Abstract
To give a firm base to argument on quantization of an LC circuit, we derive a commutation relation of electric flux and magnetic flux from quantum electrodynamics. The electric flux is defined by integration of electric field on two-dimensional surface. The magnetic flux is defined by integration of magnetic field surrounded by one-dimensional loop. It is proved that the commutator of the electric flux and the magnetic flux is equal to a crossing number of the loop and the surface. It is also proved that the flux commutator is invariant under gauge transformations and homological deformations. It is also argued that the LC-circuit system can be used as a platform for realizing EPR entanglement.
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