THE DUAL VARIABLES OF YANG-MILLS THEORY AND LOCAL GAUGE-INVARIANT VARIABLES

After adding auxiliary fields and integrating out the original variabl es, the Yang-Mills action can be expressed in terms of local gauge-inv ariant variables. This method reproduces the known solution of the two -dimensional SU(N) theory. In more than two dimensions the action spli ts into a topological part and a part proportional to cr,. We demonstr ate the procedure for SU(2) in three dimensions where we reproduce a g ravity-like theory. We discuss the four-dimensional case as well. We u se a cubic expression in the fields as a space-time metric to obtain a covariant Lagrangian. We also show how the four-dimensional SU(2) the ory can be expressed in terms of a local action with six degrees of fr eedom only.