arXiv Open Access 2023

Stochastic Mechanics and the Unification of Quantum Mechanics with Brownian Motion

Folkert Kuipers
Lihat Sumber

Abstrak

We unify Brownian motion and quantum mechanics in a single mathematical framework. In particular, we show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a Wiener process that is rotated in the complex plane. We then extend this theory to relativistic stochastic theories on manifolds using the framework of second order geometry. As a byproduct, our results suggest that a consistent path integral based formulation of a quantum theory on a Lorentzian (Riemannian) manifold requires an Ito deformation of the Poincare (Galilean) symmetry, arising due to the coupling of the quadratic variation to the affine connection.

Penulis (1)

F

Folkert Kuipers

Format Sitasi

Kuipers, F. (2023). Stochastic Mechanics and the Unification of Quantum Mechanics with Brownian Motion. https://arxiv.org/abs/2301.05467

Akses Cepat

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Informasi Jurnal
Tahun Terbit
2023
Bahasa
en
Sumber Database
arXiv
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Open Access ✓