Welcome to our reading store! Remy reads books with you！

Preface
The emergence of topological quantum field theory has been one of the most important breakthroughs which have occurred in the context of mathematical physics in the last century, a century characterized by independent 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 mathematics. Topological quantum field theories constitute the core of these phenomena, although the main driving force behind it has been the enormous effort 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 profit from each other. Although the most striking results have appeared on the mathematical side, theoretical physics has clearly also benefitted, since the corresponding developments have helped better to understand aspects of the fundamentals of field and string theory.
Topology has played an important role in the study of quantum mechanics since the late fifties, after discovering that global effects are important in
physical phenomena. Many aspects of topology have become ordinary elements in studies in quantum mechanics as well as in quantum field theory and in string theory. The origin of topological quantum field theory can be traced back to 1982, although the term itself appeared for the first time in 1987. In 1982 E. Witten studied supersymmetric quantum mechanics and supersymmetric sigma models providing a framework that led to a generalization of Morse theory. This framework was later considered by A. Floer who constructed its mathematical setting and enlarged it to a more general context. This, in turn, was reconsidered by E. Witten who, influenced by M. Atiyah, proposed the first topological quantum field theory itself in 1987. His construction consisted of a quantum field theory representation of the theory of Donaldson invariants on four-manifolds proposed in 1982.