Heisenberg Operators in Quantum Electrodynamics. I

A new analytic continuation principle is described, by means of which the calculation of matrix elements of Heisenberg operators in any quantized field theory is greatly simplified. By a "Heisenberg operator" is meant an average over a finite space-time region of a field operator in the Heisenberg representation of the theory. The analytic continuation is made by varying the characteristic masses of the fields through real values. In this way a Heisenberg operator with the physically occurring masses is derived from an operator calculated with very large fictitious masses. In the region of large masses, where real creation of particles is impossible, the operator is identical with the $S$-matrix for a suitably chosen scattering problem. The calculation reduces to the calculation of an $S$-matrix, to which the techniques of Feynman are directly applicable.