Download or read book Lectures on Algebraic Quantum Field Theory and Operator Algebras written by Bert Schroer and published by . This book was released on 2001 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Operatoralgebraic Methods in Quantum Field Theory written by Hellmut Baumgärtel and published by De Gruyter Akademie Forschung. This book was released on 1995 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the course of lectures, held from summer 1993 up to summer 1994 at the Humboldt University of Berlin (SS 93), the Technical University of Berlin (WS 93/94) and the University of Potsdam (SS 94) the author presents basic operatoralgebraic material which is necessary to establish basic concepts of the algebraic quantum field theory as well as to get essential results in this field. The original ansatz of R. Haag (and others) started with the "working hypothesis" of a net of algebras of local observables. The aim of the lectures is to show that the success of this ansatz is strongly connected with deep results in the theory of operator algebras. Some characteristic mutual relations are described. Key words are "Vacuum representations on the four-dimensional Minkowski space and on the unit sphere, DHR-superselection theory, field algebra", and others. The emphasis is to make the material presented clear and readable without missing depth. The hope is to convince the reader of the beauty and stringency of this theory. While the first part of the book describes vacuum representations on the four-dimensional Minkowski space, the second part deals with the so-called DHR-superselection theory, firstly for the automorphism case and secondly for the general case. The constructions of the field algebra and the symmetry group are included. Finally, vacuum representations on the unit sphere S1 are discussed.
Download or read book Causal Nets of Operator Algebras written by Hellmut Baumgärtel and published by De Gruyter Akademie Forschung. This book was released on 1992 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: For advanced students in mathematics and mathematicians, as well as theoretical physicists, this volume presents the theory of nets of operator algebras, in particular nets connected with a causality condition. Such nets appear in mathematical formulations of quantum statistical mechanics and of quantum field theory. In this volume, the emphasis lies on nets which are linked with the algebraic approach to quantum field theory. Assumes a basic knowledge of functional analysis, in particular in the field of operator algebras. Annotation copyright by Book News, Inc., Portland, OR
Download or read book Perturbative Algebraic Quantum Field Theory written by Kasia Rejzner and published by Springer. This book was released on 2016-03-16 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn’t require the use of divergent quantities and works on a large class of Lorenzian manifolds. We discuss in detail the examples of scalar fields, gauge theories and the effective quantum gravity. pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all, of these conceptual problems. Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses effective quantum gravity. The book aims to be accessible to researchers and graduate students, who are interested in the mathematical foundations of pQFT.
Download or read book Introduction To Quantum Group And Integrable Massive Models Of Quantum Field Theory written by Mo-lin Ge and published by World Scientific. This book was released on 1990-09-24 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings consists of 6 lectures each from Prof L Takhtajan and Prof F Smirnov which were presented during the workshop.
Download or read book Quantum Field Theory and Noncommutative Geometry written by Ursula Carow-Watamura and published by Springer Science & Business Media. This book was released on 2005-02-21 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reflects the growing collaboration between mathematicians and theoretical physicists to treat the foundations of quantum field theory using the mathematical tools of q-deformed algebras and noncommutative differential geometry. A particular challenge is posed by gravity, which probably necessitates extension of these methods to geometries with minimum length and therefore quantization of space. This volume builds on the lectures and talks that have been given at a recent meeting on "Quantum Field Theory and Noncommutative Geometry." A considerable effort has been invested in making the contributions accessible to a wider community of readers - so this volume will not only benefit researchers in the field but also postgraduate students and scientists from related areas wishing to become better acquainted with this field.
Download or read book Introduction to Algebraic and Constructive Quantum Field Theory written by John C. Baez and published by Princeton University Press. This book was released on 2014-07-14 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present a rigorous treatment of the first principles of the algebraic and analytic core of quantum field theory. Their aim is to correlate modern mathematical theory with the explanation of the observed process of particle production and of particle-wave duality that heuristic quantum field theory provides. Many topics are treated here in book form for the first time, from the origins of complex structures to the quantization of tachyons and domains of dependence for quantized wave equations. This work begins with a comprehensive analysis, in a universal format, of the structure and characterization of free fields, which is illustrated by applications to specific fields. Nonlinear local functions of both free fields (or Wick products) and interacting fields are established mathematically in a way that is consistent with the basic physical constraints and practice. Among other topics discussed are functional integration, Fourier transforms in Hilbert space, and implementability of canonical transformations. The authors address readers interested in fundamental mathematical physics and who have at least the training of an entering graduate student. A series of lexicons connects the mathematical development with the underlying physical motivation or interpretation. The examples and problems illustrate the theory and relate it to the scientific literature. Originally published in 1992. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Advances in Algebraic Quantum Field Theory written by Romeo Brunetti and published by Springer. This book was released on 2015-09-04 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text focuses on the algebraic formulation of quantum field theory, from the introductory aspects to the applications to concrete problems of physical interest. The book is divided in thematic chapters covering both introductory and more advanced topics. These include the algebraic, perturbative approach to interacting quantum field theories, algebraic quantum field theory on curved spacetimes (from its structural aspects to the applications in cosmology and to the role of quantum spacetimes), algebraic conformal field theory, the Kitaev's quantum double model from the point of view of local quantum physics and constructive aspects in relation to integrable models and deformation techniques. The book is addressed to master and graduate students both in mathematics and in physics, who are interested in learning the structural aspects and the applications of algebraic quantum field theory.
