifically designed to introduce graduate students to the functional integration method in contemporary physics as painlessly as possible, the book concentrates on the conceptual problems inherent in the path integral formalism. Throughout, the striking interplay between stochastic processes, statistical physics and quantum mechanics comes to the fore, and all the methods of fundamental interest are generously illustrated by important physical examples.

In this book the authors provide an introduction to the path integral method in quantum field theory and its applications to the analyses of quantum anomalies.

Author: Kazuo Fujikawa

Publisher: OUP Oxford

ISBN: 9780191523816

Category: Science

Page: 296

View: 914

The Feynman path integrals are becoming increasingly important in the applications of quantum mechanics and field theory. The path integral formulation of quantum anomalies, i.e. the quantum breaking of certain symmetries, can now cover all the known quantum anomalies in a coherent manner. In this book the authors provide an introduction to the path integral method in quantum field theory and its applications to the analyses of quantum anomalies. No previous knowledge of field theory beyond advanced undergraduate quantum mechanics is assumed. The book provides the first coherent introductory treatment of the path integral formulation of chiral and Weyl anomalies, with applications to gauge theory in two and four dimensions, conformal field theory and string theory. Explicit and elementary path integral calculations of most of the quantum anomalies covered are given. The conceptual basis of the path integral bosonization in two-dimensional theory, which may have applications to condensed matter theory, for example, is clarified. The book also covers the recent interesting developments in the treatment of fermions and chiral anomalies in lattice gauge theory.

With its utility in a variety of fields in physics, the subject matter is primarily developed within the context of quantum mechanics before going into specialized areas.Adding new material keenly requested by readers, this second edition ...

Author: Ashok Das

Publisher: World Scientific Publishing Company Incorporated

ISBN: STANFORD:36105123296472

Category: Science

Page: 361

View: 124

New Edition: Field Theory (3rd Edition)This unique book describes quantum field theory completely within the context of path integrals. With its utility in a variety of fields in physics, the subject matter is primarily developed within the context of quantum mechanics before going into specialized areas.Adding new material keenly requested by readers, this second edition is an important expansion of the popular first edition. Two extra chapters cover path integral quantization of gauge theories and anomalies, and a new section extends the supersymmetry chapter, where singular potentials in supersymmetric systems are described.

Starting from the earlier notions of stationary action principles, these tutorial notes shows how Schwinger’s Quantum Action Principle descended from Dirac’s formulation, which independently led Feynman to his path-integral formulation ...

Author: Kimball A. Milton

Publisher: Springer

ISBN: 9783319201283

Category: Science

Page: 116

View: 899

Starting from the earlier notions of stationary action principles, these tutorial notes shows how Schwinger’s Quantum Action Principle descended from Dirac’s formulation, which independently led Feynman to his path-integral formulation of quantum mechanics. Part I brings out in more detail the connection between the two formulations, and applications are discussed. Then, the Keldysh-Schwinger time-cycle method of extracting matrix elements is described. Part II will discuss the variational formulation of quantum electrodynamics and the development of source theory.

Author: Fiorenzo BastianelliPublish On: 2006-07-20

This book introduces the quantum mechanics of particles that move in curved space by employing path integrals and then using them to compute anomalies in quantum field theories.

Author: Fiorenzo Bastianelli

Publisher: Cambridge University Press

ISBN: 9781139456845

Category: Science

Page:

View: 383

Path integrals provide a powerful method for describing quantum phenomena. This book introduces the quantum mechanics of particles that move in curved space by employing path integrals and then using them to compute anomalies in quantum field theories. The authors start by deriving path integrals for particles moving in curved space and their supersymmetric generalizations. They then discuss the regularization schemes essential to constructing and computing these path integrals. This topic is used to introduce regularization and renormalization in quantum field theories in a wider context. These methods are then applied to discuss and calculate anomalies in quantum field theory. Such anomalies provide enormous constraints in the search for physical theories of elementary particles, quantum gravity and string theories. An advanced text for researchers and graduate students of quantum field theory and string theory, the first part is also a stand-alone introduction to path integrals in quantum mechanics.

This book is a self-contained and concise introduction to the techniques and applications of path integral quantization and functional techniques, aimed at students and practitioners.

