Bethe's hypothesis and Feynman diagrams: Exact calculation of a threebody scattering amplitude by perturbation theory
Abstract
The perturbation series for threebody scattering is discussed and summed to all orders in a nonrelativistic onedimensional theory with δfunction interaction. The summation is accomplished by analyzing three simultaneous integral equations satisfied by the threebody scattering amplitude and appropriately decomposing and recombining the kernels which appear in these equations. The homogeneous integral terms can be entirely eliminated from one equation in favor of the scattering amplitude itself, yielding an algebraic equation which is easily solved. The threeparticle incoming wave function in configuration space is constructed from the scattering amplitude and shown to be that given by Bethe's hypothesis.
 Publication:

Physical Review D
 Pub Date:
 February 1975
 DOI:
 10.1103/PhysRevD.11.838
 Bibcode:
 1975PhRvD..11..838T