DIFFEOMORPHISM COHOMOLOGY IN BELTRAMI PARAMETRIZATION .2. THE 1-FORMS

The 1-form diffeomorphism cohomologies within a local conformal Lagrangian field theory model built on a two dimensional Riemann surface with no boundary is studied. The case of scalar matter fields is considered and the complex structure is parametrized by Beltrami differential. The analysis is first performed at the classical level, and then we improve the quantum extension, introducing the current in the Lagrangian dynamics, coupled to external source fields. It is shown that the anomalies which spoil the current conservations take origin from the holomorphic region of the external fields, and only the differential spin 1 and 2 currents (as well as their c.c) could be anomalous. © 1995 American Institute of Physics.