The Ashtekar Formalism and WKB Wave Functions of N=1,2 Supergravities
  The N=1,2 supergravities with non-zero cosmological constants are investigated in the Ashtekar formalism. We solve the constraints of the N=1,2 supergravities semi-classically. The resulting WKB wave functions are expressed by exponentials of supersymmetric-extended SL(2,C) Chern-Simons functional. 
Takashi Sano