A Mathematical Definition of Path Integrals on Symplectic Manifolds

Abstract

We give a mathematical definition of some path integrals, emphasizing those relevant to the quantization of symplectic manifolds (and more generally, Poisson manifolds) $\unicode{x2013}$ in particular, the coherent state path integral. We show that Kähler manifolds provide many computable examples and we emphasize those whose Bergman kernel is constant along the diagonal.

23 pages. Some edits to examples, exposition, references in second version