The Vacuum in Quantum Electrodynamics

Abstract
Without use of perturbation calculation a general formula is derived for the vacuum induced current due to external electromagnetic field. This formula is valid for any charged field with arbitrary spin and interaction type. The terms corresponding to self-charge and observable current are shown to be of negative signs. The condition for the finiteness of the self charge is also considered. These circumstances give rise to the serious difficulties in solving the problem of divergence of self-charge etc. from the standpoint of the realistic mixed field theory. An application of this formula to induced current in the e2-approximation is stated in detail. In order to settle these difficulties entirely it is expected that the further material property may be introduced for the vacuum.