Gauss Linking Number and Electro-magnetic Uncertainty Principle

It is shown that there is a precise sense in which the Heisenberg uncertainty between fluxes of electric and magnetic fields through finite surfaces is given by (one-half h̄ times) the Gauss linking number of the loops that bound these surfaces. To regularize the relevant operators, one is naturally led to assign a framing to each loop. The uncertainty between the fluxes of electric and magnetic fields through a single surface is then given by the self-linking number of the framed loop which bounds the surface. PACS number(s): 03.70.+K, 03.65.Bz Typeset using REVTEX Electronic address: [email protected] Electronic address: [email protected] 1