Download or read book Homotopy Quantum Field Theory written by Vladimir G. Turaev and published by European Mathematical Society. This book was released on 2010 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Buchdruckerei Passavia written by and published by . This book was released on 1954 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Homotopical Quantum Field Theory written by Donald Yau and published by World Scientific. This book was released on 2019-11-11 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a general and powerful definition of homotopy algebraic quantum field theory and homotopy prefactorization algebra using a new coend definition of the Boardman-Vogt construction for a colored operad. All of their homotopy coherent structures are explained in details, along with a comparison between the two approaches at the operad level. With chapters on basic category theory, trees, and operads, this book is self-contained and is accessible to graduate students.
Download or read book Quantum Field Theory Perspective and Prospective written by Cécile Dewitt-Morette and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been said that `String theorists talk to string theorists and everyone else wonders what they are saying'. This book will be a great help to those researchers who are challenged by modern quantum field theory. Quantum field theory experienced a renaissance in the late 1960s. Here, participants in the Les Houches sessions of 1970/75, now key players in quantum field theory and its many impacts, assess developments in their field of interest and provide guidance to young researchers challenged by these developments, but overwhelmed by their complexities. The book is not a textbook on string theory, rather it is a complement to Polchinski's book on string theory. It is a survey of current problems which have their origin in quantum field theory.
Download or read book Homotopy Quantum Field Theory and Quantum Groups written by Neha Gupta and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantum Field Theory and Topology written by Albert S. Schwarz and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. It has many applications, first of all in quantum field theory, but increasingly also in other areas of physics. The main focus of this book is on the results of quantum field theory that are obtained by topological methods. Some aspects of the theory of condensed matter are also discussed. Part I is an introduction to quantum field theory: it discusses the basic Lagrangians used in the theory of elementary particles. Part II is devoted to the applications of topology to quantum field theory. Part III covers the necessary mathematical background in summary form. The book is aimed at physicists interested in applications of topology to physics and at mathematicians wishing to familiarize themselves with quantum field theory and the mathematical methods used in this field. It is accessible to graduate students in physics and mathematics.
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 Hqfts and Quantum Groups written by Neha Gupta and published by LAP Lambert Academic Publishing. This book was released on 2012 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The thesis is divided into two parts one for dimension 2 and the other for dimension 3. Part one of the thesis generalizes the de nition of an n-dimensional HQFT in terms of a monoidal functor from a rigid symmetric monoidal category X Cobn to any monoidal category A. In particular, 2-dimensional HQFTs with target K(G,1) taking values in A are generated from any Turaev G-crossed system in A and vice-versa. This is the generalization of Turaev's theory into a purely categorical set-up. Part two of the thesis generalizes the concept of a group-coalgebra, Hopf group-coalgebra, crossed Hopf group-coalgebra and quasitriangular Hopf group-coalgebra over a group scheme. Quantum double of a crossed Hopf group-scheme coalgebra is constructed in the a ne case and conjectured for non-a ne case. We can construct 3-dimensional HQFTs from modular crossed G-categories. The category of representations of a quantum double of a crossed Hopf group-coalgebra is a ribbon(quasitriangular) crossed group-category. Hence generates 3-dimensional HQFTs under certain conditions if the category becomes modular. However, systematic nding of modular crossed G-categories is largely open."
Download or read book Mathematical Aspects of Quantum Field Theories written by Damien Calaque and published by Springer. This book was released on 2015-01-06 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantum Field Theory and Manifold Invariants written by Daniel S. Freed and published by American Mathematical Society, IAS/Park City Mathematics Institute. This book was released on 2021-12-02 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lectures from the Graduate Summer School “Quantum Field Theory and Manifold Invariants” held at Park City Mathematics Institute 2019. The lectures span topics in topology, global analysis, and physics, and they range from introductory to cutting edge. Topics treated include mathematical gauge theory (anti-self-dual equations, Seiberg-Witten equations, Higgs bundles), classical and categorified knot invariants (Khovanov homology, Heegaard Floer homology), instanton Floer homology, invertible topological field theory, BPS states and spectral networks. This collection presents a rich blend of geometry and topology, with some theoretical physics thrown in as well, and so provides a snapshot of a vibrant and fast-moving field. Graduate students with basic preparation in topology and geometry can use this volume to learn advanced background material before being brought to the frontiers of current developments. Seasoned researchers will also benefit from the systematic presentation of exciting new advances by leaders in their fields.
Download or read book Quantum Field Theory written by François Gelis and published by Cambridge University Press. This book was released on 2019-07-11 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Differential Topology and Quantum Field Theory written by Charles Nash and published by Elsevier. This book was released on 1991 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed and published by . This book was released on 2019 with total page 202 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.
Download or read book Advances in Topological Quantum Field Theory written by John M. Bryden and published by Springer Science & Business Media. This book was released on 2007-09-27 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Topology for Physicists written by Albert S. Schwarz and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. Topology has profound relevance to quantum field theory-for example, topological nontrivial solutions of the classical equa tions of motion (solitons and instantons) allow the physicist to leave the frame work of perturbation theory. The significance of topology has increased even further with the development of string theory, which uses very sharp topologi cal methods-both in the study of strings, and in the pursuit of the transition to four-dimensional field theories by means of spontaneous compactification. Im portant applications of topology also occur in other areas of physics: the study of defects in condensed media, of singularities in the excitation spectrum of crystals, of the quantum Hall effect, and so on. Nowadays, a working knowledge of the basic concepts of topology is essential to quantum field theorists; there is no doubt that tomorrow this will also be true for specialists in many other areas of theoretical physics. The amount of topological information used in the physics literature is very large. Most common is homotopy theory. But other subjects also play an important role: homology theory, fibration theory (and characteristic classes in particular), and also branches of mathematics that are not directly a part of topology, but which use topological methods in an essential way: for example, the theory of indices of elliptic operators and the theory of complex manifolds.
Download or read book Quantum Field Theory Of Point Particles And Strings written by Brian Hatfield and published by CRC Press. This book was released on 2018-03-09 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 2018. The emphasis of the book is calculational, and most computations are presented in step-by-step detail. The book is unique in that it develops all three representations of quantum field theory (operator, functional Schr dinger, and path integral) for point particles and strings. In many cases, identical results are worked out in each representation to emphasize the representation-independent structures of quantum field theory
Download or read book Two dimensional Extended Homotopy Quantum Field Theories written by Kü̈rşat Sözer and published by . This book was released on 2020 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: We define two-dimensional extended homotopy quantum field theories (E-HQFTs) with aspherical targets and classify them. When the target of E-HQFT is chosen to be a K(G,1)-space, we classify oriented E-HQFTs taking values in the symmetric monoidal bicategory of algebras, bimodules, and bimodule maps by certain Frobenius G-algebras called quasi-biangular G-algebras. As an application, for any discrete group G, we verify a special case of the (G x SO(2))-structured cobordism hypothesis due to Lurie.
