BOSONIZATION AND EVEN GRASSMANN VARIABLES

We test a new approach to bosonization in relativistic field theories and many-body systems, whose purpose is to set up a perturbative schem e where the unperturbed action is the free action of the composites. T he method is of practical relevance since the free propagators of the composites can be evaluated in a number of interesting cases. This is achieved by performing a generalized change of variables in the Berezi n integral which defines the partition function of the system, whereby one assumes the composites as new integration variables. Still to be established, however, is a general procedure for deriving the free act ion of the composites starting from the one of the constituents. To sh ed light on this problem and to explore further features of the method we study a simplified version of the BCS model, whose spectrum consis ts of the excitations of the composite field associated to a Cooper pa ir. We are able to obtain the free action of this field, which display s a peculiar feature which we conjecture to characterize all the actio ns of quadratic fermionic composites, namely it does not contain a tim e derivative, Nevertheless it yields the right propagator, because, du e to the properties of the integral over even elements of a Grassmann algebra, the propagator turns out not to be the inverse of the wave op erator. (C) 1997 Elsevier Science B.V.