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 Introduction to Algebraic Quantum Field Theory written by S.S. Horuzhy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi ..., si j'avait su comment en revenir, One service mathematics has rendered the human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs, on the topmost shel.f next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

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 Ten Lectures on Operator Algebras written by William Arveson and published by American Mathematical Soc.. This book was released on 1984 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains expanded versions of ten lectures delivered at Texas Tech University in the summer of 1983. The operator algebras of the title are nonselfadjoint algebras of operators on Hilbert space.

Download or read book Quantum Symmetries on Operator Algebras written by David Emrys Evans and published by . This book was released on 1998 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last 20 years, the study of operator algebras has developed from a branch of functional analysis to a central field of mathematics with applications and connections with different areas in both pure mathematics (foliations, index theory, K-theory, cyclic homology, affine Kac--Moody algebras, quantum groups, low dimensional topology) and mathematical physics (integrable theories, statistical mechanics, conformal field theories and the string theories of elementary particles). The theory of operator algebras was initiated by von Neumann and Murray as a tool for studying group representations and as a framework for quantum mechanics, and has since kept in touch with its roots in physics as a framework for quantum statistical mechanics and the formalism of algebraic quantum field theory. However, in 1981, the study of operator algebras took a new turn with the introduction by Vaughan Jones of subfactor theory and remarkable connections were found with knot theory, 3-manifolds, quantum groups and integrable systems in statistical mechanics and conformal field theory. The purpose of this book, one of the first in the area, is to look at these combinatorial-algebraic developments from the perspective of operator algebras; to bring the reader to the frontline of research with the minimum of prerequisites from classical theory.

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 Lectures on Operator Theory written by B. V. Rajarama Bhat and published by American Mathematical Soc.. This book was released on 1999 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book resulted from the lectures held at The Fields Institute (Waterloo, ON, Canada). Leading international experts presented current results on the theory of C*-algebras and von Neumann algebras, together with recent work on the classification of C*-algebras. Much of the material in the book is appearing here for the first time and is not available elsewhere in the literature.

Download or read book Lectures on Representation Theory and Knizhnik Zamolodchikov Equations written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 1998 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is devoted to mathematical structures arising in conformal field theory and the q-deformations. The authors give a self-contained exposition of the theory of Knizhnik-Zamolodchikov equations and related topics. No previous knowledge of physics is required. The text is suitable for a one-semester graduate course and is intended for graduate students and research mathematicians interested in mathematical physics.

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 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 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 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 360 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 Computer Algebra in Quantum Field Theory written by Carsten Schneider and published by Springer Science & Business Media. This book was released on 2013-10-05 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including most recent developments. Besides that, the collection of articles also serves as an up-to-date handbook of available algorithms/software that are commonly used or might be useful in the fields of mathematics, physics or other sciences.

Download or read book Reality and Measurement in Algebraic Quantum Theory written by Masanao Ozawa and published by Springer. This book was released on 2018-11-02 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers based on presentations at the “Nagoya Winter Workshop 2015: Reality and Measurement in Algebraic Quantum Theory (NWW 2015)”, held in Nagoya, Japan, in March 2015. The foundations of quantum theory have been a source of mysteries, puzzles, and confusions, and have encouraged innovations in mathematical languages to describe, analyze, and delineate this wonderland. Both ontological and epistemological questions about quantum reality and measurement have been placed in the center of the mysteries explored originally by Bohr, Heisenberg, Einstein, and Schrödinger. This volume describes how those traditional problems are nowadays explored from the most advanced perspectives. It includes new research results in quantum information theory, quantum measurement theory, information thermodynamics, operator algebraic and category theoretical foundations of quantum theory, and the interplay between experimental and theoretical investigations on the uncertainty principle. This book is suitable for a broad audience of mathematicians, theoretical and experimental physicists, and philosophers of science.

Download or read book Lectures on Matrix Field Theory written by Badis Ydri and published by Springer. This book was released on 2016-11-22 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries. The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is treated in great detail, with a separate chapter on the multitrace approach. The last chapter offers a general introduction to non-commutative gauge theories, while two appendices round out the text. Primarily written as a self-study guide for postgraduate students – with the aim of pedagogically introducing them to key analytical and numerical tools, as well as useful physical models in applications – these lecture notes will also benefit experienced researchers by providing a reference guide to the fundamentals of non-commutative field theory with an emphasis on matrix models and fuzzy geometries.

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.