Nonuniqueness of the ADM Hamiltonian for gravity

In a Hamiltonian formulation of gravity where the metric does not play the role of one of the canonical coordinates, the Hamiltonian is not unique. The uniqueness proof of Hojman, Kuchar and Teitelboim (1976) for the gravity Hamiltonian is reinvestigated with a less restricted relation between the metric and the canonical phase space coordinate. A specific example of another Hamiltonian is given, based on Capovilla, Dell and Jacobson's (1991) one-parameter extension of complex general relativity in the connection formulation.

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