ABSTRACT
The aim of the present paper1 is to elaborate and simplify the mathematical foundations for quantum electrodynamics. This theory, created by Dirac2 and Heisenberg and Pauli,3 presents a consistent generalization of classical electrodynamics, answering the correspondence principle [...].4 The difficulties of the theory arising from the infinite self-energy of an electron are well known [...]. Nevertheless, it should not be forgotten that all the results of the quantum theory of radiation, which presents an immediate application of the correspondence principle, can be obtained from quantum electrodynamics. But we often should waive the mathematical strictness. The physical sense of “illegal” mathematical operations used there (truncating an expansion in a power series by a certain power of the fine structure constant α, throwing off divergent integrals, etc.) is that employing them one tries to eliminate the discrepancies arising from an imperfection of the theory.
