Differential Topology and Quantum Field Theory

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. Key Features • 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 Audience: 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. Covers elliptic differential and pseudo-differential operators, Atiyah-Singer index theory, topological quantum field theory, string theory, and knot theory. This book treats differential geometry, differential topology, and quantum field theory. It tackles problems of quantum field theory using differential topology as a tool. In this chapter we survey, in an informal way, some of the principal techniques used in topology.