Self-Dual Conformal Supergravity and the Hamiltonian Formulation

In terms of Dirac matrices the self-dual and anti-self-dual decomposition of conformal supergravity is given and a self-dual conformal supergravity theory is developed as a connection dynamic theory in which the basic dynamic variables 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.