Reference for Feynman-Kac

Please see p.282 of the following ref, it does not call it Feynman-Kac Formula but the whole section 5 is discussing it. It formalized the diffusion using a tensor field over a manifold which is the most general and in-depth treatment from stochastic equation perspective that I know of.

Ikeda, Nobuyuki, and Shinzo Watanabe. Stochastic differential equations and diffusion processes. Vol. 24. Elsevier, 2014.

that is also where I learnt the material from.

A rigorous treatment of the Feynman-Kac formula is given in the chapter 3 of the book "Quantum Physics: A Functional Integral Point of View" by J. Glimm and A. Jaffe: http://www.springer.com/in/book/9780387964775