Gerbes, Quantum Mechanics and Gravity

Original · EN

We prove that invariance of a quantum theory under the semiclassical vs. strong-quantum duality S/ℏℏ/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.