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The Canonical Operator in Many-Particle Problems and Quantum Field Theory

Author: Victor P. Maslov

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2022-06-21

Total Pages: 478

ISBN-13: 3110762706

In this monograph we study the problem of construction of asymptotic solutions of equations for functions whose number of arguments tends to infinity as the small parameter tends to zero. Such equations arise in statistical physics and in quantum theory of a large number of fi elds. We consider the problem of renormalization of quantum field theory in the Hamiltonian formalism, which encounters additional difficulties related to the Stückelberg divergences and the Haag theorem. Asymptotic methods for solving pseudodifferential equations with small parameter multiplying the derivatives, as well as the asymptotic methods developed in the present monograph for solving problems in statistical physics and quantum field theory, can be considered from a unified viewpoint if one introduces the notion of abstract canonical operator. The book can be of interest for researchers – specialists in asymptotic methods, statistical physics, and quantum fi eld theory as well as for graduate and undergraduate students of these specialities.

The Canonical Operator in Many-Particle Problems and Quantum Field Theory

Author: Victor P. Maslov

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2022-06-21

Total Pages: 314

ISBN-13: 3110762749

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Problem Book in Quantum Field Theory

Author: Voja Radovanovic

Publisher: Springer Science & Business Media

Published: 2008-01-24

Total Pages: 242

ISBN-13: 3540770143

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The Problem Book in Quantum Field Theory contains about 200 problems with solutions or hints that help students to improve their understanding and develop skills necessary for pursuing the subject. It deals with the Klein-Gordon and Dirac equations, classical field theory, canonical quantization of scalar, Dirac and electromagnetic fields, the processes in the lowest order of perturbation theory, renormalization and regularization. The solutions are presented in a systematic and complete manner. The material covered and the level of exposition make the book appropriate for graduate and undergraduate students in physics, as well as for teachers and researchers.

Integrable Systems, Quantum Groups, and Quantum Field Theories

Author: Alberto Ibort

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 508

ISBN-13: 9401119805

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In many ways the last decade has witnessed a surge of interest in the interplay between theoretical physics and some traditional areas of pure mathematics. This book contains the lectures delivered at the NATO-ASI Summer School on `Recent Problems in Mathematical Physics' held at Salamanca, Spain (1992), offering a pedagogical and updated approach to some of the problems that have been at the heart of these events. Among them, we should mention the new mathematical structures related to integrability and quantum field theories, such as quantum groups, conformal field theories, integrable statistical models, and topological quantum field theories, that are discussed at length by some of the leading experts on the areas in several of the lectures contained in the book. Apart from these, traditional and new problems in quantum gravity are reviewed. Other contributions to the School included in the book range from symmetries in partial differential equations to geometrical phases in quantum physics. The book is addressed to researchers in the fields covered, PhD students and any scientist interested in obtaining an updated view of the subjects.

Quantum Field Theory

Author: Mark Srednicki

Publisher: Cambridge University Press

Published: 2007-01-25

Total Pages: 664

ISBN-13: 1139462768

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Quantum field theory is the basic mathematical framework that is used to describe elementary particles. This textbook provides a complete and essential introduction to the subject. Assuming only an undergraduate knowledge of quantum mechanics and special relativity, this book is ideal for graduate students beginning the study of elementary particles. The step-by-step presentation begins with basic concepts illustrated by simple examples, and proceeds through historically important results to thorough treatments of modern topics such as the renormalization group, spinor-helicity methods for quark and gluon scattering, magnetic monopoles, instantons, supersymmetry, and the unification of forces. The book is written in a modular format, with each chapter as self-contained as possible, and with the necessary prerequisite material clearly identified. It is based on a year-long course given by the author and contains extensive problems, with password protected solutions available to lecturers at www.cambridge.org/9780521864497.

An Introduction To Quantum Field Theory

Author: Michael E. Peskin

Publisher: CRC Press

Published: 2018-05-04

Total Pages: 866

ISBN-13: 0429983182

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An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.

Current Topics in Quantum Field Theory Research

Author: O. Kovras

Publisher: Nova Publishers

Published: 2007

Total Pages: 344

ISBN-13: 9781600212833

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Quantum field theory was invented to deal simultaneously with special relativity and quantum mechanics, the two greatest discoveries of early twentieth-century physics, but it has become increasingly important to many areas of physics including quantum hall physics, surface growth, string theory, D-branes and quantum gravity as well as condensed-matter and high-energy applications and particle-physics. This important book presents leading-edge research from throughout the world.

Relativistic Quantum Mechanics and Introduction to Quantum Field Theory

Author: Anton Z. Capri

Publisher: World Scientific

Published: 2002

Total Pages: 194

ISBN-13: 9789812381378

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This invaluable textbook is divided into two parts. The first part includes a detailed discussion on the discrete transformations for the Dirac equation, as well as on the central force problem for the Dirac equation. In the second part, the external field problem is examined; pair production and vacuum polarization leading to charge renormalization are treated in detail. Relativistic Quantum Mechanic's and Introduction to Quantum Field Theory has arisen from a graduate course which the author taught for several years at the University of Alberta to students interested in particle physics and field theory.

Quantum Field Theory

Author: Kerson Huang

Publisher: John Wiley & Sons

Published: 2010-04-26

Total Pages: 439

ISBN-13: 3527408460

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Die neue Auflage des für seinen allgemeinen, praxisnahen Ansatz gelobten Lehrbuchs ist gründlich überarbeitet und erweitert. In sich abgeschlossene und deshalb gut einzeln lesbare Kapitel entwickeln zunächst die traditionellen Konzepte wie Feynman-Graphen und behandeln dann zentrale Themen wie Funktionalintegrale, statistische Mechanik sowie die Wilson-Renormierung. Aufgrund des raschen Fortschritts und der wachsenden Bedeutung von Systemen mit niedrigen Dimensionen befasst sich diese zweite Auflage insbesondere auch mit eindimensionalen Leitern und ähnlichen Systemen. Neue Übungsaufgaben (mit Lösungen) sind hinzugekommen.

Quantum Field Theory

Author: François Gelis

Publisher: Cambridge University Press

Published: 2019-07-11

Total Pages: 611

ISBN-13: 1108574386

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This modern text combines fundamental principles with advanced topics and recent techniques in a rigorous and self-contained treatment of quantum field theory.Beginning with a review of basic principles, starting with quantum mechanics and special relativity, students can refresh their knowledge of elementary aspects of quantum field theory and perturbative calculations in the Standard Model. Results and tools relevant to many applications are covered, including canonical quantization, path integrals, non-Abelian gauge theories, and the renormalization group. Advanced topics are explored, with detail given on effective field theories, quantum anomalies, stable extended field configurations, lattice field theory, and field theory at a finite temperature or in the strong field regime. Two chapters are dedicated to new methods for calculating scattering amplitudes (spinor-helicity, on-shell recursion, and generalized unitarity), equipping students with practical skills for research. Accessibly written, with numerous worked examples and end-of-chapter problems, this is an essential text for graduate students. The breadth of coverage makes it an equally excellent reference for researchers.