Gauss Linking Number and Electro-magnetic Uncertainty Principle

Abstract

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 $\hslash$ 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.

13 pages, Revtex file, 3 eps figures

References in corpus (3)

• Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
• Photon inner product and the Gauss linking number
• Mathematical Problems of Non-perturbative Quantum General Relativity

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