Effective Locality QCD calculations and the Gribov copy problem

2020 ◽  
Vol 35 (27) ◽  
pp. 2050230 ◽  
Author(s):  
T. Grandou ◽  
R. Hofmann
Keyword(s):  
Gauge Field ◽  
Strong Coupling ◽  
Degrees Of Freedom ◽  
Green's Functions ◽  
Green’S Functions ◽  
Strong Coupling Limit ◽  
Unexpected Result ◽  
Remarkable Property ◽  
Gauge Invariant

Standard functional manipulations have been proven to imply a remarkable property satisfied by the fermionic Green’s functions of QCD and dubbed effective locality. Resulting from a full gauge invariant summation of the gauge field degrees of freedom, effective locality is a non-perturbative property of QCD. This unexpected result has lead to suspect that the famous Gribov copy problem had been somewhat overlooked. It is argued that it is not so. The analysis is conducted in the strong coupling limit, relevant to the Gribov problem.

scholarly journals QCD Effective Locality: A Theoretical and Phenomenological Review

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 481
Author(s):  
Herbert M. Fried ◽  
Yves Gabellini ◽  
Thierry Grandou ◽  
Peter H. Tsang
Keyword(s):  
Degrees Of Freedom ◽  
Green's Functions ◽  
Green’S Functions ◽  
Review Article ◽  
Gauge Invariant ◽  
Invariant Integration

About ten years ago, the use of standard functional manipulations was demonstrated to imply an unexpected property satisfied by the fermionic Green’s functions of QCD and dubbed Effective Locality. This feature of QCD is non-perturbative, as it results from a full gauge invariant integration of the gluonic degrees of freedom. In this review article, a few salient theoretical aspects and phenomenological applications of this property are summarized.

scholarly journals On How QCD Gauge Invariance Gets Realized in the Context of Effective Locality

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
H. M. Fried ◽  
T. Grandou ◽  
R. Hofmann
Keyword(s):  
Gauge Invariance ◽  
Degrees Of Freedom ◽  
Green's Functions ◽  
Green’S Functions ◽  
The Way

The fermionic Green’s functions of QCD exhibit an unexpected property of effective locality, which appears to be exact, involving no approximation. This property is nonperturbative, resulting from a full integration of the elementary gluonic degrees of freedom of QCD. Recalling, correcting, and extending the derivations of effective locality, focus is put on the way nonabelian gauge invariance gets realized in the fermionic nonperturbative regime of QCD.

scholarly journals COLOR BOSONIZATION, CHIRAL PARAMETRIZATION OF GLUONIC FIELD AND QCD EFFECTIVE ACTION

2006 ◽  
Vol 21 (35) ◽  
pp. 2649-2661 ◽  
Author(s):  
VICTOR NOVOZHILOV ◽  
YURI NOVOZHILOV
Keyword(s):  
Vector Field ◽  
Gauge Field ◽  
Degrees Of Freedom ◽  
Axial Vector ◽  
Color Space ◽  
Chiral Anomaly ◽  
Chiral Field ◽  
Gauge Invariant ◽  
Low Energies ◽  
Color Vector

We develop a color bosonization approach to treat QCD gauge field ("gluons") at low energies in order to derive an effective color action of QCD taking into account the quark chiral anomaly in the case of SU(2) color. We have found that there exists such a region in the chiral sector of color space, where a gauge field coincides with chirally rotated vector field, while an induced axial vector field disappears. In this region, the unit color vector of chiral field plays a defining role, and a gauge field is parametrized in terms of chiral parameters, so that no additional degrees of freedom are introduced by the chiral field. A QCD gauge field decomposition in color bosonization is a sum of a chirally rotated gauge field and an induced axial-vector field expressed in terms of gluonic variables. An induced axial-vector field defines the chiral color anomaly and an effective color action of QCD. This action admits existence of a gauge invariant d = 2 condensate of induced axial-vector field and mass.

scholarly journals NONPERTURBATIVE GREEN'S FUNCTIONS IN THEORIES WITH EXTENDED SUPERCONFORMAL SYMMETRY

1999 ◽  
Vol 14 (17) ◽  
pp. 2659-2674 ◽  
Author(s):  
PAUL HOWE ◽  
PETER WEST
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Harmonic Superspace ◽  
Ward Identities ◽  
Gauge Invariant ◽  
Superconformal Symmetry ◽  
Supersymmetric Theories ◽  
Chiral Superfields

The multiplets that occur in four-dimensional rigidly supersymmetric theories can be described either by chiral superfields in Minkowski superspace or analytic superfields in harmonic superspace. The superconformal Ward identities for Green's functions of gauge-invariant operators of these types are derived. It is shown that there are no chiral superconformal invariants. It is further shown that Green's functions of analytic operators in harmonic superspace are severely restricted by the superconformal Ward identities when internal analyticity is taken into account.

scholarly journals INTEGRABILITY AND DUALITY IN TWO-DIMENSIONAL QCD

1995 ◽  
Vol 10 (11) ◽  
pp. 1611-1640 ◽  
Author(s):  
E. ABDALLA ◽  
M.C.B. ABDALLA
Keyword(s):  
Hilbert Space ◽  
Quantum Theory ◽  
Strong Coupling ◽  
Integrability Condition ◽  
Strong Coupling Limit ◽  
Two Dimensional ◽  
Gauge Invariant ◽  
Type Transformation

We consider bosonized QCD2, and prove that after one rewrites the theory in terms of gauge-invariant fields, there exists an integrability condition that is valid for the quantum theory as well. Furthermore, performing a duality type transformation we obtain an appropriate action for the description of the strong coupling limit, which is still integrable. We also prove that the model displays a complicated set of constraints, which restrict the dynamics of part of the theory, but which are necessary for maintaining the positive metric Hilbert space.

Green's functions in an exterior gauge field

1987 ◽  
Vol 30 (9) ◽  
pp. 780-783
Author(s):  
V. P. Barashev ◽  
I. M. Likhttsier ◽  
Sh. M. Shvartsman
Keyword(s):  
Gauge Field ◽  
Green's Functions ◽  
Green’S Functions
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