Free states of the gauge invariant canonical anticommutation relations. II

Abstract:

A class of representations of the gauge invariant subalgebra of the canonical anticommutation relations (henceforth GICAR) is studied. These representations are induced by restricting the well-known pure, nongauge invariant generalized free states of the canonical anticommutation relations (henceforth CAR). Denoting a state of the CAR by $\omega$, and the unique generalized free state of the CAR such that $\omega \left ( {a{{\left ( f \right )}^{\ast }}a\left ( g \right )} \right ) = \left ( {f,Tg} \right )$ and $\omega \left ( {a\left ( f \right )a\left ( g \right )} \right ) = \left ( {Sf,g} \right )$ by ${\omega _{S,T}}$, it is shown that a pure, nongauge invariant state ${\omega _{S,T}}$ induces a factor representation of the GICAR if and only if $Tr T\left ( {I - T} \right ) = \infty$.