https://doi.org/10.1140/epjp/s13360-023-04184-x
Letter to the Editor
Quantum mechanics from stochastic processes
INFN, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126, Napoli, Italy
Received:
24
April
2023
Accepted:
12
June
2023
Published online:
19
June
2023
We construct an explicit one-to-one correspondence between non-relativistic stochastic processes and solutions of the Schrödinger equation and between relativistic stochastic processes and solutions of the Klein–Gordon equation. The existence of this equivalence suggests that the Lorentzian path integral can be defined as an Itô integral, similar to the definition of the Euclidean path integral in terms of the Wiener integral. Moreover, the result implies a stochastic interpretation of quantum theories.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023
