The Lorentz-covariant quantization performed in the Hamiltonian path-integralformalism for massless non-Abelian gauge fields has been achieved. In thisquantization, the Lorentz condition, as a constraint, must be introducedinitially and incorporated into the Yang-Mills Lagrangian by the Lagrangeundetermined multiplier method. In this way, it is found that all Lorentzcomponents of a vector potential have thier corresponding conjugate canonicalvariables. This fact allows us to define Lorentz-invariant poisson brackets andcarry out the quantization in a Lorent-covariant manner. Key words: Non-Abeliangauge field, quantization, Hamiltonian path-integral formalism, Lorentzcovariance.
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