Abstract
We show how certain constructions of quantum mechanics, like monopoles, instantons, and the Schrödinger-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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Aguilar, M.A., Socolovsky, M. Naturalness of the space of states in quantum mechanics. Int J Theor Phys 36, 883–921 (1997). https://doi.org/10.1007/BF02435791
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DOI: https://doi.org/10.1007/BF02435791