A Chirally Symmetric Effective Action for Vector and Axial Vector Fields in a Global Color Symmetry Model of QCD

We consider the quantum field theory of a model of an extended Nambu-Jona-Lasinio type with a QCD based nonlocal fermion current-current interaction which has global SU(N c ) symmetry. We obtain an exact bosonization of this model in four Euclidean dimensions using auxiliary bilocal fields and discuss the dynamical breakdown of chiral symmetry in the massless fermion limit. A local field bosonization is obtained by decomposing the bilocal fields in terms of complete orthonormal sets of functions with the expansion coefficients, which are local functions, identified as the local meson fields. Retaining the ground state pseudoscalar, vector and pseudovector local fields we obtain a local effective action for this sector of the theory. The derivative expansion of the fermionic determinant necessary to obtain this local action is self-regularizing because of the bilocal substructure present in the model which is manifest in the form factors that are associated with the local fields. In our local action the value of each coefficient depends critically on the underlying fermionic dynamics through these form factors and the vacuum functions. As a consequence of this the vector and pseudovector fields in the theory are best interpreted as simple fermion-antifermion bound states rather than as massive Yang-Mills fields or exotic composites of the pseudoscalars; interpretations that we find are not in general admitted when models such as the GCM are treated correctly. Identifying then the physical vector and pseudovector fields with the linearly transforming chiral partners introduced by the bosonization, we obtain an effective action for this sector of the meson spectrum which predicts values for the kinematic and dynamic quantities associated with these fields.