Higher Spin Gauge Theories


Author: Lars Brink,Marc Henneaux,Mikhail A Vasiliev
Publisher: World Scientific
ISBN: 9813144114
Category: Science
Page: 404
View: 2537

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' Symmetries play a fundamental role in physics. Non-Abelian gauge symmetries are the symmetries behind theories for massless spin-1 particles, while the reparametrization symmetry is behind Einstein''s gravity theory for massless spin-2 particles. In supersymmetric theories these particles can be connected also to massless fermionic particles. Does Nature stop at spin-2 or can there also be massless higher spin theories. In the past strong indications have been given that such theories do not exist. However, in recent times ways to evade those constraints have been found and higher spin gauge theories have been constructed. With the advent of the AdS/CFT duality correspondence even stronger indications have been given that higher spin gauge theories play an important role in fundamental physics. All these issues were discussed at a recent international workshop in Singapore where the leading scientists in the field participated. This volume presents an up-to-date, detailed overview of the theories including its historic background, as well as the latest accomplishments in understanding the foundational properties of higher spin physics. Contents:PrefaceThe Higher Spin Square (Matthias R Gaberdiel and Rajesh Gopakumar)Higher Spin Representations of K(E10) (Axel Kleinschmidt and Hermann Nicolai)Scattering via Conformal Higher Spin Exchanges (A A Tseytlin)Note on Higher-Spin Equations in Four Dimensions (V E Didenko, N G Misuna and M A Vasiliev)Pseudo-Local Theories: A Functional Class Proposal (Massimo Taronna)Finite Temperature Maps in Vector/Higher Spin Duality (Antal Jevicki, Kenta Suzuki and Junggi Yoon)On (Un)Broken Higher-Spin Symmetry in Vector Models (E D Skvortsov)Extended Anti-de Sitter Hypergravity in 2 + 1 Dimensions and Hypersymmetry Bounds (Marc Henneaux, Alfredo Pérez, David Tempo and Ricardo Troncoso)Quasiconformal Group Approach to Higher Spin Algebras, Their Deformations and Supersymmetric Extensions (Murat Günaydin)BMS Modules in Three Dimensions (A Campoleoni, H A González, B Oblaka and M Riegler)Action Principles for Higher and Fractional Spin Gravities (Cesar Arias, Roberto Bonezzi, Nicolas Boulanger, Ergin Sezgin, Per Sundell, Alexander Torres-Gomez and Mauricio Valenzuela)Deriving Field Theories for Particles of Arbitrary Spin with and without Supersymmetry (Sudarshan Ananth)Reducible Higher-Spin Systems in Metric-Like and Frame-Like Formulation (Alessandro Agugliaro, Francesco Azzurli and Dmitri Sorokin)Bulk Quartic Vertices from Boundary Four-Point Correlators (X Bekaert, J Erdmenger, D Ponomarev and C Sleight)The Sky is the Limit: Free Boundary Conditions in AdS3 Chern–Simons Theory (Luis Apolo & Bo Sundborg)Higgs Mechanism and Holography of Partially Massless Higher Spin Fields (Seungho Gwak, Jaewon Kim and Soo-Jong Rey)Quartic Amplitudes for Minkowski Higher Spin (Anders K H Bengtsson)Solutions in Bosonic String Field Theory and AdS Higher Spin Algebras (Dimitri Polyakov)Comments on Higher-Spin Fields in Nontrivial Backgrounds (Rakibur Rahmana and Massimo Taronna) Readership: Researchers and academics in theoretical high energy physics. '

Higher Spin Gauge Theories


Author: Lars Brink,Marc Henneaux,Mikhail A. Vasiliev
Publisher: World Scientific Publishing Company
ISBN: 9789813144095
Category: Science
Page: 390
View: 7113

