Infra-red solutions of the Schwinger-Dyson equation for the discontinuity of the gluon propagator

1983 ◽  
Vol 74 (3) ◽  
pp. 267-276 ◽  
Author(s):  
F. Paccanoni
Keyword(s):  
Gluon Propagator ◽  
Dyson Equation ◽  
Infra Red

Infra-red behaviour of the gluon propagator in axial gauges

1983 ◽  
Vol 77 (2) ◽  
pp. 197-213 ◽  
Author(s):  
D. Atkinson ◽  
P. W. Johnson ◽  
W. J. Schoenmaker ◽  
H. A. Slim
Keyword(s):  
Gluon Propagator ◽  
Infra Red

scholarly journals Gluon dynamics from an ordinary differential equation

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
A. C. Aguilar ◽  
M. N. Ferreira ◽  
J. Papavassiliou
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Gluon Propagator ◽  
Dyson Equation ◽  
Kinetic Term ◽  
Practical Implementation ◽  
Gluon Vertex ◽  
Central Hypothesis ◽  
Approximate Form ◽  
Novel Method

AbstractWe present a novel method for computing the nonperturbative kinetic term of the gluon propagator from an ordinary differential equation, whose derivation hinges on the central hypothesis that the regular part of the three-gluon vertex and the aforementioned kinetic term are related by a partial Slavnov–Taylor identity. The main ingredients entering in the solution are projection of the three-gluon vertex and a particular derivative of the ghost-gluon kernel, whose approximate form is derived from a Schwinger–Dyson equation. Crucially, the requirement of a pole-free answer determines the initial condition, whose value is calculated from an integral containing the same ingredients as the solution itself. This feature fixes uniquely, at least in principle, the form of the kinetic term, once the ingredients have been accurately evaluated. In practice, however, due to substantial uncertainties in the computation of the necessary inputs, certain crucial components need be adjusted by hand, in order to obtain self-consistent results. Furthermore, if the gluon propagator has been independently accessed from the lattice, the solution for the kinetic term facilitates the extraction of the momentum-dependent effective gluon mass. The practical implementation of this method is carried out in detail, and the required approximations and theoretical assumptions are duly highlighted.

scholarly journals ANALYTICITY AND MINIMALITY OF NONPERTURBATIVE CONTRIBUTIONS IN PERTURBATIVE REGION FOR $\bar \alpha_{{\lc s}}$

1998 ◽  
Vol 13 (21) ◽  
pp. 1747-1756 ◽  
Author(s):  
ALEKSEY I. ALEKSEEV ◽  
BORIS A. ARBUZOV
Keyword(s):  
Gluon Propagator ◽  
Singular Term ◽  
Gluon Condensate ◽  
Dyson Equation ◽  
Ultraviolet Region ◽  
Coupling Constant ◽  
Running Coupling ◽  
Running Coupling Constant ◽  
Analytic Expression ◽  
Existing Data

It is shown that the possibility of freezing a QCD running coupling constant at zero with the approach of "forced analyticity" is not in agreement with Schwinger–Dyson equation for the gluon propagator. We propose to add to the analytic expression the well-known infrared singular term 1/q2 as well as a pole term corresponding to "excited gluon". By this example we formulate the principle of minimality of nonperturbative contributions in perturbative (ultraviolet) region, which allows us to fix ambiguities when introducing nonperturbative terms and maintain the finiteness of the gluon condensate. As a result, we obtain estimates of the gluon codensate, which agree quite well with the existing data. The value of the "excited gluon" mass is also of considerable interest.

scholarly journals A DYNAMICAL GLUON MASS SOLUTION IN MANDELSTAM'S APPROXIMATION

2005 ◽  
Vol 20 (32) ◽  
pp. 7613-7632 ◽  
Author(s):  
A. C. AGUILAR ◽  
A. A. NATALE
Keyword(s):  
Gluon Propagator ◽  
Asymptotic Expression ◽  
Full Range ◽  
Infrared Region ◽  
Landau Gauge ◽  
Dyson Equation ◽  
Renormalization Procedure ◽  
Light Cone Gauge ◽  
Gluon Mass ◽  
The One

We discuss the pure gauge Schwinger–Dyson equation for the gluon propagator in the Landau gauge within an approximation proposed by Mandelstam many years ago. We show that a dynamical gluon mass arises as a solution. This solution is obtained numerically in the full range of momenta that we have considered without the introduction of any ansatz or asymptotic expression in the infrared region. The vertex function that we use follows a prescription formulated by Cornwall to determine the existence of a dynamical gluon mass in the light cone gauge. The renormalization procedure differs from the one proposed by Mandelstam and allows for the possibility of a dynamical gluon mass. Some of the properties of this solution, such as its dependence on Λ QCD and its perturbative scaling behavior are also discussed.

Electron Microscopy of Human Gallstones

1971 ◽  
Vol 29 ◽  
pp. 296-297
Author(s):  
C. Wolpers ◽  
R. Blaschke
Keyword(s):  
Electron Microscopy ◽  
Room Temperature ◽  
Bile Pigment ◽  
X Ray Diffraction ◽  
Triclinic Crystal System ◽  
X Ray ◽  
Follow Up Study ◽  
Infra Red ◽  
Main Components

Scanning microscopy was used to study the surface of human gallstones and the surface of fractures. The specimens were obtained by operation, washed with water, dried at room temperature and shadowcasted with carbon and aluminum. Most of the specimens belong to patients from a series of X-ray follow-up study, examined during the last twenty years. So it was possible to evaluate approximately the age of these gallstones and to get information on the intensity of growing and solving.Cholesterol, a group of bile pigment substances and different salts of calcium, are the main components of human gallstones. By X-ray diffraction technique, infra-red spectroscopy and by chemical analysis it was demonstrated that all three components can be found in any gallstone. In the presence of water cholesterol crystallizes in pane-like plates of the triclinic crystal system.

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