Mass splitting in relativistic quantum field theory

Null plane integrals of certain classes of tensor densities, conserved or non-conserved, may define symmetric operators on dense subspaces of the 'in' and 'out' states. These operators annihilate the vacuum and may satisfy a Lie algebra. In particular, the possibility that a finite number of null plane charges, which includes the Poincaré generators, close on an algebra whose irreducible representations contain particles with different masses is considered. The situation in which the Lie algebra is defined on a dense domain which is not from the 'in' and 'out' states is discussed. Some algebraic hypotheses other than that of a Lie algebra in the usual sense are briefly considered; in these cases there can be no mass splitting.