Covariant extension of the Wigner transformation to non-abelian Yang-Mills symmetries for a Vlasov equation approach to the quark-gluon plasma

The Wigner transformation is generalized as a covariant operation with respect to a local gauge symmetry. The application to a quantum Klein-Gordon matter-field in the presence of the non-quantized self-consistent Yang-Mills field leads to a corresponding extension of the Vlasov equation, in the classical limit, and moreover to its quantum corrections, the leading ones of which are found to be commutator terms, characteristic for non-Abelian theories. In the application to chromodynamics a semiclassical model for a plasma of spinless quarks and gluons is obtained, which should be of use beyond the deconfinement transition