Self-dual conformal supergravity and the Hamiltonian formulation (Q5959875)

The gauge theory of the superconformal covering group SU\((2,2|1)\) is studied for a Lagrangian quadratic in the gauge curvature. In a Dirac basis, the decomposition in its self- or anti-self dual parts is presented. Finally, the \((3+1)\)-decomposition is performed and the canonical Hamiltonian is derived in a two-spinor basis. The explicit form of the Poisson brackets are deferred to an Appendix. For the chiral decomposition of simple supergravity, see also \textit{E. W. Mielke} and \textit{A. Macías} [Ann. Phys. (Leipzig) (8) 8, 301-317 (1999; Zbl 0924.53063)].