Some covariant representations of massless Fermi fields

Abstract

Studies the class of pure quasi-free gauge invariant states of the Fermion algebra. The authors show that the question of G-covariance of the corresponding representations (i.e. implementability of some group G of one-particle symmetry transformations) is related to a cohomology group with values in the Hilbert-Schmidt class. In four-dimensional space-time, this cohomology is nontrivial, thus leading to G-covariant non-Fock representations, when G is taken to be the space-time translation group together with rotations, or space-time translations together with boosts in one direction and rotations about it, and the Fermion mass is zero. In two space-time dimensions, some new fully Poincare covariant representations for free massless Fermions are constructed.