  We revisit the gravity path integral formalism of JT gravity. We explain how
to gauge fix the path integral in the presence of asymptotic boundaries and
conical defects, and resolve an ambiguity regarding the dilaton gravity
operator that creates a conical defect. Along the way we study JT gravity
coupled to matter on surfaces with defects of special opening angles, obtaining
expressions for partition and two-point functions of matter fields. The two
point function involves a summation over all geodesics on the surface,
including self-intersecting geodesics, which we formally manage to include.
