scholarly journals Lifting the Gribov ambiguity in Yang–Mills theories

2012 ◽  
Vol 712 (1-2) ◽  
pp. 97-103 ◽  
Author(s):  
J. Serreau ◽  
M. Tissier
Keyword(s):  
Yang Mills ◽  
Gribov Ambiguity

scholarly journals Quantization of Yang–Mills theory without the Gribov ambiguity

2017 ◽  
Vol 766 ◽  
pp. 231-237 ◽  
Author(s):  
Gao-Liang Zhou ◽  
Zheng-Xin Yan ◽  
Xin Zhang
Keyword(s):  
Yang Mills ◽  
Gribov Ambiguity

CLASSICAL YANG-MILLS THEORY WITH FERMIONS I: GENERAL PROPERTIES OF A SYSTEM WITH CONSTRAINTS

1995 ◽  
Vol 10 (25) ◽  
pp. 3531-3579 ◽  
Author(s):  
LUCA LUSANNA
Keyword(s):  
Principal Bundle ◽  
Winding Number ◽  
Hamiltonian Description ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Gauge Symmetries ◽  
Minkowski Space Time ◽  
Small Gauge ◽  
Simply Connected ◽  
Gribov Ambiguity

A review is made of the basic properties of the Hamiltonian description of classical Yang-Mills theory with fermions described by Grassmann-valued Dirac spinors, in the case of a trivial principal bundle with a compact, semisimple, connected, simply connected Lie structure group over Minkowski space-time. The Poincaré group is assumed to be globally implementable and only the field configurations producing finite Poincaré generators are considered. A detailed study of the Hamiltonian group of gauge transformations is made, trying to elucidate the meaning of the global gauge transformations (connected with the non-Abelian charges and with the center of the gauge group), of the winding number (connected with the large gauge transformations and with the topological charge) and of the small gauge transformations generated by the first class constraints. This leads to the identification of boundary conditions on the gauge potentials and their conjugate momenta suitable for the Hamiltonian description and allowing covariance of the non-Abelian charges. Finally, a review is made of the problem of the Gribov ambiguity, whose basis is connected with the existence of stability subgroups of gauge transformations for certain gauge potentials (gauge symmetries) and/or certain field strengths (gauge copies) in generic Sobolev spaces.

scholarly journals SU(2)×U(1) Yang–Mills theories in 3d with Higgs field and Gribov ambiguity

2013 ◽  
Vol 73 (10) ◽  
Author(s):  
M. A. L. Capri ◽  
D. Dudal ◽  
M. S. Guimaraes ◽  
I. F. Justo ◽  
S. P. Sorella ◽  
...  
Keyword(s):  
Higgs Field ◽  
Yang Mills ◽  
Gribov Ambiguity

scholarly journals The Gribov phenomenon in flat and curved spaces

2014 ◽  
Vol 11 (03) ◽  
pp. 1450018
Author(s):  
Marco de Cesare
Keyword(s):  
Integral Formula ◽  
Functional Integral ◽  
Green Functions ◽  
Ghost Propagator ◽  
Yang Mills ◽  
Color Confinement ◽  
Spacetime Curvature ◽  
Gauge Fixing ◽  
Recent Developments ◽  
Gribov Ambiguity

The quantization of Yang–Mills theories relies on the gauge-fixing procedure. However, in the non-Abelian case this procedure leads to the well-known Gribov ambiguity. In order to solve the ambiguity a modification of the functional integral formula must be introduced. As a consequence of this, the Green functions get deep modifications in the infrared. We consider, in particular, the SU (N) case and show that in the pure gauge case the ghost propagator is enhanced, while the gluon propagator is suppressed in this limit, therefore the study of the Gribov ambiguity may shed some light on the mass gap problem and on color confinement. We discuss some recent developments on the subject in the case of a curved background. We argue that the concurrent presence of a spacetime curvature and the Gribov ambiguity may introduce further modifications to the Green functions in the infrared.

scholarly journals Symmetry restoration and the gluon mass in the Landau gauge

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Urko Reinosa ◽  
Julien Serreau ◽  
Rodrigo Carmo Terin ◽  
Matthieu Tissier
Keyword(s):  
Field Theory ◽  
Sigma Model ◽  
Landau Gauge ◽  
Two Dimensions ◽  
Nonlinear Sigma Model ◽  
Yang Mills ◽  
Local Field Theory ◽  
Gauge Fixing ◽  
Gribov Ambiguity ◽  
Gribov Copies

We investigate the generation of a gluon screening mass in Yang-Mills theory in the Landau gauge. We propose a gauge-fixing procedure where the Gribov ambiguity is overcome by summing over all Gribov copies with some weight function. This can be formulated in terms of a local field theory involving constrained, nonlinear sigma model fields. We show that a phenomenon of radiative symmetry restoration occurs in this theory, similar to what happens in the standard nonlinear sigma model in two dimensions. This results in a nonzero gluon screening mass, as seen in lattice simulations.

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