scholarly journals Analytic structure of the quark propagator in a model with an infrared vanishing gluon propagator

1996 ◽  
Vol 53 (1) ◽  
pp. 446-457 ◽  
Author(s):  
Axel Bender ◽  
Reinhard Alkofer
Keyword(s):  
Gluon Propagator ◽  
Quark Propagator ◽  
Analytic Structure

scholarly journals Quark propagator, instantons, and gluon propagator

1999 ◽  
Vol 60 (6) ◽  
Author(s):  
L. S. Kisslinger ◽  
M. Aw ◽  
A. Harey ◽  
O. Linsuain
Keyword(s):  
Gluon Propagator ◽  
Quark Propagator

scholarly journals Analytic Structure of the Landau-Gauge Gluon Propagator

2012 ◽  
Vol 109 (25) ◽  
Author(s):  
Stefan Strauss ◽  
Christian S. Fischer ◽  
Christian Kellermann
Keyword(s):  
Gluon Propagator ◽  
Landau Gauge ◽  
Analytic Structure

NONPERTURBATIVE APPROACHES TO DETERMINING THE BEHAVIOR OF THE GLUON PROPAGATOR AND QUARK PROPAGATOR IN QUANTUM CHROMODYNAMICS BY SCHWINGER-DYSON EQUATIONS

1991 ◽  
Vol 06 (19) ◽  
pp. 3321-3345 ◽  
Author(s):  
A. HÄDICKE
Keyword(s):  
Quantum Chromodynamics ◽  
Gluon Propagator ◽  
Background Field ◽  
Mass Function ◽  
Field Method ◽  
Quark Propagator ◽  
Infrared Singularity ◽  
Dynamical Mass ◽  
Covariant Gauge ◽  
Background Field Method

The attempts to describe the behavior of the gluon propagator and quark propagator by using truncated Schwinger-Dyson equations and Slavnov-Taylor identities are reviewed. Special attention is paid to the problem of infrared behavior of Green’s functions. The most important attempts to calculate the gluon propagator using the axial as well as the covariant gauge are critically discussed. Furthermore, an approach concerning the gluon propagator is presented, with the background-field method as its basis. All the calculations confirm more or less the existence of an infrared singularity in the gluon propagator of the form q−4 in momentum space. The calculations to determine the behavior of the dynamical mass function of quarks, where the results concerning the gluon propagator are taken into account, show that chiral symmetry is dynamically broken. Furthermore, it turns out that there is no polelike singularity in the quark propagator. These results agree with the expectations from the confinement philosophy.

THE ANALYTIC STRUCTURE OF QUARK PROPAGATORS

1992 ◽  
Vol 07 (30) ◽  
pp. 7541-7559 ◽  
Author(s):  
S.J. STAINSBY ◽  
R.T. CAHILL
Keyword(s):  
Dyson Equation ◽  
Quark Propagator ◽  
Physical Significance ◽  
Analytic Structure ◽  
Complex Conjugate ◽  
Pinch Analysis ◽  
Branch Points ◽  
Momentum Complex ◽  
Logarithmic Functions

An approximate Schwinger-Dyson equation for the quark propagator in Euclidean QCD is solved numerically in the complex s=p2 plane, where pμ is the quark Euclidean four-momentum. Complex conjugate pairs of singularities are discovered and an analytic contour pinch analysis shows that any such singularities must be logarithmic branch points. Appropriate logarithmic functions are fitted near the branch points to accurately determine their position. The physical significance of these singularities is as yet unclear.

