# Path Integrals And Quantum Anomalies

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**Path Integrals and Quantum Anomalies**

A Book

#### by **Kazuo Fujikawa,Hiroshi Suzuki**

- Publisher : OUP Oxford
- Release : 2004-04-29
- Pages : 296
- ISBN : 019152381X
- Language : En, Es, Fr & De

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.

**Path Integrals and Anomalies in Curved Space**

A Book

#### by **Fiorenzo Bastianelli,Peter van Nieuwenhuizen**

- Publisher : Cambridge University Press
- Release : 2006-07-20
- Pages : 129
- ISBN : 1139456849
- Language : En, Es, Fr & De

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.

**Path Integrals and Anomalies in Curved Space**

A Book

#### by **Fiorenzo Bastianelli**

- Publisher : Unknown Publisher
- Release : 2006
- Pages : 379
- ISBN : 9780511317125
- Language : En, Es, Fr & De

This book introduces path integrals, a powerful method for describing quantum phenomena, and then uses them to compute anomalies in quantum field theories. An advanced text for researchers and graduate students of quantum field theory and string theory, it also provides a stand-alone introduction to path integrals in quantum mechanics.

**Path Integrals in Physics**

Volume I Stochastic Processes and Quantum Mechanics

#### by **M Chaichian,A Demichev**

- Publisher : CRC Press
- Release : 2001-07-01
- Pages : 336
- ISBN : 9780750308014
- Language : En, Es, Fr & De

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.

**Quantum Field Theory II**

A Book

#### by **Misha Shifman**

- Publisher : World Scientific Publishing Company
- Release : 2019
- Pages : 320
- ISBN : 9789813234185
- Language : En, Es, Fr & De

"Field Theory II begins with the path integral formulation of quantum field theory. Perturbation theory is generalized beyond tree level, to include radiative corrections (loops). The renormalization procedure and Wilsonean renormalization group are discussed, asymptotic freedom of non-Abelian gauge theories derived, and some applications in Quantum Chromodynamics (QCD) considered, with a brief digression into the Standard Model (SM). Sample higher order corrections are worked out. The SM case requires a study of the spontaneous breaking of the gauge symmetry, a phenomenon which would be more appropriate to call "Higgsing of the gauge bosons""--

**Path Integrals**

New Trends and Perspectives : Proceedings of the 9th International Conference : Dresden, Germany, September 23-28, 2007

#### by **Wolfhard Janke,Axel Pelster**

- Publisher : World Scientific
- Release : 2008
- Pages : 610
- ISBN : 9812837264
- Language : En, Es, Fr & De

This proceedings volume contains selected talks and poster presentations from the 9th International Conference on Path Integrals ? New Trends and Perspectives, which took place at the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany, during the period September 23?28, 2007. Continuing the well-developed tradition of the conference series, the present status of both the different techniques of path integral calculations and their diverse applications to many fields of physics and chemistry is reviewed. This is reflected in the main topics in this volume, which range from more traditional fields such as general quantum physics and quantum or statistical field theory through technical aspects like Monte Carlo simulations to more modern applications in the realm of quantum gravity and astrophysics, condensed matter physics with topical subjects such as Bose?Einstein condensation or quantum wires, biophysics and econophysics. All articles are successfully tied together by the common method of path integration; as a result, special methodological advancements in one topic could be transferred to other topics.

**Field Theory: A Path Integral Approach (Third Edition)**

A Book

#### by **Ashok Das**

- Publisher : World Scientific
- Release : 2019-02-22
- Pages : 488
- ISBN : 9811202567
- Language : En, Es, Fr & De

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.

**Methods of Contemporary Gauge Theory**

A Book

#### by **Yuri Makeenko**

- Publisher : Cambridge University Press
- Release : 2002-08-15
- Pages : 417
- ISBN : 1139441655
- Language : En, Es, Fr & De

This 2002 book introduces the quantum theory of gauge fields. Emphasis is placed on four non-perturbative methods: path integrals, lattice gauge theories, the 1/N expansion, and reduced matrix models, all of which have important contemporary applications. Written as a textbook, it assumes a knowledge of quantum mechanics and elements of perturbation theory, while many relevant concepts are pedagogically introduced at a basic level in the first half of the book. The second half comprehensively covers large-N Yang-Mills theory. The book uses an approach to gauge theories based on path-dependent phase factors known as the Wilson loops, and contains problems with detailed solutions to aid understanding. Suitable for advanced graduate courses in quantum field theory, the book will also be of interest to researchers in high energy theory and condensed matter physics as a survey of recent developments in gauge theory.

**Field Theory**

A Path Integral Approach

#### by **Anonim**

- Publisher : Unknown Publisher
- Release : 2021
- Pages : 129
- ISBN : 9814477680
- Language : En, Es, Fr & De

**The Universal Coefficient Theorem and Quantum Field Theory**

A Topological Guide for the Duality Seeker

#### by **Andrei-Tudor Patrascu**

- Publisher : Springer
- Release : 2016-09-23
- Pages : 270
- ISBN : 3319461435
- Language : En, Es, Fr & De

This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics—one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics.

