ON THE SOLUTIONS OF 2-DIMENSIONAL GAUGE-THEORIES WITH AREA-PRESERVINGSYMMETRY

We study the generalization of the exact solution of two-dimensional Y ang-Mills theory to the space of all two-dimensional gauge field theor ies with the symmetry of area-preserving diffeomorphisms. We show that these theories are exactly solvable when formulated in the space of f irst-order lagrangians. The equivalence between the space of first-ord er lagrangians and the space of original lagrangians is interpreted by the standard renormalization theory.