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Symmetries and invariants in higher-spin theory / M.A. Vasiliev -- The higher spin square / Matthias R. Gaberdiel and Rajesh Gopakumar -- Higher spin representations of K(E10) / Axel Kleinschmidt and Hermann Nicolai -- Scattering via conformal higher spin exchanges / A.A. Tseytlin -- Note on higher-spin equations in four dimensions / V.E. Didenko, N.G. Misuna and M.A. Vasiliev -- Pseudo-local theories: a functional class proposal / Massimo Taronna -- Finite temperature maps in vector/higher spin duality / Antal Jevicki, Kenta Suzuki and Junggi Yoon -- On (un)broken higher-spin symmetry in vector models / E.D. Skvortsov -- Extended anti-de sitter hypergravity in 2 + 1 dimensions and hypersymmetry bounds / Marc Henneaux, Alfredo Pérez, David Tempo and Ricardo Troncoso -- Quasiconformal group approach to higher spin algebras, their deformations and supersymmetric extensions / Murat Guenaydin -- BMS modules in three dimensions / A. Campoleoni, H.A. González, B. Oblak and M. Riegler -- Action principles for higher and fractional spin gravities / Cesar Arias, Roberto Bonezzi, Nicolas Boulanger, Ergin Sezgin, Per Sundell, Alexander Torres-Gomez and Mauricio Valenzuela -- Deriving field theories for particles of arbitrary spin with and without supersymmetry / Sudarshan Ananth -- Reducible higher-spin systems in metric-like and frame-like formulation / Alessandro Agugliaro, Francesco Azzurli and Dmitri Sorokin -- Bulk quartic vertices from boundary four-point correlators / X. Bekaert, J. Erdmenger, D. Ponomarev and C. Sleight -- The sky is the limit: free boundary conditions in AdS3 Chern-Simons theory / Luis Apolo and Bo Sundborg -- Higgs mechanism and holography of partially massless higher spin fields / Seungho Gwak, Jaewon Kim and Soo-Jong Rey -- Quartic amplitudes for Minkowski higher spin / Anders K.H. Bengtsson -- Solutions in bosonic string field theory and AdS higher spin algebras / Dimitri Polyakov -- Comments on higher-spin fields in nontrivial backgrounds / Rakibur Rahman and Massimo Taronna

Higher Spin Gauge Theories


Author: Nicolas Boulanger,Andrea Campoleoni
Publisher: MDPI
ISBN: 303842997X
Category: Mathematics
Page: 457
View: 6367

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This book is a printed edition of the Special Issue "Higher Spin Gauge Theories" that was published in Universe

String Fields, Higher Spins And Number Theory


Author: Polyakov Dimitri
Publisher: World Scientific
ISBN: 9813233419
Category: Science
Page: 212
View: 4540

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The book aims to analyze and explore deep and profound relations between string field theory, higher spin gauge theories and holography — the disciplines that have been on the cutting edge of theoretical high energy physics and other fields. These intriguing relations and connections involve some profound ideas in number theory, which appear to be part of a unifying language to describe these connections.

Gauge Theory and Variational Principles


Author: David Bleecker
Publisher: Courier Corporation
ISBN: 0486151875
Category: Science
Page: 208
View: 5304

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Covers principal fiber bundles and connections; curvature; particle fields, Lagrangians, and gauge invariance; inhomogeneous field equations; free Dirac electron fields; calculus on frame bundle; and unification of gauge fields and gravitation. 1981 edition

The Many Faces of the Superworld

Yuri Golfand Memorial Volume
Author: M Shifman
Publisher: World Scientific
ISBN: 9814493708
Category: Science
Page: 688
View: 6645

