Poincaré, de Sitter, and conformal gravity on the lattice

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Abstract
A unified treatment of Poincaré, de Sitter, and conformal gravity on a Euclidean lattice is given following the gauge-group formulations on the continuum. The vierbeins are naturally located on the links. A discussion is given of the role of the sign of the volume element in four-dimensional space. Exact reflection positivity is proved without any restriction on the observable quantities, and we state the boundedness properties of the Lagrangian which assure the existence of a positive self-adjoint Hamiltonian. A doubling phenomenon for the graviton on the lattice is found and discussed.

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