Differential Topology and Quantum Field Theory

Differential Topology and Quantum Field Theory
Author :
Publisher : Elsevier
Total Pages : 404
Release :
ISBN-10 : 0125140762
ISBN-13 : 9780125140768
Rating : 4/5 (62 Downloads)

Synopsis Differential Topology and Quantum Field Theory by : Charles Nash

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

Geometric and Topological Methods for Quantum Field Theory

Geometric and Topological Methods for Quantum Field Theory
Author :
Publisher : American Mathematical Soc.
Total Pages : 272
Release :
ISBN-10 : 9780821840627
ISBN-13 : 0821840622
Rating : 4/5 (27 Downloads)

Synopsis Geometric and Topological Methods for Quantum Field Theory by : Sylvie Paycha

This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures): Anomalies and noncommutative geometry, Deformation quantisation and Poisson algebras, Topological quantum field theory and orbifolds. These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.

Topological Quantum Field Theory and Four Manifolds

Topological Quantum Field Theory and Four Manifolds
Author :
Publisher : Springer Science & Business Media
Total Pages : 235
Release :
ISBN-10 : 9781402031779
ISBN-13 : 1402031777
Rating : 4/5 (79 Downloads)

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

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.

Geometry and Quantum Field Theory

Geometry and Quantum Field Theory
Author :
Publisher : American Mathematical Soc.
Total Pages : 476
Release :
ISBN-10 : 0821886835
ISBN-13 : 9780821886830
Rating : 4/5 (35 Downloads)

Synopsis Geometry and Quantum Field Theory by : Daniel S. Freed

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.

Lectures on Field Theory and Topology

Lectures on Field Theory and Topology
Author :
Publisher : American Mathematical Soc.
Total Pages : 202
Release :
ISBN-10 : 9781470452063
ISBN-13 : 1470452065
Rating : 4/5 (63 Downloads)

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

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.

Conformal Field Theory and Topology

Conformal Field Theory and Topology
Author :
Publisher : American Mathematical Soc.
Total Pages : 188
Release :
ISBN-10 : 082182130X
ISBN-13 : 9780821821305
Rating : 4/5 (0X Downloads)

Synopsis Conformal Field Theory and Topology by : Toshitake Kohno

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.

Topology, Geometry and Quantum Field Theory

Topology, Geometry and Quantum Field Theory
Author :
Publisher : Cambridge University Press
Total Pages : 596
Release :
ISBN-10 : 0521540496
ISBN-13 : 9780521540490
Rating : 4/5 (96 Downloads)

Synopsis Topology, Geometry and Quantum Field Theory by : Ulrike Luise Tillmann

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.

Geometric and Algebraic Topological Methods in Quantum Mechanics

Geometric and Algebraic Topological Methods in Quantum Mechanics
Author :
Publisher : World Scientific
Total Pages : 715
Release :
ISBN-10 : 9789812701268
ISBN-13 : 9812701265
Rating : 4/5 (68 Downloads)

Synopsis Geometric and Algebraic Topological Methods in Quantum Mechanics by : G. Giachetta

In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry''s geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.

A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics

A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics
Author :
Publisher : Morgan & Claypool Publishers
Total Pages : 171
Release :
ISBN-10 : 9781643273747
ISBN-13 : 1643273744
Rating : 4/5 (47 Downloads)

Synopsis A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics by : Antonio Sergio Teixeira Pires

In the last years there have been great advances in the applications of topology and differential geometry to problems in condensed matter physics. Concepts drawn from topology and geometry have become essential to the understanding of several phenomena in the area. Physicists have been creative in producing models for actual physical phenomena which realize mathematically exotic concepts and new phases have been discovered in condensed matter in which topology plays a leading role. An important classification paradigm is the concept of topological order, where the state characterizing a system does not break any symmetry, but it defines a topological phase in the sense that certain fundamental properties change only when the system passes through a quantum phase transition. The main purpose of this book is to provide a brief, self-contained introduction to some mathematical ideas and methods from differential geometry and topology, and to show a few applications in condensed matter. It conveys to physicists the basis for many mathematical concepts, avoiding the detailed formality of most textbooks.

Dirichlet Branes and Mirror Symmetry

Dirichlet Branes and Mirror Symmetry
Author :
Publisher : American Mathematical Soc.
Total Pages : 698
Release :
ISBN-10 : 9780821838488
ISBN-13 : 0821838482
Rating : 4/5 (88 Downloads)

Synopsis Dirichlet Branes and Mirror Symmetry by :

Research in string theory has generated a rich interaction with algebraic geometry, with exciting work that includes the Strominger-Yau-Zaslow conjecture. This monograph builds on lectures at the 2002 Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string theory and algebraic geometry.