ON WITTEN'S EFFECTIVE LAGRANGIAN FOR CHIRAL FIELD

Wess and Zumino's effective Lagrangian for the chiral field is derived by a new method which shows the direct relationship between the Lagrangian and the difference of the left handed and right handed Chern-Simons topological invariants. The resulting Lagrangian is explicitly left and right antisymmetric and equal to the one obtained in a previous letter by a different method.