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Coulomb gauge Yang-Mills theory within the first order formalism isconsidered with a view to deriving the propagator Dyson-Schwinger equations.The first order formalism is studied with special emphasis on the BRSinvariance and it is found that there exists two forms of invariance -invariance under the standard BRS transform and under a second, non-standardtransform. The field equations of motion and symmetries are derived explicitlyand certain exact relations that simplify the formalism are presented. It isshown that the Ward-Takahashi identity arising from invariance under thenon-standard part of the BRS transform is guaranteed by the functionalequations of motion. The Feynman rules and the general decomposition of thetwo-point Green's functions are derived. The propagator Dyson-Schwingerequations are derived and certain aspects (energy independence of ghost Green'sfunctions and the cancellation of energy divergences) are discussed.Comment: 23 pages, 2 figure

Propagator Dyson-Schwinger equations of Coulomb gauge Yang-Mills theory within the first order formalism