Elementary and composite particles in the V-θ sector of the Lee model

Abstract

The V-θ sector of the Lee model is examined with a view of understanding composite particles as elementary particles with vanishing renormalization constant, in the presence of inelasticity. It is shown that a composite bound state in the V-θ sector is equivalent to an elementary one in a second field theory, with the wave function renormalization constant of the elementary particle tending to zero. However unlike the case where the scattering is purely elastic, there does not seem to be any simple and useful relation between the phase of the elastic scattering amplitude at infinite energies and the compositeness of the bound states in the V-θ channel. The meaning of a vanishing vertex renormalization constant is also studied in the second field theory and it is shown that the simultaneous vanishing of both the vertex and wave function renormalization constant constitute the field theoretic definition of bootstrap.