Composite and Background Fields in Non-Abelian Gauge Models

A joint introduction of composite and background fields into non-Abelian quantum gauge theories is suggested based on the symmetries of the generating functional of Green's functions, with the systematic analysis focused on quantum Yang-Mills theories, including the properties of the generating functional of vertex Green's functions (effective action). For the effective action in such theories, gauge dependence is found in terms of a nilpotent operator with composite and background fields, and on-shell independence from gauge fixing is established. The basic concept of a joint introduction of composite and background fields into non-Abelian gauge theories is extended to the Volovich-Katanaev model of two-dimensional gravity with dynamical torsion, as well as to the Gribov-Zwanziger theory.