  We consider the first order form of the Einstein-Hilbert action and quantize
it using the path integral. Two gauge fixing conditions are imposed so that the
graviton propagator is both traceless and transverse. It is shown that these
two gauge conditions result in two complex Fermionic vector ghost fields and
one real Bosonic vector ghost field. All Feynman diagrams to any order in
perturbation theory can be constructed from two real Bosonic fields, two
Fermionic ghost fields and one real Bosonic ghost field that propagate. These
five fields interact through just five three point vertices and one four point
vertex.
