A symmetry of massless fields

Abstract

It is proved that there exists an additional intrinsic symmetry in the left‐handed and right‐handed fermions (and other fields). The corresponding group of transformations is induced by the Poincaré translations in the space–time manifold. This symmetry predicts an additional intrinsic energy‐momentum for fermions. Considering this symmetry as local leads to introduction of a gauge field and of a nonintegrable phase angle, the corresponding Berry‐type phase depends on the topology of the Riemannian space–time manifold as determined by the vierbein. This additional symmetry provides us with the possibility of considering the fermions as gauge fields on the nonvector bundle.