NONPERTURBATIVE QUARK PROPAGATOR APPROACH TO QCD AT LARGE DISTANCES

1994 ◽  
Vol 09 (05) ◽  
pp. 759-793 ◽  
Author(s):  
V. SH. GOGOHIA
Keyword(s):  
Gluon Propagator ◽  
Chiral Limit ◽  
Renormalization Constant ◽  
Quark Propagator ◽  
Quark Confinement ◽  
Quark Sector ◽  
Symmetry Breakdown ◽  
Gauge Fixing ◽  
Covariant Gauge ◽  
Multiplicative Renormalizability

A nonperturbative approach to QCD at large distances in the context of the Schwinger-Dyson equations and corresponding Slavnov-Taylor identity in the quark sector is presented. Making only one widely accepted assumption that the full gluon propagator becomes an infrared singular like (q2)−2 in the arbitrary covariant gauge, we find three and only three confinement-type solutions for the quark propagator (quark confinement theorem). Two of them vanish after the removal of the infrared regulation parameter. The third solution does not depend on this latter parameter, but it has no pole and it implies dynamical chiral symmetry breakdown (DCSB), which means a close connection between quark confinement and DCSB. We also show that multiplication solely by the quark infrared renormalization constant would make all the Green’s functions infrared finite (multiplicative renormalizability). The final forms of the renormalized (infrared finite) quark SD equations do not explicitly depend on a gauge-fixing parameter (“gauge invariance”). Our approach is free of ghost complications despite the fact that they play an essential role in nonperturbative dynamics. Our approach also implies the existence of a characteristic scale at which confinement, DCSB and other nonperturbative effects become essential. We solve explicitly the SD equation with corresponding ST identity for the above-mentioned IR finite quark propagator in the chiral limit and apply an effective potential in order to determine completely this solution.

QUARK-GLUON VERTEX AND STRUCTURE OF MESONS AND DIQUARKS

1994 ◽  
Vol 09 (38) ◽  
pp. 3551-3563 ◽  
Author(s):  
S.J. STAINSBY ◽  
R.T. CAHILL
Keyword(s):  
Form Factors ◽  
Quark Propagator ◽  
The Other ◽  
Analytic Structure ◽  
Complex Conjugate ◽  
Branch Points ◽  
Conjugate Pair ◽  
Gluon Vertex ◽  
Scalar Diquark ◽  
Complex Conjugate Pair

Two quark propagators with different analytic structure are employed in Bethe-Salpeter type equations for the pion and scalar diquark form factors. One of the quark propagators has been calculated with the inclusion of a trivial (bare) quark-gluon vertex and, as a consequence, contains a complex conjugate pair of logarithmic branch points. The other quark propagator is obtained using a non-trivial (dressed) vertex ansatz and is entire, with an essential singularity at infinity. The effects of these different quark propagators on the BSE solutions are compared.

scholarly journals WHAT THE INFRARED BEHAVIOR OF QCD VERTEX FUNCTIONS IN LANDAU GAUGE CAN TELL US ABOUT CONFINEMENT

2007 ◽  
Vol 16 (09) ◽  
pp. 2720-2732 ◽  
Author(s):  
R. ALKOFER ◽  
C. S. FISCHER ◽  
F. J. LLANES-ESTRADA ◽  
K. SCHWENZER
Keyword(s):  
Renormalization Group ◽  
Chiral Symmetry ◽  
Gluon Propagator ◽  
Landau Gauge ◽  
Quark Propagator ◽  
Lattice Data ◽  
Gluon Vertex ◽  
Infrared Behavior ◽  
Renormalization Group Equations ◽  
Infrared Singularities

The infrared behavior of Landau gauge QCD vertex functions is investigated employing a skeleton expansion of the Dyson–Schwinger and Renormalization Group equations. Results for the ghost-gluon, three-gluon, four-gluon and quark-gluon vertex functions are presented. Positivity violation of the gluon propagator, and thus gluon confinement, is demonstrated. Results of the Dyson–Schwinger equations for a finite volume are compared to corresponding lattice data. It is analytically demonstrated that a linear rising potential between heavy quarks can be generated by infrared singularities in the dressed quark-gluon vertex. The selfconsistent mechanism that generates these singularities necessarily entails the scalar Dirac amplitudes of the full vertex and the quark propagator. These can only be present when chiral symmetry is broken, either explicitly or dynamically.

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