Conformal Field Theory and Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Conformal Field Theory and Topology write by Toshitake Kohno. This book was released on 2002. Conformal Field Theory and Topology available 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.
Conformal Field Theory and Topology
Conformal Field Theory and Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Conformal Field Theory and Topology write by Toshitake Kohno. This book was released on 2002. Conformal Field Theory and Topology available in PDF, EPUB and Kindle. The aim of this book is to provide the reader with an introduction to conformal field theory and its applications to topology. The author starts with a description of geometric aspects of conformal field theory based on loop groups. By means of the holonomy of conformal field theory he defines topological invariants for knots and 3-manifolds. He also gives a brief treatment of Chern-Simons perturbation theory.
Topology, Geometry and Quantum Field Theory
Topology, Geometry and Quantum Field Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topology, Geometry and Quantum Field Theory write by Ulrike Luise Tillmann. This book was released on 2004-06-28. Topology, Geometry and Quantum Field Theory available 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.
Lectures on Field Theory and Topology
Lectures on Field Theory and Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Field Theory and Topology write by Daniel S. Freed. This book was released on 2019-08-23. Lectures on Field Theory and Topology available 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.
Differential Topology and Quantum Field Theory
Differential Topology and Quantum Field Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Topology and Quantum Field Theory write by Charles Nash. This book was released on 1991. Differential Topology and Quantum Field Theory available 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
