Lorentz-covariantquantization of massless non-Abelian gauge fields in theHamiltonian path-integral formalism

Abstract

The Lorentz-covariant quantization performed in the Hamiltonianpath-integral formalism for massless non-Abelian gauge fields has beenachieved. In this quantization, the Lorentz condition, as a constraint, mustbe introduced initially and incorporated into the Yang-Mills Lagrangian bythe Lagrange undetermined multiplier method. In this way, it is found thatall Lorentz components of a vector potential have their correspondingconjugate canonical variables. This fact allows us to defineLorentz-invariant Poisson brackets and carry out the quantization in aLorentz-covariant manner.