Mostly right, but one correction: You actually _can_ calculate with the physical Lagrangian. This is what lattice gauge theory simulations do. But it's incon

Mostly right, but one correction: You actually _can_ calculate with the physical Lagrangian. This is what lattice gauge theory simulations do. But it's inconvenient and difficult in perturbation theory, so physicists use the Fadeev-Popov ghost trick instead. The resulting computations are _entirely_ mathematically equivalent, not "(mostly)".