  Unitarily implementable Bogoliubov transformations for charged, relativistic
bos\-ons and fermions are discussed, and explicit formulas for the 2-cocycles
appearing in the group product of their implementers are derived. In the
fermion case this provides a simple field theoretic derivation of the
well-known cocycle of the group of unitary Hilbert space operators modeled on
the Hilbert Schmidt class and closely related to the loop groups. In the boson
case the cocycle is obtained for a similar group of pseudo-unitary (symplectic)
operators. I also derive explcite formulas for the phases of one-parameter
groups of implementers and, more generally, families of implementers which are
unitary propagators with parameter dependent generators.

High Energy Physics - Theory