Hamiltonian Analysis of Plebanski Theory

Details Hamiltonian Analysis of Plebanski Theory Hamiltonian Analysis of Plebanski Theory

2004-04-09

arxiv.org/abs/gr-qc/0404041v2

Class.Quant.Grav. 21 (2004) 5203-5220

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages, no figures, references added

Scientific paper

10.1088/0264-9381/21/22/012

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 sub-spaces 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.

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