Remarks on the non-uniqueness of the canonical energy-momentum tensor of classical field theories

We discuss the influence of divergences in the framework of classical field theory. The example of a point-like scalar particle interacting with a scalar field shows how a divergence changes the equation of motion of the particle. Then we discuss extended particle models on a two-fold connected space-time. The ''particles'' have an inner boundary, the section of which with a space-like hypersurface shall be a two-dimensionally closed surface. The boundary is given by the requirement that the canonical energy-momentum tensor tsub(k)sup(l) fulfills the condition Tsub(k)sup(l)nsub(l)=0 (nsub(l)=normal vector to the boundary). Thirdly, we look for such a canonical energy-momentum tensor giving for a field configuration, which can only be supported on a space bounded region, a free boundary. All these considerations shall show that one obtains different answers to certain questions, if one starts from different canonical energy-momentum tensors. Only the field equations can tell one whether the objects considered here are stable or not. (author)