Author: SWANSON

Publisher: IOP Publishing Limited

ISBN: 0750335459

Category: Mathematical physics

Page: 241

View: 454

This book is a self-contained and concise introduction to the techniques and applications of path integral quantization and functional techniques, aimed at students and practitioners. The first half of the text focuses on quantum mechanics, including a review of the action formulation of classical mechanics and quantum mechanics in the Dirac operator and state formalism, and further examination of the path integral. The second part examines relativistic field theories, reviewing special relativity, as well as derivation of the path integral representation of the vacuum transition element for quantized scalar, spinor, and vector fields from the coherent state representation of the respective field theories. Key Features Concise introduction to the derivation and methods of path integral approaches to quantum mechanics and quantum field theory. Self-contained guide for students and practitioners

Quantum field theory is hardly comprehensible without path integrals: the goal of this book is to introduce students to this topic within the context of ordinary quantum mechanics and non-relativistic many-body theory, before facing the ...

Author: Jean Zinn-Justin

Publisher: Oxford University Press

ISBN: 9780198566755

Category: Mathematics

Page: 320

View: 800

Quantum field theory is hardly comprehensible without path integrals: the goal of this book is to introduce students to this topic within the context of ordinary quantum mechanics and non-relativistic many-body theory, before facing the problems associated with the more involved quantum field theory formalism.

A succinct introduction to the powerful and flexible combination of Hamiltonian operators and path integrals in quantum mathematics, with a practical emphasis on methodological and mathematical aspects.

Author: Belal E. Baaquie

Publisher: Cambridge University Press

ISBN: 9781107009790

Category: Science

Page: 436

View: 501

Introduces the powerful and flexible combination of Hamiltonian operators and path integrals in quantum mathematics.

This unique book describes quantum field theory completely within the context of path integrals.

Author: Ashok Das

Publisher: World Scientific

ISBN: 9789811202568

Category: Science

Page: 488

View: 169

This unique book describes quantum field theory completely within the context of path integrals. With its utility in a variety of fields in physics, the subject matter is primarily developed within the context of quantum mechanics before going into specialized areas.All the existing chapters of the previous edition have been expanded for more clarity. The chapter on anomalies and the Schwinger model has been completely rewritten for better logical clarity. Two new chapters have been added at the request of students and faculty worldwide. The first describes Schwinger's proper time method with simple examples both at zero and at finite temperature while the second develops the idea of zeta function regularization with simple examples.This latest edition is a comprehensive and much expanded version of the original text.

This text is based on course-tested notes for graduate students and, as such, its style is essentially pedagogical, requiring only some basics of mathematics, statistical physics, and quantum field theory.

Author: Andreas Wipf

Publisher: Springer

ISBN: 9783642331053

Category: Science

Page: 390

View: 312

Over the past few decades the powerful methods of statistical physics and Euclidean quantum field theory have moved closer together, with common tools based on the use of path integrals. The interpretation of Euclidean field theories as particular systems of statistical physics has opened up new avenues for understanding strongly coupled quantum systems or quantum field theories at zero or finite temperatures. Accordingly, the first chapters of this book contain a self-contained introduction to path integrals in Euclidean quantum mechanics and statistical mechanics. The resulting high-dimensional integrals can be estimated with the help of Monte Carlo simulations based on Markov processes. The most commonly used algorithms are presented in detail so as to prepare the reader for the use of high-performance computers as an “experimental” tool for this burgeoning field of theoretical physics. Several chapters are then devoted to an introduction to simple lattice field theories and a variety of spin systems with discrete and continuous spins, where the ubiquitous Ising model serves as an ideal guide for introducing the fascinating area of phase transitions. As an alternative to the lattice formulation of quantum field theories, variants of the flexible renormalization group methods are discussed in detail. Since, according to our present-day knowledge, all fundamental interactions in nature are described by gauge theories, the remaining chapters of the book deal with gauge theories without and with matter. This text is based on course-tested notes for graduate students and, as such, its style is essentially pedagogical, requiring only some basics of mathematics, statistical physics, and quantum field theory. Yet it also contains some more sophisticated concepts which may be useful to researchers in the field. Each chapter ends with a number of problems – guiding the reader to a deeper understanding of some of the material presented in the main text – and, in most cases, also features some listings of short, useful computer programs.

The book ends with appendices covering mathematical fundamentals and enrichment topics, plus selected biographical notes on pioneers of quantum mechanics and quantum field theory.

