ON matrix superpropagators I

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