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 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.

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.

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.

The Electromagnetic Field

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Electromagnetic Field ◽  
Gauge Invariance ◽  
Maxwell’S Equations ◽  
Green's Functions ◽  
Maxwell's Equations ◽  
Green’S Functions ◽  
Invariance Properties

The electromagnetic field. A brief review of Maxwell’s equations with a discussion of their invariance properties, both relativistic and gauge invariance. The formalism of Green’s functions is developed, including some physical applications.

OPERATOR REGULARIZATION AND THE DIVERGENCE OF THE SUPERCURRENT

1987 ◽  
Vol 02 (03) ◽  
pp. 785-796 ◽  
Author(s):  
D. G. C. McKEON ◽  
T. N. SHERRY
Keyword(s):  
Effective Action ◽  
Gauge Invariance ◽  
Green's Functions ◽  
Green’S Functions ◽  
Perturbative Expansion ◽  
Feynman Diagrams ◽  
Spinor Particle ◽  
Yang Mills ◽  
Loop Level ◽  
The One

Operator regularization is introduced as a procedure to compute Green's functions perturbatively. At the one-loop level the effective action is regularized by means of the ζ-function. A perturbative expansion due to Schwinger allows one to compute from the ζ-function one-loop one-particle irreducible Green's functions. By regulating in this way, we do not have to compute Feynman diagrams, we avoid having to introduce a regulating parameter into the initial Lagrangian and we do not encounter any divergent integrals. This procedure is illustrated for N = 1 super Yang-Mills theory in which the one-loop one-particle irreducible Green's function associated with the decay of the supercurrent into a vector and a spinor particle is treated. Gauge invariance is automatically maintained and the usual anomaly in the divergence of the super-current is recovered.

scholarly journals Effective locality and chiral symmetry breaking in QCD

2019 ◽  
Vol 34 (40) ◽  
pp. 1950335 ◽  
Author(s):  
T. Grandou ◽  
P. H. Tsang
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Degrees Of Freedom ◽  
Green's Functions ◽  
Green’S Functions ◽  
Chiral Symmetry Breaking ◽  
Dynamical Chiral Symmetry Breaking

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, and called 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, at eikonal and quenching approximation at least, the relation of effective locality to dynamical chiral symmetry breaking is examined.

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