An Algebraic Description of Perturbation Theory in Quantum Electrodynamics

Abstract

We use an algebraic formulation of the electromagnetic field, in which various quantization procedures can be described, to discuss perturbation calculations. We show that the Feynman rules and the second order calculation of the self-energy of the electron can be developed on the basis of the Fermi method of quantization. The algebraic approach clarifies the problems in defining the vacuum and other states, which are associated with calculations in terms of field algebra operators. We demonstrate that the 'vacuum' state defined on the field algebra by Schwinger leads to incorrect results in the self-energy calculation.