Download or read book Quantum Groups Quantum Categories and Quantum Field Theory written by Jürg Fröhlich and published by Springer. This book was released on 2006-11-15 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews recent results on low-dimensional quantum field theories and their connection with quantum group theory and the theory of braided, balanced tensor categories. It presents detailed, mathematically precise introductions to these subjects and then continues with new results. Among the main results are a detailed analysis of the representation theory of U (sl ), for q a primitive root of unity, and a semi-simple quotient thereof, a classfication of braided tensor categories generated by an object of q-dimension less than two, and an application of these results to the theory of sectors in algebraic quantum field theory. This clarifies the notion of "quantized symmetries" in quantum fieldtheory. The reader is expected to be familiar with basic notions and resultsin algebra. The book is intended for research mathematicians, mathematical physicists and graduate students.
Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2019-08-23 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.
Download or read book Geometric Algebraic and Topological Methods for Quantum Field Theory written by Leonardo Cano and published by World Scientific. This book was released on 2016-09-06 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on lectures held at the 8th edition of the series of summer schools in Villa de Leyva since 1999, this book presents an introduction to topics of current interest at the interface of geometry, algebra, analysis, topology and theoretical physics. It is aimed at graduate students and researchers in physics or mathematics, and offers an introduction to the topics discussed in the two weeks of the summer school: operator algebras, conformal field theory, black holes, relativistic fluids, Lie groupoids and Lie algebroids, renormalization methods, spectral geometry and index theory for pseudo-differential operators.
Download or read book Motives Quantum Field Theory and Pseudodifferential Operators written by Alan L. Carey and published by American Mathematical Soc.. This book was released on 2010 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles related to the conference ``Motives, Quantum Field Theory, and Pseudodifferntial Operators'' held at Boston University in June 2008, with partial support from the Clay Mathematics Institute, Boston University, and the National Science Foundation. There are deep but only partially understood connections between the three conference fields, so this book is intended both to explain the known connections and to offer directions for further research. In keeping with the organization of the conference, this book contains introductory lectures on each of the conference themes and research articles on current topics in these fields. The introductory lectures are suitable for graduate students and new Ph.D.'s in both mathematics and theoretical physics, as well as for senior researchers, since few mathematicians are expert in any two of the conference areas. Among the topics discussed in the introductory lectures are the appearance of multiple zeta values both as periods of motives and in Feynman integral calculations in perturbative QFT, the use of Hopf algebra techniques for renormalization in QFT, and regularized traces of pseudodifferential operators. The motivic interpretation of multiple zeta values points to a fundamental link between motives and QFT, and there are strong parallels between regularized traces and Feynman integral techniques. The research articles cover a range of topics in areas related to the conference themes, including geometric, Hopf algebraic, analytic, motivic and computational aspects of quantum field theory and mirror symmetry. There is no unifying theory of the conference areas at present, so the research articles present the current state of the art pointing towards such a unification.
Download or read book Lectures on Algebraic Quantum Groups written by Ken Brown and published by Birkhäuser. This book was released on 2012-12-06 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.
Download or read book Local Quantum Physics written by Rudolf Haag and published by Springer. This book was released on 1992 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Classical and Quantum Theory of Fields written by Henryk Arodz and published by Springer. This book was released on 2017-04-22 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. It aims to deliver a unique combination of classical and quantum field theory in one compact course.
Download or read book Integrable Systems Quantum Groups and Quantum Field Theories written by Alberto Ibort and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Operator Algebras and Applications written by David E. Evans and published by Cambridge University Press. This book was released on 1989 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: These volumes form an authoritative statement of the current state of research in Operator Algebras. They consist of papers arising from a year-long symposium held at the University of Warwick. Contributors include many very well-known figures in the field.
