Publication date:
Available online 5 April 2017
Source:Differential Geometry and its Applications
Author(s): Josef Janyška, Marco Modugno
We discuss several features of the classical quantum potential appearing in Covariant Quantum Mechanics. In particular, we compare the “observed potential” $A[K,G,o]$ of the joined spacetime connection K with the potential $A^{\uparrow }$ of the cosymplectic phase 2-form $\mathrm{\Omega }[K,G]$ and with the potential $A^{\uparrow }$ of the upper quantum connection ${\text{Ч}}^{\uparrow }$. Moreover, we discuss the distinguished observer $o[\mathrm{\Psi }]$ and the distinguished timelike potential $A[\mathrm{\Psi }]$ associated with a non-vanishing quantum section Ψ. We show that the above objects play a natural role in the context of the kinetic quantum momentum $\mathrm{Q}[\mathrm{\Psi }]$, of the quantum probability current $\mathrm{J}[\mathrm{\Psi }]$, of the Schrödinger operator $\mathrm{S}[\mathrm{\Psi }]$ and of the classical fluid associated with a non-vanishing quantum section Ψ.