Towards an effective bilocal theory from quantum chromodynamics in a background field

1983 ◽  
Vol 27 (10) ◽  
pp. 2423-2432 ◽  
Author(s):  
J. A. Magpantay
Keyword(s):  
Quantum Chromodynamics ◽  
Background Field

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.

scholarly journals Differential Dyson–Schwinger equations for quantum chromodynamics

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Marco Frasca
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Chromodynamics ◽  
Background Field ◽  
Low Energy ◽  
Quantum Field ◽  
Approximate Form ◽  
Energy Behavior ◽  
Hooft Limit ◽  
Dynamical Breaking

Abstract Using a technique devised by Bender, Milton and Savage, we derive the Dyson–Schwinger equations for quantum chromodynamics in differential form. We stop our analysis to the two-point functions. The ’t Hooft limit of color number going to infinity is derived showing how these equations can be cast into a treatable even if approximate form. It is seen how this limit gives a sound description of the low-energy behavior of quantum chromodynamics by discussing the dynamical breaking of chiral symmetry and confinement, providing a condition for the latter. This approach exploits a background field technique in quantum field theory.

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