Vertex Functions and the Unitarity Relation

It is shown that a unitarity relation holds for vertex functions in a form analogous to the one for form factors and that the one-particle irreducible parts of scattering amplitudes satisfy unitarity by themselves. The second half of the present work considers the case of nonrelativistic $S$-wave scattering with one bound state. Interrelations among the $S$ matrix, the denominator function, and functions for the bound state, such as the form factor, the propagator, and the vertex function are discussed under certain general restrictions.