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Stochastic quantization on Lorentzian manifolds

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Version 2 2023-06-12, 09:51
Version 1 2023-06-09, 23:47
journal contribution
posted on 2023-06-12, 09:51 authored by Folkert Johannes Kuipers
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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Publication status

  • Published

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  • Published version

Journal

The Journal of High Energy Physics

ISSN

1126-6708

Publisher

Springer Nature

Page range

1-49

Article number

a28

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2021-05-06

First Open Access (FOA) Date

2021-05-06

First Compliant Deposit (FCD) Date

2021-05-06

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