scholarly journals Nonperturbative confinement in quantum chromodynamics. II. Mandelstam’s gluon propagator

1982 ◽  
Vol 23 (10) ◽  
pp. 1917-1924 ◽  
Author(s):  
D. Atkinson ◽  
P. W. Johnson ◽  
K. Stam
Keyword(s):  
Quantum Chromodynamics ◽  
Gluon Propagator

scholarly journals QCD IN THE INFRARED WITH EXACT ANGULAR INTEGRATIONS

1998 ◽  
Vol 13 (13) ◽  
pp. 1055-1062 ◽  
Author(s):  
D. ATKINSON ◽  
J. C. R. BLOCH
Keyword(s):  
Fixed Point ◽  
Quantum Chromodynamics ◽  
Gluon Propagator ◽  
Simple Pole ◽  
Exact Calculation ◽  
Ghost Propagator ◽  
Infrared Behavior ◽  
Infrared Limit

In a previous paper we have shown that in quantum chromodynamics the gluon propagator vanishes in the infrared limit, while the ghost propagator is more singular than a simple pole. These results were obtained after angular averaging, but here we go beyond this approximation and perform an exact calculation of the angular integrals. The powers of the infrared behavior of the propagators are changed substantially. We find the very intriguing result that the gluon propagator vanishes in the infrared exactly like p2, whilst the ghost propagator is exactly as singular as 1/p4. We also find that the value of the infrared fixed point of the QCD coupling is much decreased: it is now equal to 4π/3.

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.

General exact solutions for the full gluon propagator in QCD with the mass gap

2016 ◽  
Vol 31 (28n29) ◽  
pp. 1645027
Author(s):  
V. Gogokhia ◽  
G. G. Barnaföldi
Keyword(s):  
Quantum Chromodynamics ◽  
Nonlinear Interaction ◽  
Invariant Theory ◽  
Gluon Propagator ◽  
Gauge Invariant ◽  
Self Energy ◽  
Mass Gap ◽  
Scale Point ◽  
Formal Solutions ◽  
Nonlinear Iteration

We have explicitly shown that Quantum Chromodynamics is a color gauge invariant theory with non-zero mass gap, which has been defined as the value of the regularized full gluon self-energy at a finite scale point. The mass gap itself is mainly generated by the nonlinear interaction of massless gluon modes. All this allows one to establish the structure of the full gluon propagator in the explicit presence of the mass gap. In this case, the two independent general types of formal solutions for the full gluon propagator as a function of the regularized mass gap have been found: (i) The nonlinear iteration solution at which the gluons remain massless is explicitly present. (ii) Existence of the solution with an effective gluon mass is also demonstrated.

scholarly journals Nonperturbative confinement in quantum chromodynamics. III. Improved gluon propagator

1984 ◽  
Vol 25 (6) ◽  
pp. 2095-2098 ◽  
Author(s):  
D. Atkinson ◽  
H. Boelens ◽  
S. J. Hiemstra ◽  
P. W. Johnson ◽  
W. J. Schoenmaker ◽  
...  
Keyword(s):  
Quantum Chromodynamics ◽  
Gluon Propagator
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