Canonical Quantization of Non-Abelian Gauge Fields

A canonical quantization is applied in an unambiguous way to a non-abelian gauge field under a condition of the Coulomb gauge. The ambiguity with respect to the order of quantized field variables is avoided by performing a transition from the classical to the quantum theory before removing the constraint imposed on the state vectors. The constraint which causes a big trouble with the violation of the unitarity of the S-matrix is transformed into a simple one which shows that the physical state vectors should be functionals of the transversal field variables. The Hamiltonian derived after this transformation becomes a complicated functional of the transversal fields.