Advances In Algebraic Quantum Field Theory

Author : Romeo Brunetti,Claudio Dappiaggi,Klaus Fredenhagen,Jakob Yngvason
Publisher : Springer
Page : 453 pages
File Size : 50,7 Mb
Release : 2015-09-04
Category : Science
ISBN : 9783319213538

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Advances in Algebraic Quantum Field Theory by Romeo Brunetti,Claudio Dappiaggi,Klaus Fredenhagen,Jakob Yngvason Pdf

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.

Author : Romeo Brunetti,Claudio Dappiaggi,Klaus Fredenhagen,Jakob Yngvason
Publisher : Unknown
Page : 128 pages
File Size : 48,8 Mb
Release : 2015
Category : Electronic
ISBN : 3319213547

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Advances in Algebraic Quantum Field Theory by Romeo Brunetti,Claudio Dappiaggi,Klaus Fredenhagen,Jakob Yngvason Pdf

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.

Author : Kasia Rejzner
Publisher : Springer
Page : 180 pages
File Size : 46,7 Mb
Release : 2016-03-16
Category : Science
ISBN : 9783319259017

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Perturbative Algebraic Quantum Field Theory by Kasia Rejzner Pdf

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.

Author : Felix Finster,Olaf Müller,Marc Nardmann,Jürgen Tolksdorf,Eberhard Zeidler
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 50,6 Mb
Release : 2012-02-08
Category : Mathematics
ISBN : 9783034800433

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Quantum Field Theory and Gravity by Felix Finster,Olaf Müller,Marc Nardmann,Jürgen Tolksdorf,Eberhard Zeidler Pdf

One of the most challenging problems of contemporary theoretical physics is the mathematically rigorous construction of a theory which describes gravitation and the other fundamental physical interactions within a common framework. The physical ideas which grew from attempts to develop such a theory require highly advanced mathematical methods and radically new physical concepts. This book presents different approaches to a rigorous unified description of quantum fields and gravity. It contains a carefully selected cross-section of lively discussions which took place in autumn 2010 at the fifth conference "Quantum field theory and gravity - Conceptual and mathematical advances in the search for a unified framework" in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.

Author : S. S. Horuzhy
Publisher : Unknown
Page : 316 pages
File Size : 54,8 Mb
Release : 1990-06-30
Category : Electronic
ISBN : 9400911807

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Introduction to Algebraic Quantum Field Theory by S. S. Horuzhy Pdf

Author : Damien Calaque,Thomas Strobl
Publisher : Springer
Page : 556 pages
File Size : 45,6 Mb
Release : 2015-01-06
Category : Science
ISBN : 9783319099491

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Mathematical Aspects of Quantum Field Theories by Damien Calaque,Thomas Strobl Pdf

Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.

Author : John M. Bryden
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 55,7 Mb
Release : 2007-09-27
Category : Mathematics
ISBN : 9781402027727

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Advances in Topological Quantum Field Theory by John M. Bryden Pdf

This volume is the conference proceedings of the NATO ARW during August 2001 at Kananaskis Village, Canada on 'New Techniques in Topological Quantum Field Theory'. This conference brought together specialists from a number of different fields all related to Topological Quantum Field Theory. The theme of this conference was to attempt to find new methods in quantum topology from the interaction with specialists in these other fields. The featured articles include papers by V. Vassiliev on combinatorial formulas for cohomology of spaces of Knots, the computation of Ohtsuki series by N. Jacoby and R. Lawrence, and a paper by M. Asaeda and J. Przytycki on the torsion conjecture for Khovanov homology by Shumakovitch. Moreover, there are articles on more classical topics related to manifolds and braid groups by such well known authors as D. Rolfsen, H. Zieschang and F. Cohen.

Author : Jürg Fröhlich,Thomas Kerler
Publisher : Springer
Page : 438 pages
File Size : 41,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540476115

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Quantum Groups, Quantum Categories and Quantum Field Theory by Jürg Fröhlich,Thomas Kerler Pdf

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.

Author : Rudolf Haag
Publisher : Springer
Page : 384 pages
File Size : 47,6 Mb
Release : 1992
Category : Science
ISBN : UOM:39015025241590

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Local Quantum Physics by Rudolf Haag Pdf

Author : Vladimir G. Turaev
Publisher : European Mathematical Society
Page : 300 pages
File Size : 55,7 Mb
Release : 2010
Category : EMS tracts in mathematics
ISBN : 3037190868

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Homotopy Quantum Field Theory by Vladimir G. Turaev Pdf

Homotopy Quantum Field Theory (HQFT) is a branch of Topological Quantum Field Theory founded by E. Witten and M. Atiyah. It applies ideas from theoretical physics to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a fixed target space. This book is the first systematic exposition of Homotopy Quantum Field Theory. It starts with a formal definition of an HQFT and provides examples of HQFTs in all dimensions. The main body of the text is focused on $2$-dimensional and $3$-dimensional HQFTs. A study of these HQFTs leads to new algebraic objects: crossed Frobenius group-algebras, crossed ribbon group-categories, and Hopf group-coalgebras. These notions and their connections with HQFTs are discussed in detail. The text ends with several appendices including an outline of recent developments and a list of open problems. Three appendices by M. Muger and A. Virelizier summarize their work in this area. The book is addressed to mathematicians, theoretical physicists, and graduate students interested in topological aspects of quantum field theory. The exposition is self-contained and well suited for a one-semester graduate course. Prerequisites include only basics of algebra and topology.

