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 GAUGE FIXING IDENTITY IN THE BACKGROUND FIELD METHOD OF QCD IN PURE GAUGE

2010 ◽  
Vol 25 (20) ◽  
pp. 3885-3898
Author(s):  
GOURANGA C. NAYAK
Keyword(s):  
Background Field ◽  
Heavy Ion ◽  
High Energy ◽  
Field Method ◽  
Coulomb Gauge ◽  
Factorization Theorem ◽  
Pure Gauge ◽  
Gauge Fixing ◽  
Covariant Gauge ◽  
Background Field Method

In this paper we derive a gauge fixing identity by varying the covariant gauge fixing term in [Formula: see text] in the background field method of QCD in pure gauge. Using this gauge fixing identity, we establish a relation between [Formula: see text] in QCD and [Formula: see text] in background field method of QCD in pure gauge. We show the validity of this gauge fixing identity, in general noncovariant and general Coulomb gauge fixings respectively. This gauge fixing identity is used to prove factorization theorem in QCD at high energy colliders and in nonequilibrium QCD at high energy heavy-ion colliders.

scholarly journals NONCOMMUTATIVITY AND NON-ANTICOMMUTATIVITY PERTURBATIVE QUANTUM GRAVITY

2012 ◽  
Vol 27 (13) ◽  
pp. 1250075 ◽  
Author(s):  
MIR FAIZAL
Keyword(s):  
Quantum Gravity ◽  
Lagrangian Density ◽  
Background Field ◽  
Field Method ◽  
Gauge Fixing ◽  
Perturbative Quantum ◽  
Background Field Method

In this paper, we will study perturbative quantum gravity on supermanifolds with both noncommutativity and non-anticommutativity of spacetime coordinates. We shall first analyze the BRST and the anti-BRST symmetries of this theory. Then we will also analyze the effect of shifting all the fields of this theory in background field method. We will construct a Lagrangian density which apart from being invariant under the extended BRST transformations is also invariant under on-shell extended anti-BRST transformations. This will be done by using the Batalin–Vilkovisky (BV) formalism. Finally, we will show that the sum of the gauge-fixing term and the ghost term for this theory can be elegantly written down in superspace with a two Grassmann parameter.

scholarly journals FIELD DECOMPOSITION AND THE GROUND STATE STRUCTURE OF SU(2) YANG–MILLS THEORY

2002 ◽  
Vol 17 (25) ◽  
pp. 3681-3688 ◽  
Author(s):  
LISA FREYHULT
Keyword(s):  
Effective Potential ◽  
Ground State ◽  
Scalar Fields ◽  
Background Field ◽  
Field Method ◽  
Gauge Fields ◽  
Ground State Structure ◽  
State Structure ◽  
Yang Mills ◽  
Background Field Method

We compute the effective potential of SU(2) Yang–Mills theory using the background field method and the Faddeev–Niemi decomposition of the gauge fields. In particular, we find that the potential will depend on the values of two scalar fields in the decomposition and that its structure will give rise to a symmetry breaking.

scholarly journals Boundary contributions of on-shell recursion relations with multiple-line deformation

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
Chang Hu ◽  
Xiao-Di Li ◽  
Yi Li
Keyword(s):  
Recursion Relation ◽  
Background Field ◽  
Field Method ◽  
Tree Level ◽  
Link Type ◽  
Multiple Line ◽  
Boundary Operators ◽  
Background Field Method ◽  
The Right ◽  
Boundary Behaviors

AbstractThe on-shell recursion relation has been recognized as a powerful tool for calculating tree-level amplitudes in quantum field theory, but it does not work well when the residue of the deformed amplitude $$\hat{A}(z)$$ A ^ ( z ) does not vanish at infinity of z. However, in such a situation, we still can get the right amplitude by computing the boundary contribution explicitly. In Arkani-Hamed and Kaplan (JHEP 04:076. 10.1088/1126-6708/2008/04/076. arXiv:0801.2385, 2008), the background field method was first used to analyze the boundary behaviors of amplitudes with two deformed external lines in different theories. The same method has been generalized to calculate the explicit boundary operators of some amplitudes with BCFW-like deformation in Jin and Feng (JHEP 04:123. 10.1007/JHEP04(2016)123. arXiv:1507.00463, 2016). In this paper, we will take a step further to generalize the method to the case of multiple-line deformation, and to show how the boundary behaviors (even the boundary contributions) can be extracted in the method.

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