An analysis of the first-order form of gauge theories

The first-order form of a Maxwell theory and U(1) gauge theory in which a gauge invariant mass term appears is analyzed using the Dirac procedure. The form of the gauge transformation that leaves the action invariant is derived from the constraints present. A nonabelian generalization is similarly analyzed. This first-order three dimensional massive gauge theory is rewritten in terms of two interacting vector fields. The constraint structure when using light-cone coordinates is considered. The relationship between first- and second-order forms of the two-dimensional Einstein-Hilbert action is explored where a Lagrange multiplier is used to ensure their equivalence.