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.

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 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 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 Effective locality and gauge invariance

2018 ◽  
Vol 182 ◽  
pp. 02051
Author(s):  
T. Grandou
Keyword(s):  
Gauge Invariance ◽  
Degrees Of Freedom ◽  
Green's Functions ◽  
Green’S Functions ◽  
Perturbative Regime ◽  
The Way

A few years ago, based on standard functional manipulations, an unexpected property was proven to be 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 integration of the fermionic and gluonic degrees of freedom. Previous derivations of effective locality are reviewed, corrected, and enlarged. Focussing on the way nonabelian gauge invariance is realized in the non-perturbative regime of QCD, the meaning of effective locality is proposed.

scholarly journals AXIAL ANOMALY THROUGH ANALYTIC REGULARIZATION

1999 ◽  
Vol 14 (03) ◽  
pp. 177-183 ◽  
Author(s):  
L. A. MANZONI ◽  
B. M. PIMENTEL ◽  
J. L. TOMAZELLI
Keyword(s):  
Quantum Electrodynamics ◽  
Vacuum Polarization ◽  
Green's Functions ◽  
Green’S Functions ◽  
Gauge Invariant ◽  
Axial Anomaly ◽  
Analytic Regularization ◽  
Correct Implementation

In this work we consider the two-point Green's functions in (1+1)-dimensional quantum electrodynamics and show that the correct implementation of analytic regularization gives a gauge invariant result for the vacuum polarization amplitude and the correct coefficient for the axial anomaly.

scholarly journals On the non-perturbative realization of QCD gauge-invariance

2017 ◽  
Vol 32 (33) ◽  
pp. 1730030 ◽  
Author(s):  
H. M. Fried ◽  
T. Grandou ◽  
R. Hofmann
Keyword(s):  
Gauge Invariance ◽  
Degrees Of Freedom ◽  
Green's Functions ◽  
Green’S Functions ◽  
Abelian Gauge ◽  
Perturbative Regime ◽  
The Way

A few years ago the use of standard functional manipulations was demonstrated to imply an unexpected property satisfied by the fermionic Green’s functions of QCD: effective locality. This feature of QCD is non-perturbative as it results from a full integration of the gluonic degrees of freedom. In this paper, previous derivations of effective locality are reviewed, corrected, and enhanced. Focusing on the way non-Abelian gauge-invariance is realized in the non-perturbative regime of QCD, the deeper meaning of effective locality is discussed.

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