Some Theoretical Consequences of a Particle Having Mass Zero

Abstract

When the mass is zero, the operator ${\ensuremath{\gamma}}_{5}$ commutes with the Hamiltonian of a noninteracting spinor field. This leads to the possibility of a two-component neutrino that has been employed in connection with parity-nonconserving neutrino reactions. Every representation of the full inhomogeneous Lorentz group describing a free particle of arbitrary nonzero spin can be split in the same way when the mass is zero. In particular, a reduction of the free electromagnetic field from six components to three, is exhibited in a way exactly analogous to the reduction of four-component massless spinors to two components. This illustrates the fact that parity nonconservation, when it occurs, cannot be a result of any intrinsic property of a free field, but must, instead, be ascribed to particular interactions occurring in nature.The possibility of relating the ${\ensuremath{\gamma}}_{5}$ degeneracy of the massless spin one-half field to its invariance under conformal coordinate transformations is discussed. The two-component free Dirac particle is invariant under the conformal point transformations, and also under the reciprocal radius transformations. Some different definitions of the conformal group are distinguished.