Paper [1952a]: On the Definition of the Renormalization Constants in Quantum Electrodynamics

Abstract

Pauli was very impressed by this paper which he labeled as Källén “looking behind the veil of Dyson’s power series”. He wrote about it to several people (see the chapter on “Non-perturbative Renormalization” in PART IV).

In this paper Källén takes his first steps to go beyond perturbation theory in quantum electrodynamics. He uses the Heisenberg representation for the electron and the photon field operators and expresses the renormalization constants in terms of spectral functions. The charge renormalization constant L emerges in the vacuum expectation value of the commutator of the photon field and its time-derivative (see Eq. (40)) and is related to Källén’s weight function Π which appears in the vacuum expectation value of the commutator of the current operator at two different space-time points. The definition of the mass renormalization constant K is carried through in a similar way by considering the vacuum expectation value of the anticommutator of the fermionic current (the right-hand side of the Dirac equation) taken at two different space-time points.