vector fields rather than scalars and to correlation functions of two different fields uses standard techniques. Again one finds that off-shell propagators and the vertex functions depend explicitly on the choice of field.

It is clear what is going on here. Neither the off-shell propagators nor the vertex functions are directly observable. From a theoretical point of view, the values of these quantities depend explicitly on which arbitrary choice of field one makes. Various combinations of the propagators and the vertex functions correspond to physical quantities and it is only these combinations which can be measured. Choosing a particular field amounts to making a bookkeeping choice—it only determines whether some bit of the physics will be found in the vertex or in the propagator.

The point we wish to stress is that knowledge, however precise, of the off-shell propagator contains no physical information unless one specifies the choice of the quantum field or equivalently unless one has knowledge of how the field couples to the rest of the system—[*i.e.*]{} knowledge of the vertex functions which arise from the same field choice. Thus, a model for the off-shell propagator in the absence of a [*consistent*]{} model for the vertex functions is 