Polaron variational methods in the particle representation of field theory. II. Numerical results for the propagator

For the scalar Wick-Cutkosky model in the particle representation we perform a similar variational calculation for the two-point function as was done by Feynman for the polaron problem. We employ a quadratic nonlocal trial action with a retardation function for which several Ansaetze are used. The variational parameters are determined by minimizing the variational function and in the most general case the nonlinear variational equations are solved numerically. We obtain the residue at the pole, study analytically and numerically the instability of the model at larger coupling constants, and calculate the width of the dressed particle. copyright 1996 The American Physical Society