Removal of spurious center of mass effects in nuclear many-body systems - art. no. 044323

The problem of the motion of the center of mass in nuclear many-body system s is revisited. In the first part of the work, the counterterms needed to f ulfill the translational and Galilean invariances are solved through the ex act albeit perturbative expansion underlying the random-phase approximation . Collective variables are introduced in the second part of the work. The i nherent problems of overcounting and infrared divergencies are solved by me ans of the BRST invariance. Consistency between the two procedures is achie ved by use of the same perturbative expansion. The formalism is applied to the calculation of matrix elements of some of the electroweak operators whi ch are active in the (mu (-),e(-)) conversion process, to show the influenc e of center of mass effects upon transitions induced by vector terms of the weak current.