Gerbes, Quantum Mechanics and Gravity

Abstract

We prove that invariance of a quantum theory under the semiclassical vs. strong-quantum duality $S/\hslash ⟷\hslash /S$, 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.

10 pages, 1 figure available upon request

References in corpus (1)

• An Introduction to Noncommutative Spaces and their Geometry