Self-Dual Conformal Supergravity and the Hamiltonian Formulation
  In terms of Dirac matrices the self-dual and anti-self-dual decomposition of a conformal supergravity is given and a self-dual conformal supergravity theory is developed as a connection dynamic theory in which the basic dynamic variabes include the self-dual spin connection i.e. the Ashtekar connection rather than the triad. The Hamiltonian formulation and the constraints are obtained by using the Dirac-Bergmann algorithm.   PACS numbers: 04.20.Cv, 04.20.Fy,04.65.+e 
Guoying Chee and Yanhua Jia