Differential Topology and Quantum Field Theory


  • Charles Nash, St. Patrick's College, Maynooth, Ireland

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.
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Graduate students and research workers in theoretical physics, high energy physics, particularly quantum field theorists. Graduate students in mathematics doing differential geometry or topology. Theoretical physicists in statistical mechanics or solid state theory.


Book information

  • Published: October 1992
  • ISBN: 978-0-12-514076-8

Table of Contents

A Topological Preliminary. Elliptic Operators. Cohomology of Sheaves and Bundles. Index Theory for Elliptic Operators. Some Algebraic Geometry. Infinite Dimensional Groups. Morse Theory. Instantons and Monopoles. The Elliptic Geometry of Strings. Anomalies. Conformal Quantum Field Theories. Topological Quantum Field Theories. References.