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This invaluable volume is dedicated to the memory of Yuri Golfand, one of the discoverers of supersymmetry. Together with his student, he constructed in 1970 the superextension of the Poincaré algebra and obtained the first four-dimensional supersymmetric field theory, a version of supersymmetric QED. Golfand died in 1994 in Israel. Did the pioneers of supersymmetry — Neveu, Schwarz, Ramond, Golfand, Volkov, Wess, Zumino and others — foresee in the early 1970's that they would be opening to us the gates of the superworld? The superworld will become one of the most important components of our understanding of Nature — a component that will stay with us forever. This book is a compilation of the original papers and review articles, devoted to various aspects of supersymmetry, written by the outstanding researchers in the field, theorists whose work shaped the present day theory and continues to make a profound impact on the frontier directions of the current development. A wide range of topics is covered — from subtle results in the superstring theory to supersymmetry-based phenomenology. Most of the articles have been prepared specifically for this volume. The first part of the book consists of the Editor's essay presenting the basic stages of Golfand's life and work, the memoirs of his widow, Mrs N Koretz-Golfand and of his student, Dr E Likhtman. Also included is the article of Prof. M Marinov “Revealing the Path to the Superworld”, outlining the main ideas that paved the way to the discovery of supersymmetry. The historical part of the book concludes with the English translation of the Golfand-Likhtman paper on supersymmetry published in 1972 in the Tamm Memorial Volume. Contents:Part II — The Present: From Symmetry to Supersymmetry (J Wess)Duality Invariant Born-Infeld Theory (D Brace et al.)Bäcklund Transformations in 10D SUSY Yang–Mills Theories (J-L Gervais)Representations of Extended Supersymmetries in Two Dimensions (A M Semikhatov)Supersymmetric Quantum Mechanics from Light Cone Quantization (S Hellerman & J Polchinski)Supersymmetric Index of Three-Dimensional Gauge Theory (E Witten)Vacuum Structure in Supersymmetric Yang–Mills Theories with Any Gauge Group (V G Kac & A V Smilga)The Superworld (N Seiberg)Brane Dynamics and Gauge Theory (D Kutasov)Confining Phase of Three Dimensional Supersymmetric Quantum Electrodynamics (M J Strassler)Z-D Brane Box Models and Non-Chiral Dihedral Quivers (B Feng et al.)Threebranes and Conformal Gauge Theories (I R Klebanov)Extremal Correlators in the AdS/CFT Correspondence (E D'Hoker et al.)Two Outcomes for Two Old (Super-)Problems (S Deser)Anomalies in Supersymmetric Theories (M T Grisaru)Some Properties of Type I′ String Theory (J H Schwarz)Dirac Equations, Light Cone Supersymmetry, and Superconformal Algebras (L Brink & P Ramond)Born-Infeld Action, Supersymmetry, and String Theory (A A Tseytlin)The Freckled Instantons (A Losev et al.)About R-Parity and the Supersymmetric Standard Model (P Fayet)M-Theory and Hypercharge (N D Lambert & P C West)Constraints on Extra Time Dimensions (G Dvali et al.)Higher Spin Gauge Theories: Star-Product and AdS Space (M A Vasiliev)Some Thermodynamical Aspects of String Theory (S A Abel et al.)Logarithmic Unification from Symmetries Enhanced in the Sub-Millimeter Infrared (N Arkani-Hamed et al.)A Toy Model for Supergravity and Superspace (P van Nieuwenhuizen) Readership: Graduate students, researchers and lecturers in theoretical high energy physics and historians of science. Keywords:Discovery of Supersymmetry;Pioneers of Supersymmetry;Golfand;Witten Index;Seiberg Duality;Supersymmetric Anomalies;Supergravity;Superspace

Modifications of Einstein's Theory of Gravity at Large Distances


Author: Eleftherios Papantonopoulos
Publisher: Springer
ISBN: 331910070X
Category: Science
Page: 426
View: 7826

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In the last few years modified gravity theories have been proposed as extensions of Einstein's theory of gravity. Their main motivation is to explain the latest cosmological and astrophysical data on dark energy and dark matter. The study of general relativity at small scales has already produced important results (cf e.g. LNP 863 Quantum Gravity and Quantum Cosmology) while its study at large scales is challenging because recent and upcoming observational results will provide important information on the validity of these modified theories. In this volume, various aspects of modified gravity at large scales will be discussed: high-curvature gravity theories; general scalar-tensor theories; Galileon theories and their cosmological applications; F(R) gravity theories; massive, new massive and topologically massive gravity; Chern-Simons modifications of general relativity (including holographic variants) and higher-spin gravity theories, to name but a few of the most important recent developments. Edited and authored by leading researchers in the field and cast into the form of a multi-author textbook at postgraduate level, this volume will be of benefit to all postgraduate students and newcomers from neighboring disciplines wishing to find a comprehensive guide for their future research.

Gauge/Gravity Duality


Author: Martin Ammon,Johanna Erdmenger
Publisher: Cambridge University Press
ISBN: 1107010349
Category: Science
Page: 548
View: 9348

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The first textbook on this important topic, for graduate students and researchers in particle and condensed matter physics.

Gauge Fields, Knots and Gravity


Author: John Baez,Javier P Muniain
Publisher: World Scientific Publishing Company
ISBN: 9813103248
Category: Science
Page: 480
View: 8102

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This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations. The relation of gauge theory to the newly discovered knot invariants such as the Jones polynomial is sketched. Riemannian geometry is then introduced in order to describe Einstein's equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory.

