Journal of High Energy Physics (May 2021)

Stochastic quantization on Lorentzian manifolds

  • Folkert Kuipers

DOI
https://doi.org/10.1007/jhep05(2021)028
Journal volume & issue
Vol. 2021, no. 5
pp. 1 – 51

Abstract

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

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