Abstract
The problem of the motion of the center of mass in nuclear many-body systems is revisited. In the first part of the work, the counterterms needed to fulfill the translational and Galilean invariances are solved through the exact albeit perturbative expansion underlying the random-phase approximation. Collective variables are introduced in the second part of the work. The inherent problems of overcounting and infrared divergencies are solved by means of the BRST invariance. Consistency between the two procedures is achieved by use of the same perturbative expansion. The formalism is applied to the calculation of matrix elements of some of the electroweak operators which are active in the $({\ensuremath{\mu}}^{\ensuremath{-}}{,e}^{\ensuremath{-}})$ conversion process, to show the influence of center of mass effects upon transitions induced by vector terms of the weak current.
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