Abstract
We show how certain constructions of quantum mechanics, like monopoles, instantons, and the Schrodinger-von Neumann equation, are related to geometric functors which are representable. We study the differential geometry of the projective bundle associated with an infinite-dimensional separable Hilbert space, and we construct a universal connection which, is described as a subspace of skwe-Hermitian operators. This connection is responsible for the Berry phase.
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