2021/01/31 by Folkert Kuipers · 12 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Canonical quantization #Differential geometry #Noncommutative and Quantum Gravity Theories #Quantization (signal processing) #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum gravity #Scalar (mathematics) #Stochastic differential equation #Stochastic quantization #gr-qc #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1007/jhep05(2021)028
published in Journal of High Energy Physics 2021(5) (Springer Nature) · 48 pages; v2: minor revisions
openalex created_date 2021/02/15 · arxiv created 2021/05/01 · openalex publication_date 2021/05/01 · arxiv updated 2021/05/07 · openalex updated_date 2026/08/05
A bstract 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.