On the structure of symmetry generators

In a field theoretic framework we investigate generators of symmetry transformations induced by conserved local, not necessarily translationally covariant currents. Assuming the invariance of the vacuum and a mass gap, it is shown that the generator on one-particle states in general can be any polynomial of the generators of the Poincaré group and the internal symmetries. We give an example showing that the generator, defined as an integral over a conserved current, in spite of leaving the vacuum invariant, need not be self-adjoint.Supported by a DAAD grant