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 which leaves the action invariant is derived from the constraints present. A non-Abelian 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.