  Canonical transformations (Bogoliubov transformations) for fermions with an
infinite number of degrees of freedom are studied within a calculus of
superanalysis. A continuous representation of the orthogonal group is
constructed on a Grassmann module extension of the Fock space. The pull-back of
these operators to the Fock space yields a unitary ray representation of the
group that implements the Bogoliubov transformations.
