VertexFunction Poles and the Bootstrap Condition in Field Theory
Abstract
We discuss the implications of maintaining finite mass renormalization when the wavefunction renormalization constant Z_{3} of an elementary particle is set equal to zero, making only the approximations of twoparticle unitarity. We show that this defines a fieldtheory bootstrap for the elementary particle which is completely equivalent to the usual type of bootstrap based on the ND method. As Z_{3} goes to zero the vertex function and inverse propagator develop poles which move to μ^{2}, the elementaryparticle mass, in the limit. For nonzero Z_{3} this pole does not contribute to the scattering amplitude, but at Z_{3}=0 it cancels the elementaryparticle pole in the singleparticle reducible part, leaving the dynamical pole in the irreducible part. We suggest, further, that in this limit the bootstrapped state is a Regge pole.
 Publication:

Physical Review
 Pub Date:
 December 1965
 DOI:
 10.1103/PhysRev.140.B1643
 Bibcode:
 1965PhRv..140.1643G