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Gerbes, Quantum Mechanics and Gravity

J. M. Isidro
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Abstract

We prove that invariance of a quantum theory under the semiclassical vs. strong-quantum duality $S/\hbar\longleftrightarrow\hbar/S$, where S is the classical action, is equivalent to noncommutativity (of the Heisenberg-algebra type) of the coordinates of the space on which S is defined. We place these facts in correspondence with gerbes and Neveu-Schwarz B-fields and discuss their implications for a quantum theory of gravity. Feynman's propagator turns out to be closely related to the trivialisation of a gerbe on configuration space.

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J. M. Isidro. 2006-04-03. Gerbes, Quantum Mechanics and Gravity. https://arxiv.org/abs/hep-th/0510075

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