Effective low energy Lagrangian for QCD

The peculiar collective excitations of gluons, related to the Lorentz transformations of the conjugate field tensor, were proposed in a previous paper. The pseudoscalar mesons are related in the same way to the chiral transformations of quarks. We discuss these relations, including the U (1) problem, and derive the low energy effective Lagrangian for all these collective excitations. This Lagrangian contains the potential for the U (1) field due to axial anomalies.