Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction

The validity of the rules given in previous papers for the solution of problems in quantum electrodynamics is established. Starting with Fermi's formulation of the field as a set of harmonic oscillators, the effect of the oscillators is integrated out in the Lagrangian form of quantum mechanics. There results an expression for the effect of all virtual photons valid to all orders in $\frac{e^2}{\hslash c}$. It is shown that evaluation of this expression as a power series in $\frac{e^2}{\hslash c}$ gives just the terms expected by the aforementioned rules.