Conformal Field Theory And Topology PDF Download
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| Author | : Toshitake Kohno |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 188 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 9780821821305 |
Download Conformal Field Theory and Topology Book in PDF, ePub and Kindle
Geometry and physics have been developed with a strong influence on each other. One of the most remarkable interactions between geometry and physics since 1980 has been an application of quantum field theory to topology and differential geometry. This book focuses on a relationship between two-dimensional quantum field theory and three-dimensional topology which has been studied intensively since the discovery of the Jones polynomial in the middle of the 1980s and Witten's invariantfor 3-manifolds derived from Chern-Simons gauge theory. An essential difficulty in quantum field theory comes from infinite-dimensional freedom of a system. Techniques dealing with such infinite-dimensional objects developed in the framework of quantum field theory have been influential in geometryas well. This book gives an accessible treatment for a rigorous construction of topological invariants originally defined as partition functions of fields on manifolds. The book is organized as follows: The Introduction starts from classical mechanics and explains basic background materials in quantum field theory and geometry. Chapter 1 presents conformal field theory based on the geometry of loop groups. Chapter 2 deals with the holonomy of conformal field theory. Chapter 3 treatsChern-Simons perturbation theory. The final chapter discusses topological invariants for 3-manifolds derived from Chern-Simons perturbation theory.
| Author | : Ulrike Luise Tillmann |
| Publisher | : Cambridge University Press |
| Total Pages | : 596 |
| Release | : 2004-06-28 |
| Genre | : Mathematics |
| ISBN | : 9780521540490 |
Download Topology, Geometry and Quantum Field Theory Book in PDF, ePub and Kindle
The symposium held in honour of the 60th birthday of Graeme Segal brought together leading physicists and mathematicians. Its topics were centred around string theory, M-theory, and quantum gravity on the one hand, and K-theory, elliptic cohomology, quantum cohomology and string topology on the other. Geometry and quantum physics developed in parallel since the recognition of the central role of non-abelian gauge theory in elementary particle physics in the late seventies and the emerging study of super-symmetry and string theory. With its selection of survey and research articles these proceedings fulfil the dual role of reporting on developments in the field and defining directions for future research. For the first time Graeme Segal's manuscript 'The definition of Conformal Field Theory' is published, which has been greatly influential over more than ten years. An introduction by the author puts it into the present context.
| Author | : Daniel S. Freed |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 186 |
| Release | : 2019-08-23 |
| Genre | : Algebraic topology |
| ISBN | : 1470452065 |
Download Lectures on Field Theory and Topology Book in PDF, ePub and Kindle
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.
| Author | : A. Kashiwara |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 492 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461207053 |
Download Topological Field Theory, Primitive Forms and Related Topics Book in PDF, ePub and Kindle
As the interaction of mathematics and theoretical physics continues to intensify, the theories developed in mathematics are being applied to physics, and conversely. This book centers around the theory of primitive forms which currently plays an active and key role in topological field theory (theoretical physics), but was originally developed as a mathematical notion to define a "good period mapping" for a family of analytic structures. The invited papers in this volume are expository in nature by participants of the Taniguchi Symposium on "Topological Field Theory, Primitive Forms and Related Topics" and the RIMS Symposium bearing the same title, both held in Kyoto. The papers reflect the broad research of some of the world's leading mathematical physicists, and should serve as an excellent resource for researchers as well as graduate students of both disciplines.
| Author | : Charles Nash |
| Publisher | : Elsevier |
| Total Pages | : 404 |
| Release | : 1991 |
| Genre | : Mathematics |
| ISBN | : 9780125140768 |
Download Differential Topology and Quantum Field Theory Book in PDF, ePub and Kindle
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 | : Martin Schottenloher |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 153 |
| Release | : 2008-09-15 |
| Genre | : Science |
| ISBN | : 3540706909 |
Download A Mathematical Introduction to Conformal Field Theory Book in PDF, ePub and Kindle
Part I gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. The conformal groups are determined and the appearence of the Virasoro algebra in the context of the quantization of two-dimensional conformal symmetry is explained via the classification of central extensions of Lie algebras and groups. Part II surveys more advanced topics of conformal field theory such as the representation theory of the Virasoro algebra, conformal symmetry within string theory, an axiomatic approach to Euclidean conformally covariant quantum field theory and a mathematical interpretation of the Verlinde formula in the context of moduli spaces of holomorphic vector bundles on a Riemann surface.
| Author | : Michio Kaku |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 542 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461205034 |
Download Strings, Conformal Fields, and M-Theory Book in PDF, ePub and Kindle
Building on the foundations laid in his Introduction to Superstrings and M Theory, Professor Kaku discusses such topics as the classification of conformal string theories, knot theory, the Yang-Baxter relation, quantum groups, and the insights into 11-dimensional strings recently obtained from M-theory. New chapters discuss such topics as Seiberg-Witten theory, M theory and duality, and D-branes. Throughout, the author conveys the vitality of the current research and places readers at its forefront. Several chapters reviewing the fundamentals of string theory, making the presentation of the material self-contained while keeping overlap with the earlier book to a minimum.
| Author | : Michio Kaku |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 544 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1468403974 |
Download Strings, Conformal Fields, and Topology Book in PDF, ePub and Kindle
Following on the foundations laid in his earlier book "Introduction to Superstrings", Professor Kaku discusses such topics as the classification of conformal string theories, the non-polynomial closed string field theory, matrix models, and topological field theory. The presentation of the material is self-contained, and several chapters review material expounded in the earlier book. This book provides students with an understanding of the main areas of current progress in string theory, placing the reader at the forefront of current research.
| Author | : Michio Kaku |
| Publisher | : |
| Total Pages | : 560 |
| Release | : 1991 |
| Genre | : Mathematics |
| ISBN | : |
Download Strings, Conformal Fields, and Topology Book in PDF, ePub and Kindle
| Author | : Daniel S. Freed |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 476 |
| Release | : 1995 |
| Genre | : Science |
| ISBN | : 9780821886830 |
Download Geometry and Quantum Field Theory Book in PDF, ePub and Kindle
The first title in a new series, this book explores topics from classical and quantum mechanics and field theory. The material is presented at a level between that of a textbook and research papers making it ideal for graduate students. The book provides an entree into a field that promises to remain exciting and important for years to come.
