The Interaction Representation of the Proca Field

The methods used by Schwinger in quantum electrodynamics can be generalized in such a way that they become applicable to meson theory. This is shown by an example. The method used seems slightly simpler than the method proposed by the Japanese school. It turns out that the covariant field variables in interaction representation are not simply the transformed of the covariant variables used in Heisenberg representation. Also it turns out to be necessary to confine the space-like surfaces used in many applications to flat surfaces perpendicular to the time direction. The direct interaction between two particles through the meson field is obtained by a canonical transformation similar to the first approximation Schwinger transformation in quantum electrodynamics.The example of a neutral vector meson field discussed in the present paper has been chosen in such a way as to show the analogy to quantum electrodynamics. The interaction energy between particles obtained by Schwinger's relativistic treatment in meson theory (and also obtainable by the other usual perturbation methods) goes over into the M{}ller interaction for vanishing meson mass.