A Mathematical Definition of Path Integrals on Symplectic Manifolds

We give a mathematical definition of some path integrals, emphasizing those relevant to the quantization of symplectic manifolds (and more generally, Poisson manifolds) $\text{unicode}x2013$ 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.