Gravitation and Gauge Symmetries


Author: M Blagojevic
Publisher: CRC Press
ISBN: 142003426X
Category: Science
Page: 522
View: 3473

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In the course of the development of electromagnetic, weak and strong interactions, the concept of (internal) gauge invariance grew up and established itself as an unavoidable dynamical principle in particle physics. It is less known that the principle of equivalence, and the basic dynamical properties of the gravitational interaction can also be expressed as a (spacetime) gauge symmetry. Gravitation and Gauge Symmetries sheds light on the connection between the intrinsic structure of gravity and the principle of gauge invariance, which may lead to a consistent unified field theory. The first part of the book gives a systematic account of the structure of gravity as a theory based on spacetime gauge symmetries. Some basic properties of space, time, and gravity are reviewed in the first, introductory chapter. The next chapter deals with elements of global Poincaré and conformal symmetries, which are necessary for the exposition of their localizations; the structure of the corresponding gauge theories of gravity is explored in chapters 3 and 4. Then, in chapters 5 and 6, we present the basic features of the constrained Hamiltonian of Poincaré gauge theory, discuss the relation between gauge symmetries and conservation laws, and introduce the concept of gravitational energy and other conserved quantities. The second part of the book explores the most promising attempts to build a unified field theory containing gravity, on the basis of the gauge principle. The author presents the possibility to constrict the theory of gravity as a nonlinear field theory in flat spacetime. The final chapters yield an exposition of the ideas of supersymmetry and supergravity, Kaluza-Klein theory, and string theory. Gravitation and Gauge Symmetries will be of interest to postgraduate students and researchers in gravitation, high energy physics and mathematical physics.

Gauge Field Theories


Author: Stefan Pokorski
Publisher: Cambridge University Press
ISBN: 9780521478168
Category: Science
Page: 609
View: 6600

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An expanded and up-dated book examining gauge theories and their symmetries.

Lectures on the Infrared Structure of Gravity and Gauge Theory


Author: Andrew Strominger
Publisher: Princeton University Press
ISBN: 1400889855
Category: Science
Page: 200
View: 6481

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A short, graduate-level synthesis of recent developments in theoretical physics, from a pioneer in the fieldshort, graduate-level synthesis of recent developments in theoretical physics, from a pioneer in the field Lectures on the Infrared Structure of Gravity and Gauge Theory presents an accessible, graduate-level synthesis of a frontier research area in theoretical physics. Based on a popular Harvard University course taught by the author, this book gives a concise introduction to recent discoveries concerning the structure of gravity and gauge theory at very long distances. These discoveries unite three disparate but well-developed subjects in physics. The first subject is the soft theorems, which were found by particle physicists in the 1950s to control the behavior of low-energy photons and are essential for all collider predictions. The second subject is asymptotic symmetries, found by general relativists in the 1960s to provide a surprising, infinite number of exact relations between distinct physical phenomena. The third subject is the memory effect, the measurement of which is sought in upcoming gravitational wave observations. An exploration of the physical and mathematical equivalence of these three subjects has provided a powerful new perspective on old results and led to a plethora of new results, involving symmetries of QED, gluon scattering amplitudes, flat-space holography in quantum gravity, black hole information, and beyond. Uniquely connective and cutting-edge, Lectures on the Infrared Structure of Gravity and Gauge Theory takes students and scholars to the forefront of new developments in the discipline. Materials are presented in a "lecture notes" style with problem sets included Concise and accessible pedagogical approach Topics include soft theorems, the memory effect, asymptotic symmetries with applications to QED, Yang-Mills theory, quantum gravity, and black holes

Quantum Field Theory of Many-Body Systems

From the Origin of Sound to an Origin of Light and Electrons
Author: Xiao-Gang Wen
Publisher: Oxford University Press on Demand
ISBN: 0198530943
Category: Science
Page: 505
View: 3739

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This book is a pedagogical and systematic introduction to new concepts and quantum field theoretical methods in condensed matter physics, which may have an impact on our understanding of the origin of light, electrons and other elementary particles in the universe. Emphasis is on clear physical principles, while at the same time bringing students to the fore of today's research.

