Stochastic quantization on Lorentzian manifolds

A bstract We embed Nelson’s theory of stochastic quantization in the Schwartz-Meyer second order geometry framework. The result is a non-perturbative quantum mechanics on (pseudo-)Riemannian manifolds. Within this approach, we derive differential equations for massive spin-0 test particles charged under scalar potentials, vector potentials and gravity. Furthermore, associated Schrödinger equation. resulting show that must be conformally coupled to gravity conclude with discussion some prospects