Ghost-free non-Abelian gauge theory mixing of gauge-invariant operators

Abstract

For a long time the homogeneous axial gauge has been known to be free of Faddeev-Popov ghosts. Nevertheless, only recently in a systematic study using modern firld-theoretic methods has it been shown by the authors that the S-matrix is covariant (gauge-independent) and unitary in such a “singular” gauge. This gauge is particularly well adapted to discuss the problem of mixing of gauge-invariant operators, the latter being important for the discussion of the small distance behaviour in asymptotically free theories of strong interactions. Here we want to give a theoretical basis for calculations in space-like or time-like axial gauges. By-products of our considerations are the proof of Lorentz covariance for the counterterms in the renormalized Lagrangian, for the parameters of spontaneous symmetry breaking and for the functions in renormalization group equations in such a non-covariant gauge.