Gerbes and Heisenberg's Uncertainty Principle

Abstract

We prove that a gerbe with a connection can be defined on classical phase space, taking the U(1)-valued phase of certain Feynman path integrals as Cech 2-cocycles. A quantisation condition on the corresponding 3-form field strength is proved to be equivalent to Heisenberg's uncertainty principle.Comment: 12 pages, 1 figure available upon reques