Analytic regularization in the Lee model with positive definite and indefinite metric

Abstract

Analytic regularization is applied to the Lee model without a cut-off function. The cases of positive definite and indefinite metric are considered. The V-particle propagator is computed in the interaction picture with the help of perturbation theory and subsequently analytically regularized. One may then identify four distinct cases corresponding to different values of the parameters introduced. If the metric is positive definite, contradictions show up in every case. In one case the regularized propagator is equivalent to the propagator given by the usual renormalization. If the metric is indefinite, no contradictions show up. In one case (dipole ghost case) it is shown that the regularized propagator is equivalent to the propagator which one obtains by introducing a cut-off\(\hat \omega \) and performing the limit\(\hat \omega \to \infty \)\] at the end.