Gauss linking number and the electromagnetic uncertainty principle

Abhay Ashtekar, Alejandro Corichi
1997 Physical Review D, Particles and fields  
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 ħ 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.
doi:10.1103/physrevd.56.2073 fatcat:jlbzmvfi2ff3nmhgahwxi7pta4