Abstract. We study the Hamiltonian formulation of Plebanski theory in both the Euclidean and Lorentzian cases. A careful analysis of the constraints shows that the system is non-regular, i.e., the rank of the Dirac matrix is non-constant on the non-reduced phase space. We identify the gravitational and topological sectors which are regular subspaces of the non-reduced phase space. The theory can be restricted to the regular subspace which contains the gravitational sector. We explicitly identify first- and second-class constraints in this case. We compute the determinant of the Dirac matrix and the natural measure for the path integral of the Plebanski theory (restricted to the gravitational sector). This measure is the analogue of the Leutwyler–Fradkin–Vilkovisky measure of quantum gravity.

PACS numbers: 04.60.−m, 04.60.Ds

Print publication: Issue 22 (21 November 2004)
Received 18 June 2004, in final form 29 September 2004
Published 29 October 2004