ON matrix superpropagators I

Given the free propagator of a matrix‐valued field φ_αβ in the form <φ_αβ(x), φ_γδ (0)> = (1/2) (δ_αγδ_βδ +δ_αδδ_βγ − 2cδ_αβδ_γδ) Δ (x), we derive an integral representation for the matrix superpropagator <φNαβ(x),φNγδ(0)> <φ αβ N (x),φ γδ N (0)> for arbitrary N, and apply this to find the exponentially parametrized gravity superpropagator <|−g(x)|^ω g _αβ (x), |−g(0)|^ω g _γδ (0)> with g _μν(x) ≡ [exp κφ(x)]_μν. Other applications are also mentioned.