[en] All meaningful Dirac brackets are computed, in the Coulomb gauge, for a SU(2) Yang-Mills field coupled with spin-1/2 field. The theory is quantized by abstracting the equal-time commutators from the corresponding Dirac brackets. Our results turn out to be in full agreement with those obtained by Schwinger through a significantly different method. Thus, the equivalence of both quantization schemes becomes reasonably established at the level of the operator formalism. The advantages of the quantization procedure mounted on the Dirac bracket formalism are discussed. The role played by the classical picture in the process of elaboration of the quantum dynamics becomes clarified. (Author)