Hamiltonian analysis of metric-affine-R 2 theory

Abstract

Determining the number of propagating degrees of freedom inmetric-affine theories of gravity requires the use of Hamiltonianconstraint analysis, except in some subclasses of theories. Wedevelop the technicalities necessary for such analyses andapply them to the Weyl-invariant and projective-invariantcase of metric-affine-R 2 theory that is known to propagatejust the graviton. This serves as a check of the formalismand a case study where we introduce appropriate ADM variablesfor the distortion 3-tensor tensor and its time derivatives,that will be useful when analyzing more general metric-affinetheories where the physical spectrum is not known.