The Momentum–space Bosonization of the Nambu–jona-lasinio Model with Vector and Axial-vector Mesons

The momentum-space bosonization method is extended to the case of a Nambu–Jona-Lasinio type model with vector and axial-vector mesons. The method presented gives the possibility of deriving any meson vertex function to all orders in momenta and to the leading order in 1/Nc. Two-point functions, which describe one-particle transitions to the hadronic vacuum, and meson selfenergies are considered. We find new relations which generalize the well-known KSFR relation and both the first and the second Weinberg sum rules. These result from a consistent treatment of higher order terms in the momentum expansion. CRN 93–57 December 1993