Abstract
It is shown that non-relativistic quantum geometries over five-dimensional Bargmann manifolds can be constructed by using geometro-stochastic methods recently developed in the general relativistic context. These geometries are formulated in terms of soldered Hilbert bundles E whose typical fibres are carriers of stochastically localised quantum states. Parallel transport is executed by means of quantum connections obtained by regarding each E as a bundle associated with the principal bundle of Bargmann frames. The resulting quantum gauge theory of the extended Galilei group gives rise to a geometro-stochastic propagator which is shown to agree with the one determined by the Schrodinger equation with a gravitational potential.
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