Progress of Theoretical Physics Vol. 3 No. 4 (1948) pp. 456-458 The Problem of Vacuum Polarization H. Umezawa and E. Yamada Progress of Theoretical Physics Vol. 7 No. 5 (1952) pp. 591-592 Remark on the Self Energy Problem of the Photon O. Hara and H. Shimazu
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Umezawa et al. (1948) studied this question.