Quantum Gauge Theories

Spin One and Two
Author: Günter Scharf
Publisher: Wiley-VCH
ISBN: 9780471414803
Category: Science
Page: 260
View: 1575

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An innovative new treatment of particle physics using quantum gauge theory as its basis If regarded as operator theories, ghost fields play a very important role in quantum gauge theory, which forms the basis of modern particle physics. The author argues that all known forces in nature-electromagnetism, weak and strong forces, and gravity-follow in a unique way from the basic principle of quantum gauge invariance. Using that as a starting point, this volume discusses gauge theories as quantum theories, as part of a streamlined modern approach. The simplicity of using only this one method throughout the book allows the reader a clear understanding of the mathematical structure of nature, while this modern and mathematically well-defined approach elucidates the standard theory of particle physics without overburdening the reader with the full range of various ideas and methods. Though the subject matter requires a basic knowledge of quantum mechanics, the book's unprecedented and uncomplicated coverage will offer readers little difficulty. This revolutionary volume is suitable for graduate students and researchers alike and includes a completely new treatment of gravity as well as important new ideas on massive gauge fields.

Quantum Field Theory and the Standard Model


Author: Matthew D. Schwartz
Publisher: Cambridge University Press
ISBN: 1107034736
Category: Science
Page: 863
View: 3134

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Modern introduction to quantum field theory for graduates, providing intuitive, physical explanations supported by real-world applications and homework problems.

60 Years of YangCMills Gauge Field Theories

C N Yang's Contributions to Physics
Author: L Brink,K K Phua
Publisher: World Scientific
ISBN: 9814725579
Category: Science
Page: 540
View: 8665

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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.

An Elementary Primer for Gauge Theory


Author: K Moriyasu
Publisher: World Scientific
ISBN: 981433801X
Category: Science
Page: 184
View: 6552

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Gauge theory is now recognized as one of the most revolutionary discoveries in physics since the development of quantum mechanics. This primer explains how and why gauge theory has dramatically changed our view of the fundamental forces of nature. The text is designed for the non-specialist. A new, intuitive approach is used to make the ideas of gauge theory accessible to both scientists and students with only a background in quantum mechanics. Emphasis is placed on the physics rather than the formalism.

Geometrodynamics of Gauge Fields

On the Geometry of Yang-Mills and Gravitational Gauge Theories
Author: Eckehard W. Mielke
Publisher: Springer
ISBN: 3319297341
Category: Science
Page: 373
View: 5854

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This monograph aims to provide a unified, geometrical foundation of gauge theories of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate-free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included. By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are developed. Since the discovery of the Higgs boson, concepts of spontaneous symmetry breaking in gravity have come again into focus, and, in this revised edition, these will be exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de Sitter type gauge theory in the spirit of Yang-Mills, some new progress in its topological form is presented. After symmetry breaking, Einstein’s standard general relativity with cosmological constant emerges as a classical background. The geometrical structure of BRST quantization with non-propagating topological ghosts is developed in some detail.

Renormalization and Effective Field Theory


Author: Kevin Costello
Publisher: American Mathematical Soc.
ISBN: 0821852884
Category: Mathematics
Page: 251
View: 9595

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This book tells mathematicians about an amazing subject invented by physicists and it tells physicists how a master mathematician must proceed in order to understand it. Physicists who know quantum field theory can learn the powerful methodology of mathematical structure, while mathematicians can position themselves to use the magical ideas of quantum field theory in ``mathematics'' itself. The retelling of the tale mathematically by Kevin Costello is a beautiful tour de force. --Dennis Sullivan This book is quite a remarkable contribution. It should make perturbative quantum field theory accessible to mathematicians. There is a lot of insight in the way the author uses the renormalization group and effective field theory to analyze perturbative renormalization; this may serve as a springboard to a wider use of those topics, hopefully to an eventual nonperturbative understanding. --Edward Witten Quantum field theory has had a profound influence on mathematics, and on geometry in particular. However, the notorious difficulties of renormalization have made quantum field theory very inaccessible for mathematicians. This book provides complete mathematical foundations for the theory of perturbative quantum field theory, based on Wilson's ideas of low-energy effective field theory and on the Batalin-Vilkovisky formalism. As an example, a cohomological proof of perturbative renormalizability of Yang-Mills theory is presented. An effort has been made to make the book accessible to mathematicians who have had no prior exposure to quantum field theory. Graduate students who have taken classes in basic functional analysis and homological algebra should be able to read this book.