Relation between scattering amplitude and Bethe-Salpeter wave function in quantum field theory

Understand

We discuss an exact relation between the two-particle scattering amplitude and the Bethe-Salpeter (BS) wave function inside the interaction range in quantum field theory.

• In the relation the reduced BS wave function defined by the BS wave function plays an essential role.
• Through the relation the on-shell and half off-shell amplitudes can be calculated.
• We also show that the solution of Schr\"odinger equation with the effective potential determined from the BS wave function gives a correct on-shell scattering amplitude only at the momentum where the effective potential is determined.