Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
38 (1997), S. 173-181
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
A class of diffusion processes controlled by the geometry of the manifold on which they evolve is considered. The kinetic energy of such diffusions is shown to be a geometric object expressed in terms of the curvature and torsion tensors. This gives rise to an action functional leading to a variational principle, from which a nontrivial critical geometry with nonvanishing torsion emerges. The resulting criticality condition is related to the Schrödinger equation in a manner that reproduces the features of Nelson's stochastic approach to quantum mechanics. © 1997 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.531848
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