Authors: Diego L. Rapoport
We review the relation between space-time geometries with torsion fields (the so-called Riemann-Cartan-Weyl (RCW) geometries) and their associated Brownian motions. In this setting, the metric conjugate of the tracetorsion one-form is the drift vector field of the Brownian motions. Thus, in the present approach space-time fluctuations as Brownian motions are -in distinction with Nelson's Stochastic Mechanics- space-time structures. Thus, space and time have a fractal structure. We discuss the relations with Nottale's theory of Scale Relativity, which stems from Nelson's approach. We characterize the Schroedinger equation in terms of the RCW geometries and Brownian motions. In this work, the Schroedinger field is a torsion generating field. The potential functions on Schroedinger equations can be alternatively linear or nonlinear on the wave function, leading to nonlinear and linear creation-annihilation of particles by diffusion systems.
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[v1] 18 Apr 2008
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