Differential Topology and Quantum Field TheoryThe 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.
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Contents
CHAPTER | 1 |
Elliptic Operators | 27 |
Cohomology of Sheaves and Bundles | 56 |
27 | 64 |
Fredholm operators and KX | 88 |
CHAPTER V | 137 |
The moduli space | 152 |
7 | 165 |
CHAPTER VII | 192 |
CHAPTER VIII | 216 |
5 | 250 |
CHAPTER IX | 259 |
CHAPTER XI | 301 |
Operator products fusion rules and axiomatics | 313 |
Topological Quantum Field Theories | 322 |
| 361 | |
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Common terms and phrases
action acts algebra anomaly apply base boundary calculation called chapter Chern closed cohomology compact complex compute condition conformal connection consider construct coordinates corresponding critical points defined definition denote determined difference differential dimension dimensional discussion element elliptic elliptic operator equation equivalence exact example existence expression exterior derivative fact fibre field finite formula function gauge given gives Hence holomorphic homotopy integral introduce invariant isomorphism K-theory known line bundle manifold means metric natural obtain operator polynomial positive provides rank referred relation replace representation require respectively restriction result Rham sheaf Sign simply smooth space structure surface symbol theorem theory topological transformation trivial usual valued vanishes vector bundles write zero