Abstract
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.
Highlights
In the main part of the article, we implement the first approach as a starting point of our systematic analysis, assuming the composite fields to be local, whereas in the remaining part we show how the first and second approaches can be extended beyond the given assumptions by considering the Volovich–Katanaev model of two-dimensional gravity with dynamical torsion [50] and the Gribov–Zwanziger theory [23,24]
We have approached the issue of a joint introduction of composite and background fields into non-Abelian quantum gauge models on the basis of symmetries exhibited by the generating functional of Green’s functions
Our systematic analysis of the problem focuses on quantum Yang–Mills theories and local composite fields
Summary
Composite [1,2] and background [3,4,5] fields are widely used in quantum gauge theories. Implemented in the Gribov–Zwanziger model [23,24] being a quantum Yang–Mills theory in Landau gauge and including an additive horizon functional in terms of a non-local composite field [77]. As an extension of our second approach (3)–(5) beyond the Yang–Mills case, the quantized two-dimensional gravity [75] is modified by the presence of local composite fields, and the corresponding background effective action is found to be gauge-invariant in a way similar to the Yang–Mills case. Unless specified by an arrow, derivatives with respect to fields and sources are regarded as left-hand ones
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