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Differential Topology and Quantum Field Theory by Charles Nash
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About this book :-
Differential Topology and Quantum Field Theory written by
Charles Nash
The twentieth century has been witness to a great burgeoning of mathematics and physics. In the early part of the centry the new physical theories of relativity and quantum mechanics made extensive use of the machinery of differential goemetry and Hilbert spaces. Some time later quantum field theory begin to pose difficult mathematical problems. As a partial response to this the subject of axiomatic quantum field theory was born. The main thrust of this approach was to tackle the formidable problems of quantum field theory head on using the most powerful mathematical tools available the bulk of these tools being drawn from analysis. More recently there has been considerable evidence that the way forward in these problems is considerably illuminated if, in addition to analysis, one uses differential topology. There have also been advances in the differential topology of dimenstions there and four which have drawn extensively on physical sources, the principal source being Yang Mills theories.
Thus there has been a genuinely two sided interaction between the worlds of mathematics and mathematical physics. This book is intended as an informal introduction to some of these mathematical and physical indeas. It should be of use to graduate students and other research workers talking an interest in this material for the first time (Charles Nash)
Book Detail :-
Title: Differential Topology and Quantum Field Theory
Edition:
Author(s): Charles Nash
Publisher: Academic Press
Series:
Year: 1991
Pages: 398
Type: PDF
Language: English
ISBN: 9780125140751,0125140754
Country: US
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About Author :-
Author Charles Nash is a Professor of Mathematics at the National University of Ireland. His main research interests are quantum field theory and differential topology.
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Book Contents :-
Differential Topology and Quantum Field Theory written by
Charles Nash
cover the following topics.
1. A Topological Preliminary
2. Elliptic Operators
3. Cohomology of Sheaves and Bundles
4. Index Theory for Elliptic Operators
5. Some Algebraic Geometry
6. Infinite Dimensional Groups
7. Morse Theory
8. Instantons and Monoploes
9. The Ellipic Geometry of Strings
10. Anomalies
11. Conformal Quantum Field Theories
12. Topological Quantum Field Theories
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