  Coulomb gauge Yang-Mills theory within the first order formalism is
considered with a view to deriving the propagator Dyson-Schwinger equations.
The first order formalism is studied with special emphasis on the BRS
invariance and it is found that there exists two forms of invariance -
invariance under the standard BRS transform and under a second, non-standard
transform. The field equations of motion and symmetries are derived explicitly
and certain exact relations that simplify the formalism are presented. It is
shown that the Ward-Takahashi identity arising from invariance under the
non-standard part of the BRS transform is guaranteed by the functional
equations of motion. The Feynman rules and the general decomposition of the
two-point Green's functions are derived. The propagator Dyson-Schwinger
equations are derived and certain aspects (energy independence of ghost Green's
functions and the cancellation of energy divergences) are discussed.
