scholarly journals Infrared behavior of the gluon propagator in the lattice Landau gauge: The three-dimensional case

1999 ◽  
Vol 60 (3) ◽  
Author(s):  
Attilio Cucchieri
Keyword(s):  
Gluon Propagator ◽  
Three Dimensional ◽  
Landau Gauge ◽  
Dimensional Case ◽  
Infrared Behavior

scholarly journals INFRARED-SUPPRESSED GLUON PROPAGATOR IN 4D YANG–MILLS THEORY IN A LANDAU-LIKE GAUGE

2007 ◽  
Vol 22 (32) ◽  
pp. 2429-2438 ◽  
Author(s):  
ATTILIO CUCCHIERI ◽  
AXEL MAAS ◽  
TEREZA MENDES
Keyword(s):  
Finite Volume ◽  
Gluon Propagator ◽  
Three Dimensional ◽  
Landau Gauge ◽  
Coulomb Gauge ◽  
Dimensional Case ◽  
Gauge Parameter ◽  
Reflection Positivity ◽  
Yang Mills ◽  
Transverse Gluon

The infrared behavior of the gluon propagator is directly related to confinement in QCD. Indeed, the Gribov–Zwanziger scenario of confinement predicts an infrared vanishing (transverse) gluon propagator in Landau-like gauges, implying violation of reflection positivity and gluon confinement. Finite-volume effects make it very difficult to observe (in the minimal Landau gauge) an infrared suppressed gluon propagator in lattice simulations of the four-dimensional case. Here we report results for the SU(2) gluon propagator in a gauge that interpolates between the minimal Landau gauge (for gauge parameter λ equal to 1) and the minimal Coulomb gauge (corresponding to λ = 0). For small values of λ we find that the spatially-transverse gluon propagator D tr (0, |p|), considered as a function of the spatial momenta |p|, is clearly infrared suppressed. This result is in agreement with the Gribov–Zwanziger scenario and with previous numerical results in the minimal Coulomb gauge. We also discuss the nature of the limit λ→0 (complete Coulomb gauge) and its relation to the standard Coulomb gauge (λ = 0). Our findings are corroborated by similar results in the three-dimensional case, where the infrared suppression is observed for all considered values of λ.

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.

Use of reciprocity theorem for obtaining Rayleigh wave radiation patterns

1966 ◽  
Vol 56 (4) ◽  
pp. 925-936 ◽  
Author(s):  
I. N. Gupta
Keyword(s):  
Rayleigh Wave ◽  
Rayleigh Waves ◽  
Three Dimensional ◽  
Reciprocity Theorem ◽  
Point Sources ◽  
Dimensional Case ◽  
Wave Radiation ◽  
Radiation Patterns ◽  
Homogeneous Half Space ◽  
Double Couple

abstract The reciprocity theorem is used to obtain Rayleigh wave radiation patterns from sources on the surface of or within an elastic semi-infinite medium. Nine elementary line sources first considered are: horizontal and vertical forces, horizontal and vertical double forces without moment, horizontal and vertical single couples, center of dilatation (two dimensional case), center of rotation, and double couple without moment. The results are extended to the three dimensional case of similar point sources in a homogeneous half space. Haskell's results for the radiation patterns of Rayleigh waves from a fault of arbitrary dip and direction of motion are reproduced in a much simpler manner. Numerical results on the effect of the depth of these sources on the Rayleigh wave amplitudes are shown for a solid having Poisson's ratio of 0.25.

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