Amputation of external propagators

Amputation removes the external propagator factors from a momentum-space correlation function. For a connected four-point function, its diagrammatic external lines each carry a full two-point function; multiplying by the corresponding inverse two-point kernels leaves an interaction kernel.

This operation helps separate propagation to and from the interaction from the interaction itself. It is part of the connection between Green functions and scattering amplitudes, although physical external states also require on-shell limits and the appropriate pole-residue normalization. An amputated connected function need not be one-particle irreducible: it may still contain internal lines whose removal disconnects it. External-line removal and internal irreducibility are distinct operations.