A method is described whereby the S-matrix can be formulated directly in the Heisenberg representation. This has the advantage over the customary formulation in the interaction representation in that the concepts of space-like surfaces and their normals need never be introduced. Quantum electrodynamics and the $\beta$ formalism of charged mesons are treated as illustrative examples; in particular, it is shown that general rules for writing down the elements of the S-matrix for the latter case may be immediately inferred.

In the second part of this paper, a covariant procedure, independent of the canonical formalism, is carried out for making the transition from the Heisenberg to the interaction representation and is applied to several typical cases; in this way, the S-matrix of the Heisenberg picture is identified with that of other authors.

• Received 17 May 1950

DOI:https://doi.org/10.1103/PhysRev.79.972