Stochastic geometry and origin of quantum potential

Davide Fiscaletti

Blagovest A. Nikolov, D. A. Trifonov

Ignazio Francesco Licata

Preface Space-Time Geometry & Quantum Events The Transaction as a Quantum Concept Stochastic Foundation of Quantum Mechanics & the Origin of Particle Spin Fractal Space-Time as an Underlying Structure of the Standard Model Relativity of Scales, Fractal Space & Quantum Potentials Three Possible Implications of Space-Time Discreteness Quantum Computing Space-Time Metric Gauge Fields in Deformed Special Relativity Non-Local Granular Space-Time Foam as an Ultimate Arena at the Planck Scale Structural Approach to the Elementary Particle Theory Forming Physical Fields & Pseudometric & Metric Manifolds. Noncommutativity & Discrete Structures in Classical & Quantum Physics Index.

Alexey V. Golovnev

We consider the thin layer quantization with use of only the most elementary notions of differential geometry. We consider this method in higher dimensions and get an explicit formula for quantum potential. For codimension 1 surfaces the quantum potential is presented in terms of principal curvatures, and equivalence with Prokhorov quantization method is proved. It is shown that, in contrast with original da Costa method, Prokhorov quantization can be generalized directly to higher codimensions.

S. Twareque Ali, James A. Brooke, Paul Busch +2 more

Working within the framework of stochastic quantum mechanics, we prove that a mild reality constraint on the radial part of the resolution generator renders the (probability) current, for a single particle with only positive (or only negative) energies and having arbitrary integer spin, conserved. The result is proven both nonrelativistically and relativistically. This extends some earlier results that had been obtained for spinless systems. We argue that the origin of such a conservation law is a consequence of the particular geometry of space–time predicated by the formalism of stochastic quantum mechanics.