by K. Kraus and R. F. Streater. J. Phys., A14, 1981.
We study the class of pure quasifree gauge-invariant states of the Fermion algebra. We 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 shown to be non-trivial, 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 Poincaré covariant representations for free Fermions are constructed.
These representations are not necessarily locally related to the free theory. For representations that are obtained by local automorphisms, see my paper with Hermaszewski, and the later paper with Gallone, Sparzani and Ubertone Twisted condensates of quantised fields.
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© by Ray Streater; modified 26/3/2000 and 13/6/00.