2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185215We give a path integral expression for the quantum amplitude to produce a black hole from particle collisions. When expanded about an appropriate classical solution it yields the leading order contribution to the production amplitude in a curvature expansion. Classical solutions describing black hole production resulting from two particle scattering at non-zero impact parameter, combined with our formalism, indicate a geometric cross section for the quantum process. In TeV gravity scenarios these solutions may exhibit large curvatures, but (modulo a mild assumption about quantum gravity) corrections to the semi-classical cross section are small.10 pages, latex; Minor revisions, to appear in Physics Letters BHigh Energy Physics - PhenomenologyGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theorytext