**60 Years of YangCMills Gauge Field Theories**

C N Yang's Contributions to Physics

#### by **L Brink,K K Phua**

- Publisher : World Scientific
- Release : 2016-04-21
- Pages : 540
- ISBN : 9814725579
- Language : En, Es, Fr & De

During the last six decades, Yang–Mills theory has increasingly become the cornerstone of theoretical physics. It is seemingly the only fully consistent relativistic quantum many-body theory in four space-time dimensions. As such it is the underlying theoretical framework for the Standard Model of Particle Physics, which has been shown to be the correct theory at the energies we now can measure. It has been investigated also from many other perspectives, and many new and unexpected features have been uncovered from this theory. In recent decades, apart from high energy physics, the theory has been actively applied in other branches of physics, such as statistical physics, condensed matter physics, nonlinear systems, etc. This makes the theory an indispensable topic for all who are involved in physics. The conference celebrated the exceptional achievements using Yang–Mills theory over the years but also many other truly remarkable contributions to different branches of physics from Prof C N Yang. This volume collects the invaluable talks by Prof C N Yang and the invited speakers reviewing these remarkable contributions and their importance for the future of physics. Contents:The Future of Physics — Revisited (C N Yang)Quantum Chromodynamics — The Perfect Yang–Mills Gauge Field Theory (David Gross)Maximally Supersymmetric Yang–Mills Theory: The Story of N = 4 Yang–Mills Theory (Lars Brink)The Lattice and Quantized Yang–Mills Theory (Michael Creutz)Yang–Mills Theories at High Energy Accelerators (George Sterman)Yang–Mills Theory at 60: Milestones, Landmarks and Interesting Questions (Ling-Lie Chau)Discovery of the First Yang–Mills Gauge Particle — The Gluon (Sau Lan Wu)Yang–Mills Gauge Theory and Higgs Particle (Tai Tsun Wu & Sau Lan Wu)Scenario for the Renormalization in the 4D Yang–Mills Theory (L D Faddeev)Statistical Physics in the Oeuvre of Chen Ning Yang (Michael E Fisher)Quantum Vorticity in Nature (Kerson Huang)Yang–Mills Theory and Fermionic Path Integrals (Kazuo Fujikawa)Yang–Mills Gauge Theory and the Higgs Boson Family (Ngee-Pong Chang)On the Physics of the Minimal Length: The Questions of Gauge Invariance (Lay Nam Chang, Djordje Minic, Ahmed Roman, Chen Sun & Tatsu Takeuchi)Generalization of the Yang–Mills Theory (G Savvidy)Some Thoughts about Yang–Mills Theory (A Zee)Gauging Quantum Groups: Yang–Baxter Joining Yang–Mills (Yong-Shi Wu)The Framed Standard Model (I) — A Physics Case for Framing the Yang–Mills Theory? (Chan Hong-Mo & Tsou Sheung Tsun)The Framed Standard Model (II) — A First Test Against Experiment (Chan Hong-Mo & Tsou Sheung Tsun)On the Study of the Higgs Properties at a Muon Collider (Mario Greco)Aharonov–Bohm Types of Phases in Maxwell and Yang–Mills Field Theories (Bruce H J McKellar)Yang–Mills for Historians and Philosophers (R P Crease)Gauge Concepts in Theoretical Applied Physics (Seng Ghee Tan & Mansoor B A Jalil)Yang–Yang Equilibrium Statistical Mechanics: A Brilliant Method (Xi-Wen Guan & Yang-Yang Chen)Chern–Simons Theory, Vassiliev Invariants, Loop Quantum Gravity and Functional Integration Without Integration (Louis H Kauffman)The Scattering Equations and Their Off-Shell Extension (York-Peng Yao)Feynman Geometries (Sen Hu & Andrey Losev)Particle Accelerator Development: Selected Examples (Jie Wei)A New Storage-Ring Light Source (Alex Chao)New Contributions to Physics by Prof C N Yang: 2009–2011 (Zhong-Qi Ma)Brief Overview of C N Yang's 13 Important Contributions to Physics (Yu Shi) Readership: Graduate students and scientists working in high energy physics, statistical physics and condensed matter physics.

**Field Theory**

A Path Integral Approach - 3rd Edition

#### by **Ashok Das**

- Publisher : World Scientific Publishing Company
- Release : 2019-02-11
- Pages : 488
- ISBN : 9789811202667
- Language : En, Es, Fr & De

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.

**Quantum Field Theory**

A Book

#### by **Eduardo Fradkin**

- Publisher : Princeton University Press
- Release : 2021-03-23
- Pages : 760
- ISBN : 0691189552
- Language : En, Es, Fr & De

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

**Field Theory**

A Path Integral Approach

#### by **Ashok Das**

- Publisher : World Scientific Publishing Company Incorporated
- Release : 2006-01-01
- Pages : 361
- ISBN : 9789812568489
- Language : En, Es, Fr & De

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.

