On equivalence of parabolic and hyperbolic super-Hamiltonians

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Abstract
Three types of super‐Hamiltonians occur in generally covariant field theories: linear in the momenta (hypersurface kinematics), parabolic in the momenta (parametrized field theories on a given Riemannian background), and hyperbolic in the momenta (geometrodynamics). Three simple models are discussed in which the linear or parabolic super‐Hamiltonian can be cast, essentially by a canonical transformation, into an equivalent hyperbolic form: (1) The scalar field propagating on a (1+1) ‐dimensional flat Minkowskian background, (2) hypersurface kinematics on a (1+n) ‐dimensional flat Minkowskian background, and (3) geometrodynamics of a (1+2) ‐dimensional vacuum spacetime. The implications for constraint quantization are mentioned.

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