Morse Theory in Field Theory

Abstract

We describe a geometrical interpretation of Topological Quantum Mechanics (TQM). Basics of the general topological theories are briefly discussed as well. The appropriate correspondence between objects of TQM and the algebraic topology is pointed out. It is proved that the correlators in TQM can be expressed via intersection numbers of some submanifolds of the target space with paths of steepest descent between critical points. Another correspondence is only conjectured, namely the correspondence between correlators and an integral of Massey products on cohomology classes of the target manifold.