Author: Florian Scheck

Publisher: Springer Science & Business Media

ISBN: 9783642345630

Category: Science

Page: 741

View: 540

Scheck’s Quantum Physics presents a comprehensive introductory treatment, ideally suited for a two-semester course. Part One covers the basic principles and prime applications of quantum mechanics, from the uncertainty relations to many-body systems. Part Two introduces to relativistic quantum field theory and ranges from symmetries in quantum physics to electroweak interactions. Numerous worked-out examples as well as exercises, with solutions or hints, enables the book’s use as an accompanying text for courses, and also for independent study. For both parts, the necessary mathematical framework is treated in adequate form and detail. The book ends with appendices covering mathematical fundamentals and enrichment topics, plus selected biographical notes on pioneers of quantum mechanics and quantum field theory. The new edition was thoroughly revised and now includes new sections on quantization using the path integral method and on deriving generalized path integrals for bosonic and fermionic fields.

The book covers the theory of Quantum Gravitation from the point of view of Feynman path integrals.

Author: Herbert W. Hamber

Publisher: Springer Science & Business Media

ISBN: 9783540852933

Category: Science

Page: 342

View: 796

"Quantum Gravitation" approaches the subject from the point of view of Feynman path integrals, which provide a manifestly covariant approach in which fundamental quantum aspects of the theory such as radiative corrections and the renormalization group can be systematically and consistently addressed. It is shown that the path integral method is suitable for both perturbative as well as non-perturbative studies, and is already known to offer a framework for the theoretical investigation of non-Abelian gauge theories, the basis for three of the four known fundamental forces in nature. The book thus provides a coherent outline of the present status of the theory gravity based on Feynman’s formulation, with an emphasis on quantitative results. Topics are organized in such a way that the correspondence to similar methods and results in modern gauge theories becomes apparent. Covariant perturbation theory are developed using the full machinery of Feynman rules, gauge fixing, background methods and ghosts. The renormalization group for gravity and the existence of non-trivial ultraviolet fixed points are investigated, stressing a close correspondence with well understood statistical field theory models. The final chapter addresses contemporary issues in quantum cosmology such as scale dependent gravitational constants and quantum effects in the early universe.

Based on a two-semester course held at the University of Heidelberg, Germany, this book provides a solid basis for postgraduate students wishing to obtain a more profound understanding of the foundations of Quantum Field Theory.

Author: Klaus D Rothe

Publisher: World Scientific

ISBN: 9789811221941

Category: Science

Page: 352

View: 584

Based on a two-semester course held at the University of Heidelberg, Germany, this book provides an adequate resource for the lecturer and the student. The contents are primarily aimed at graduate students who wish to learn about the fundamental concepts behind constructing a Relativistic Quantum Theory of particles and fields. So it provides a comprehensive foundation for the extension to Quantum Chromodynamics and Weak Interactions, that are not included in this book.

Providing a self-contained step-by-step explanation, this book provides a guide to path integral methods for readers with a basic knowledge of quantum mechanics

Author: Taro Kashiwa

Publisher: Oxford University Press on Demand

ISBN: 0198517718

Category: Science

Page: 216

View: 458

Providing a self contained step by step explanation, this book will guide the reader with a basic knowledge of quantum mechanics, to a sufficiently comprehensive level as well as to the frontier of contemporary physics. For the last two decades there has been a ceaseless growth of the areawhere the path integral (PI) method plays an important role: the main reasons are its intuitive aspect and ease of handling. However, this has raised questions elsewhere and in this book fundamental issues are resolved by starting from the canonical operator formalism to lead the reader to a morecomprehensive level. Containing the most recent topics such as the lattice fermion problem in quantum field theory as well as the quantum Monte Carlo method in statistical mechanics this book will suit graduate students of quantum physics.

This unique book describes quantum field theory completely within the context of path integrals.

Author: Ashok Das

Publisher: World Scientific Publishing Company

ISBN: 9811202664

Category: Path integrals

Page: 488

View: 176

This unique book describes quantum field theory completely within the context of path integrals. With its utility in a variety of fields in physics, the subject matter is primarily developed within the context of quantum mechanics before going into specialized areas. All the existing chapters of the previous edition have been expanded for more clarity. The chapter on anomalies and the Schwinger model has been completely rewritten for better logical clarity. Two new chapters have been added at the request of students and faculty worldwide. The first describes Schwinger's proper time method with simple examples both at zero and at finite temperature while the second develops the idea of zeta function regularization with simple examples. This latest edition is a comprehensive and much expanded version of the original text.