《PhysRev.75.651 Quantum Electrodynamics. II. Vacuum Polarization and Self-Energy》.pdf

PHYSICAL REVIEW VOLUM E ZS, F EB RUAR Y 15, 1949 Quantum Electrodynamics. II. Vacuum Polarization and Self-Energy JULIAN SCH%INGER Department of Physics, Harvard University, Cambridge, Massachusetts (Received November 1, 1948) The covariant formulation of quantum electrodynamics, vacuum and is therefore undisturbed in its passage through developed in a previous paper, is here applied to two space. The absence of a light quantum self-energy effect — elementary problems the polarization of the vacuum and is thus indicated. The current induced at a point consists, the self-energies of the electron and photon. In the first more precisely, of two parts: a logarithmically divergent section the vacuum of the non-interacting electromagnetic multiple of the external current at that point, which and matter fields is covariantly defined as that state for produces an unobservable renormalization of charge, and which the eigenvalue of an arbitrary time-like component a more involved finite contribution, which is the physically of the energy-momentum four-vector is an absolute significant induced current. The latter agrees with the minimum. It is remarked that this definition must be results of previous investigations. The modification of the compatible with the requirement that the vacuum expec- matter field properties arising from interaction with the tation values of a physical quantity in various coord