  We give a variational formulation of General Relativity, with coupling to a
cosmological constant, to scalar fields, to vector fields and to spinor fields
(all with possible mass and interaction terms). Among the matter fields, we
include ghosts corresponding to diffeomorphism and Yang-Mills gauge symmetries,
with kinetic terms given by gauge fixing conditions leading to hyperbolic
equations of motion for all fields. The distinguishing characteristic of our
Lagrangian density is its polynomiality, in all dynamical fields and Lagrange
multipliers, and its validity for any number of spacetime dimensions.
