Padé approximation of two-point functions and the calculation of resonances

Abstract

Abstract The application of the method of Pade approximants to two-point functions of spin 0 and spin 1 2 is discussed in connection with the calculation of resonances in renormalizable Lagrangian field theory. The resonances which are considered belong to the Peierls class: they are excited states of a particle, with the same quantum numbers as the particle except parity, corresponding to complex poles of the propagator on an unphysical Riemann sheet of the energy plane. The diagonal Pade approximants are found to be particularly suited for approximating the mass function in the modified propagator, with regard to consistency wit the Kallen-Lehmann representation. Contrary to perturbative approximation, they open a way for avoiding ghost difficulties, yielding a finite wave renormalization constant. The analytic continuation of the propagator in the Pade approximation scheme is derived from that of the perturbation theory terms. A resonance equation is obtained on the real axis, the roots of which provide information on the masses of the possible resonances. The [1,1] Pade approximant is considered in the particular cases of the V-propagator in the Lee model and the nucleon propagator in the Yukawa model.