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Differential Topology and Quantum Field Theory

1991 Mathematics
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Release : 1991
Genre : Mathematics
Kind : eBook
Book Rating : 768/5 ( reviews)

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Book Synopsis Differential Topology and Quantum Field Theory by : Charles Nash

Download or read book Differential Topology and Quantum Field Theory written by Charles Nash. This book was released on 1991. 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

Differential Topology and Quantum Field Theory

1991 Mathematics
Download Differential Topology and Quantum Field Theory PDF Online Free

Author :
Release : 1991
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Differential Topology and Quantum Field Theory by : Charles Nash

Download or read book Differential Topology and Quantum Field Theory written by Charles Nash. This book was released on 1991. 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 on quantum field theory are presented in a style reflecting the genuinely two-sided interaction between mathematical physics and applied mathematics. The author, following on from his previous work, covers elliptic differential and pseudo-differential operators, Atiyah-Singer Index theory, Morse theory, instantons and monopoles, topological quantim 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. -- from back cover

Topological Quantum Field Theory and Four Manifolds

2007-07-18 Science
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Release : 2007-07-18
Genre : Science
Kind : eBook
Book Rating : 777/5 ( reviews)

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Book Synopsis Topological Quantum Field Theory and Four Manifolds by : Jose Labastida

Download or read book Topological Quantum Field Theory and Four Manifolds written by Jose Labastida. This book was released on 2007-07-18. Available in PDF, EPUB and Kindle. Book excerpt: The emergence of topological quantum ?eld theory has been one of the most important breakthroughs which have occurred in the context of ma- ematical physics in the last century, a century characterizedbyindependent developments of the main ideas in both disciplines, physics and mathematics, which has concluded with two decades of strong interaction between them, where physics, as in previous centuries, has acted as a source of new mat- matics. Topological quantum ?eld theories constitute the core of these p- nomena, although the main drivingforce behind it has been the enormous e?ort made in theoretical particle physics to understand string theory as a theory able to unify the four fundamental interactions observed in nature. These theories set up a new realm where both disciplines pro?t from each other. Although the most striking results have appeared on the mathema- calside,theoreticalphysicshasclearlyalsobene?tted,sincethecorresponding developments have helped better to understand aspects of the fundamentals of ?eld and string theory.

Conformal Field Theory and Topology

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 305/5 ( reviews)

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Book Synopsis Conformal Field Theory and Topology by : Toshitake Kohno

Download or read book Conformal Field Theory and Topology written by Toshitake Kohno. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on Field Theory and Topology

2019-08-23 Algebraic topology
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Release : 2019-08-23
Genre : Algebraic topology
Kind : eBook
Book Rating : 065/5 ( reviews)

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Book Synopsis Lectures on Field Theory and Topology by : Daniel S. Freed

Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed. This book was released on 2019-08-23. 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.

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