**Functional Integration**

Action and Symmetries

#### by **Pierre Cartier,Cecile DeWitt-Morette**

- Publisher : Cambridge University Press
- Release : 2006-11-30
- Pages : 129
- ISBN : 1139462881
- Language : En, Es, Fr & De

Functional integration successfully entered physics as path integrals in the 1942 PhD dissertation of Richard P. Feynman, but it made no sense at all as a mathematical definition. Cartier and DeWitt-Morette have created, in this book, a fresh approach to functional integration. The book is self-contained: mathematical ideas are introduced, developed, generalised and applied. In the authors' hands, functional integration is shown to be a robust, user-friendly and multi-purpose tool that can be applied to a great variety of situations, for example: systems of indistinguishable particles; Aharonov–Bohm systems; supersymmetry; non-gaussian integrals. Problems in quantum field theory are also considered. In the final part the authors outline topics that can be profitably pursued using material already presented.

**Phase Space Methods for Degenerate Quantum Gases**

A Book

#### by **Bryan J. Dalton,John Jeffers,Stephen M. Barnett**

- Publisher : Oxford University Press, USA
- Release : 2015
- Pages : 432
- ISBN : 0199562741
- Language : En, Es, Fr & De

This is a text and reference book on phase space theory for post-graduate students and researchers in the fields of condensed matter, cold quantum gases, and quantum optics who already have a basic understanding of quantum theory. The aim of the book is to provide a theoretical framework for understanding the physics of degenerate quantum gases, which occur in all these fields. The phase space theory is outlined both in terms of a treatment involving separatesingle particle states or modes and in terms of a treatment involving quantum fields. The book contains detailed derivations of all the key results, includes chapters covering necessary backgroundmathematics, with many exercises being provided for readers who wish to check their understanding.

**Quantum Field Theory**

From Basics to Modern Topics

#### by **François Gelis**

- Publisher : Cambridge University Press
- Release : 2019-07-11
- Pages : 129
- ISBN : 1108574386
- Language : En, Es, Fr & De

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.

**Instantons and Large N**

An Introduction to Non-Perturbative Methods in Quantum Field Theory

#### by **Marcos Mariño**

- Publisher : Cambridge University Press
- Release : 2015-09-30
- Pages : 389
- ISBN : 1107068525
- Language : En, Es, Fr & De

Highly pedagogical textbook for graduate students, exploring advanced topics of quantum field theory with detailed derivations and worked examples.

**Introduction to Quantum Field Theory**

A Book

#### by **Horatiu Nastase**

- Publisher : Cambridge University Press
- Release : 2019-10-17
- Pages : 129
- ISBN : 1316999548
- Language : En, Es, Fr & De

Quantum Field Theory provides a theoretical framework for understanding fields and the particles associated with them, and is the basis of particle physics and condensed matter research. This graduate level textbook provides a comprehensive introduction to quantum field theory, giving equal emphasis to operator and path integral formalisms. It covers modern research such as helicity spinors, BCFW construction and generalized unitarity cuts; as well as treating advanced topics including BRST quantization, loop equations, and finite temperature field theory. Various quantum fields are described, including scalar and fermionic fields, Abelian vector fields and Quantum ElectroDynamics (QED), and finally non-Abelian vector fields and Quantum ChromoDynamics (QCD). Applications to scattering cross sections in QED and QCD are also described. Each chapter ends with exercises and an important concepts section, allowing students to identify the key aspects of the chapter and test their understanding.

**Aspects of Bottom-up Hidden Sector Models**

A Book

#### by **Philipp Klose**

- Publisher : Presses universitaires de Louvain
- Release : 2020-11-26
- Pages : 216
- ISBN : 2390610021
- Language : En, Es, Fr & De

The standard model (SM) of particle physics is a hugely successful theory of nature, but it is incomplete. E.g., it cannot explain finite SM neutrino masses or the origin of the primordial baryon asymmetry (BAU). One way to address such problems is to postulate the existence of new but hidden particles. This thesis studies such "hidden sectors" in two ways: 1) An effective theory approach, where electroweak (EW) and GeV scale portal effective theories (PETs) are constructed that couple the SM to a generic light hidden mediator of spin 0, 1⁄2, or 1. The EW scale PETs include all portal operators of dimension d≤5. The GeV scale PETs additionally include all leading order (LO) flavour changing portal operators of dimension d≤6,7. They are used to derive a LO PET chiral perturbation theory Lagrangian that describes hidden sector induced light meson transitions in fixed target experiments like NA62 or SHiP. 2) An investigation of the type-I seesaw model, which couples the SM to n≥2 sterile neutrinos that can generate a BAU via “leptogenesis”. It is shown that thermal and spectator effects can result in a sign-flip and strong relative enhancement of the BAU in high-scale leptogenesis with two hierarchical sterile neutrinos of vanishing initial abundance. Much lighter sterile neutrinos may be detected via lepton number violating (LNV) decays at colliders, but LNV decays could be suppressed relative to lepton number conserving decays for 't Hooft natural parameter choices. It is shown that the corresponding parameter space consists of three regions: (a)with unsuppressed LNV decays, (b)with suppressed LNV decays, (c)with suppressed and unsuppressed LNV decays.