101 research outputs found
Gauge (in)dependence and background field formalism
It is shown that the gauge invariance and gauge dependence properties of
effective action for Yang-Mills theories should be considered as two
independent issues in the background field formalism. Application of this
formalism to formulate the functional renormalization group approach is
discussed. It is proven that there is a possibility to construct the
corresponding average effective action invariant under the gauge
transformations of background vector field. Nevertheless, being gauge invariant
this action remains gauge dependent on-shell.Comment: 14 pages, v2: typos corrected, v3:minor correction in Eqs. (2.24),
v4: a reference added, misprints corrected, accepted for publication in PL
Gribov horizon beyond the Landau gauge
Gribov and Zwanziger proposed a modification of Yang-Mills theory in order to
cure the Gribov copy problem. We employ field-dependent BRST transformations to
generalize the Gribov-Zwanziger model from the Landau gauge to general R_xi
gauges. The Gribov horizon functional is presented in explicit form, in both
the non-local and local variants. Finally, we show how to reach any given gauge
from the Landau one.Comment: 1+6 pages; v2: one ref. and 3 clarifications added, published versio
Representation of a gauge field via intrinsic "BRST" operator
We show that there exists a representation of a matrix valued gauge field via
intrinsic "BRST" operator assigned to matrix valued generators of a gauge
algebra. In this way, we reproduce the standard formulation of the ordinary
Yang - Mills theory. In the case of a generating quasigroup/groupoid, we give a
natural counterpart to the Yang - Mills action. The latter counterpart does
also apply as to the most general case of an involution for matrix-valued gauge
generators.Comment: 15 pages, no figures, Section 6 extended with (6.14), (6.15); v3:
Section 7 added, minor corrections; v4: Section 4, minor corrections; v5:
formula (4.11) modifie
- …