scholarly journals Roles of the quark field in the infrared lattice Coulomb gauge and Landau gauge QCD

2008 ◽  
Author(s):  
Sadataka Furui ◽  
Hideo Nakajima
Keyword(s):  
Landau Gauge ◽  
Coulomb Gauge ◽  
Quark Field

scholarly journals Gauge-fixed Lattice QCD and the dispersion relation of Wilson fermions

2022 ◽  
Vol 258 ◽  
pp. 02003
Author(s):  
Giuseppe Burgio ◽  
Hannes Vogt
Keyword(s):  
Dispersion Relation ◽  
Lattice Qcd ◽  
Correlation Functions ◽  
Landau Gauge ◽  
Coulomb Gauge ◽  
Tree Level ◽  
Wilson Fermions

We show that, when investigating Wilson-fermions correlation functions on the lattice, one is bound to encounter major difficulties in defining their dispersion relation, even at tree level. The problem is indeed quite general and, although we stumbled upon it while studying Coulomb-gauge applications, it also affects gauge fixed studies in covariant gauges, including their most popular version, Landau gauge. In this paper we will discuss a solution to this problems based on a redefinition of the kinematic momentum of the fermion.

GAUGE INDEPENDENCE OF THE FERMION DAMPING RATE IN A HOT PLASMA - LANDAU GAUGE VS COULOMB GAUGE

1993 ◽  
Vol 08 (08) ◽  
pp. 739-748
Author(s):  
H. NAKKAGAWA ◽  
A. NIÉGAWA ◽  
B. PIRE
Keyword(s):  
Perturbation Theory ◽  
Gluon Propagator ◽  
Landau Gauge ◽  
Coulomb Gauge ◽  
Leading Order ◽  
Loop Order ◽  
Hard Thermal Loop ◽  
Hot Plasma ◽  
Damping Rate

The damping rate of a heavy muon/quark in a hot QED/QCD plasma is calculated in the Landau gauge to the effective one-loop order in the resummed perturbation theory of Braaten and Pisarski. For both a muon/quark at rest and in an energetic case we obtain to leading order the same result as in the Coulomb gauge. Resummation of hard-thermal loop corrections to the photon/gluon propagator is of key importance for this gauge independence.

scholarly journals Mass spectra of heavy pseudoscalars using instantaneous Bethe–Salpeter equation with different kernels

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Wei Li ◽  
Ying-Long Wang ◽  
Tai-Fu Feng ◽  
Guo-Li Wang
Keyword(s):  
Mass Spectra ◽  
Scalar Potential ◽  
Landau Gauge ◽  
Mass Splitting ◽  
Coulomb Gauge ◽  
Exchange Vector ◽  
Feynman Gauge ◽  
Vector Potentials ◽  
Time Component ◽  
Linear Scalar

Abstract We solved the instantaneous Bethe–Salpeter equation for heavy pseudoscalars in different kernels, where the kernels are obtained using linear scalar potential plus one gluon exchange vector potentials in Feynman gauge, Landau gauge, Coulomb gauge and time-component Coulomb gauge. Since we cannot give a complete QCD-based calculation, the results are gauge dependent. We compared the obtained mass spectra of heavy pseudoscalars between different kernels, found that using the same parameters we obtain the smallest mass splitting in time-component Coulomb gauge, the similar largest mass splitting in Feynman and Coulomb gauges, middle size splitting in Landau gauge.

scholarly journals INFRARED-SUPPRESSED GLUON PROPAGATOR IN 4D YANG–MILLS THEORY IN A LANDAU-LIKE GAUGE

2007 ◽  
Vol 22 (32) ◽  
pp. 2429-2438 ◽  
Author(s):  
ATTILIO CUCCHIERI ◽  
AXEL MAAS ◽  
TEREZA MENDES
Keyword(s):  
Finite Volume ◽  
Gluon Propagator ◽  
Three Dimensional ◽  
Landau Gauge ◽  
Coulomb Gauge ◽  
Dimensional Case ◽  
Gauge Parameter ◽  
Reflection Positivity ◽  
Yang Mills ◽  
Transverse Gluon

The infrared behavior of the gluon propagator is directly related to confinement in QCD. Indeed, the Gribov–Zwanziger scenario of confinement predicts an infrared vanishing (transverse) gluon propagator in Landau-like gauges, implying violation of reflection positivity and gluon confinement. Finite-volume effects make it very difficult to observe (in the minimal Landau gauge) an infrared suppressed gluon propagator in lattice simulations of the four-dimensional case. Here we report results for the SU(2) gluon propagator in a gauge that interpolates between the minimal Landau gauge (for gauge parameter λ equal to 1) and the minimal Coulomb gauge (corresponding to λ = 0). For small values of λ we find that the spatially-transverse gluon propagator D tr (0, |p|), considered as a function of the spatial momenta |p|, is clearly infrared suppressed. This result is in agreement with the Gribov–Zwanziger scenario and with previous numerical results in the minimal Coulomb gauge. We also discuss the nature of the limit λ→0 (complete Coulomb gauge) and its relation to the standard Coulomb gauge (λ = 0). Our findings are corroborated by similar results in the three-dimensional case, where the infrared suppression is observed for all considered values of λ.

GAUGE FIXING, UNITARITY AND PHASE SPACE PATH INTEGRALS

1992 ◽  
Vol 07 (21) ◽  
pp. 5245-5279 ◽  
Author(s):  
MARTIN LAVELLE ◽  
DAVID MCMULLAN
Keyword(s):  
Phase Space ◽  
Path Integral ◽  
Wide Class ◽  
Gauge Theories ◽  
Path Integrals ◽  
Landau Gauge ◽  
Coulomb Gauge ◽  
Restricted Version ◽  
Feynman Gauge ◽  
Gauge Fixing

We analyse the extent to which path integral techniques can be used to directly prove the unitarity of gauge theories. After reviewing the limitations of the most widely used approaches, we concentrate upon the method which is commonly regarded as solving the problem, i.e. that of Fradkin and Vilkovisky. We show through explicit counterexamples that their main theorem is incorrect. A proof is presented for a restricted version of their theorem. From this restricted theorem we are able to rederive Faddeev’s unitary phase space results for a wide class of canonical gauges (which includes the Coulomb gauge) and for the Feynman gauge. However, we show that there are serious problems with the extensions of this argument to the Landau gauge and hence the full Lorentz class. We conclude that there does not yet exist any satisfactory path integral discussion of the covariant gauges.

scholarly journals Perturbative linearization of super-Yang-Mills theories in general gauges

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Hannes Malcha ◽  
Hermann Nicolai
Keyword(s):  
Large Class ◽  
Fourth Order ◽  
Landau Gauge ◽  
Third Order ◽  
Yang Mills ◽  
Free Theory ◽  
Non Linear ◽  
Functional Measure ◽  
Non Local ◽  
Jacobi Determinant

Abstract Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant of the transformation equals the product of the fermionic determinants obtained by integrating out the gauginos and ghosts at least on the gauge hypersurface. While this transformation has been known so far only for the Landau gauge and to third order in the Yang-Mills coupling, we here extend the construction to a large class of (possibly non-linear and non-local) gauges, and exhibit the conditions for all statements to remain valid off the gauge hypersurface. Finally, we present explicit results to second order in the axial gauge and to fourth order in the Landau gauge.

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