Euclidian Yang-Mills theory in constant background fields and unstable modes

Within Euclidean SU(2) Yang-Mills theory considered in certain constant non-Abelian background fields the explicit construction of gluon and ghost Green functions is presented, paying special attention to unstable modes. The propagators obtained turn out to be purely real. The propagator expressions given for two different background fields are related to each other in the coincidence limit of these background configurations. On the basis of the derived results the imaginary part of the Euclidean Yang-Mill theory effective action is discussed, showing that no higher-loop corrections beyond the well known 1-loop results appear. Also arguments are given that the 1-loop imaginary part should not be trusted. (author)