Modular Theory and Bogoliubov Automorphisms of Clifford Algebras

Let π c be a covariance C quasifree representation of the Clifford algebra over a real Hilbert space on which I + C 2 is invertible. We determine explicitly the modular data for π c and show that a Bogoliubov automorphism is weakly inner for π c if and only if its generating orthogonal transformation lies in the Blattner group. We employ a model in which all quasifree representations act on one canonical Hilbert space, exhibiting the property that the modular conjugation is independent of C . This refines earlier work of Carey, Shale and Stinespring.