Author : Alexander Cardona,Carolina Neira-Jiménez,Hernán Ocampo,Sylvie Paycha,Andrés F Reyes-Lega
Publisher : World Scientific
Page : 380 pages
File Size : 53,9 Mb
Release : 2013-11-15
Category : Mathematics
ISBN : 9789814460064

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Geometric, Algebraic and Topological Methods for Quantum Field Theory by Alexander Cardona,Carolina Neira-Jiménez,Hernán Ocampo,Sylvie Paycha,Andrés F Reyes-Lega Pdf

Based on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics. It is aimed at graduate students in physics or mathematics with interests in geometric, algebraic as well as topological methods and their applications to quantum field theory. This volume contains the written notes corresponding to lectures given by experts in the field. They cover current topics of research in a way that is suitable for graduate students of mathematics or physics interested in the recent developments and interactions between geometry, topology and physics. The book also contains contributions by younger participants, displaying the ample range of topics treated in the school. A key feature of the present volume is the provision of a pedagogical presentation of rather advanced topics, in a way which is suitable for both mathematicians and physicists. Contents:Lectures:Spectral Geometry (B Iochum)Index Theory for Non-compact G-manifolds (M Braverman and L Cano)Generalized Euler Characteristics, Graph Hypersurfaces, and Feynman Periods (P Aluffi)Gravitation Theory and Chern-Simons Forms (J Zanelli)Noncommutative Geometry Models for Particle Physics (M Marcolli)Noncommutative Spacetimes and Quantum Physics (A P Balachandran)Integrability and the AdS/CFT Correspondence (M Staudacher)Compactifications of String Theory and Generalized Geometry (M Graña and H Triendl)Short Communications:Groupoids and Poisson Sigma Models with Boundary (A Cattaneo and I Contreras)A Survey on Orbifold String Topology (A Angel)Grothendieck Ring Class of Banana and Flower Graphs (P Morales-Almazán)On the Geometry Underlying a Real Lie Algebra Representation (R Vargas Le-Bert) Readership: Researchers in geometry and topology, mathematical physics. Keywords:Geometry;Topology;Geometric Methods;Quantum Field Theory;Renormalization;Index Theory;Noncommutative Geometry;Quantization;String Theory;Key Features:Unique style aimed at a mixed readership of mathematicians and physicistsIdeal for self-study or use in advanced courses or seminars

Author : John M. Bryden
Publisher : Unknown
Page : 364 pages
File Size : 42,7 Mb
Release : 2014-09-01
Category : Electronic
ISBN : 9401751374

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Advances in Topological Quantum Field Theory by John M. Bryden Pdf

Author : Michael Dütsch
Publisher : Springer
Page : 536 pages
File Size : 45,9 Mb
Release : 2019-03-18
Category : Mathematics
ISBN : 9783030047382

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From Classical Field Theory to Perturbative Quantum Field Theory by Michael Dütsch Pdf

This book develops a novel approach to perturbative quantum field theory: starting with a perturbative formulation of classical field theory, quantization is achieved by means of deformation quantization of the underlying free theory and by applying the principle that as much of the classical structure as possible should be maintained. The resulting formulation of perturbative quantum field theory is a version of the Epstein-Glaser renormalization that is conceptually clear, mathematically rigorous and pragmatically useful for physicists. The connection to traditional formulations of perturbative quantum field theory is also elaborated on, and the formalism is illustrated in a wealth of examples and exercises.

Author : Charles Nash
Publisher : Elsevier
Page : 404 pages
File Size : 46,6 Mb
Release : 1991
Category : Mathematics
ISBN : 0125140762

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Differential Topology and Quantum Field Theory by Charles Nash Pdf

The remarkable developments in differential topology and how these recent advances have been applied as a primary research tool in quantum field theory are presented here in a style reflecting the genuinely two-sided interaction between mathematical physics and applied mathematics. The author, following his previous work (Nash/Sen: Differential Topology for Physicists, Academic Press, 1983), covers elliptic differential and pseudo-differential operators, Atiyah-Singer index theory, topological quantum field theory, string theory, and knot theory. The explanatory approach serves to illuminate and clarify these theories for graduate students and research workers entering the field for the first time. Treats differential geometry, differential topology, and quantum field theory Includes elliptic differential and pseudo-differential operators, Atiyah-Singer index theory, topological quantum field theory, string theory, and knot theory Tackles problems of quantum field theory using differential topology as a tool

Author : Thomas-Paul Hack
Publisher : Springer
Page : 0 pages
File Size : 48,7 Mb
Release : 2015-08-27
Category : Science
ISBN : 331921893X

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Cosmological Applications of Algebraic Quantum Field Theory in Curved Spacetimes by Thomas-Paul Hack Pdf

This book provides a largely self-contained and broadly accessible exposition on two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according to the Standard Model of Cosmology; and a fundamental study of the perturbations in inflation. The two central sections of the book dealing with these applications are preceded by sections providing a pedagogical introduction to the subject. Introductory material on the construction of linear QFTs on general curved spacetimes with and without gauge symmetry in the algebraic approach, physically meaningful quantum states on general curved spacetimes, and the backreaction of quantum fields in curved spacetimes via the semiclassical Einstein equation is also given. The reader should have a basic understanding of General Relativity and QFT on Minkowski spacetime, but no background in QFT on curved spacetimes or the algebraic approach to QFT is required.>