Canonical quantization of Bianchi class A models in N=2 supergravity

The theory of N = 2 supergravity is applied to Bianchi class A models. Their canonical formulation is addressed for two cases: when the O(2) internal symmetry is (a) global or (b) local. A cosmological constant and mass-like term for the gravitinos are required in the latter but are absent in the former. For the case of global O(2) symmetry, it is shown that the presence of a Maxwell field in the supersymmetry constraints is sufficient to imply a non-conservation of the fermionic number. This effect corresponds to a mixing between different Lorentz invariant fermionic sectors in the wave function of the universe. It is similar to what a cosmological constant term would have caused but considerably different from what occurs in FRW and Bianchi models in N = 1 supergravity with scalar fields and fermionic partners. The nonconservation effect is interpreted from the point of view of N = 2 supergravity theory. For case (b), we obtain the more general solution of the gauge constraint. Possible quantum physical states are then discussed regarding previous works where Ashtekar variables have been used. These states can be obtained from an N = 2 supersymmetric Chern-Simons functional. Some comments concerning the physical validity of the Chern-Simons solution and its transformation into metric representation variables are included.