Linear covariant gauges on the lattice

Linear covariant gauges, such as Feynman gauge, are very useful in perturbative calculations. Their non-perturbative formulation is, however, highly non-trivial. In particular, it is a challenge to define linear covariant gauges on a lattice. We consider a class of gauges in lattice gauge theory that coincides with the perturbative definition of linear covariant gauges in the formal continuum limit. The corresponding gauge-fixing procedure is described and analyzed in detail, with an application to the pure SU(2) case. In addition, results for the gluon propagator in the two-dimensional case are given.

[1]  H. Verschelde,et al.  New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach , 2008 .

[2]  High-temperature limit of Landau-gauge Yang-Mills theory , 2004, hep-ph/0408074.

[3]  A. Cucchieri,et al.  What's up with IR gluon and ghost propagators in Landau gauge? A puzzling answer from huge lattices , 2007 .

[4]  S. Furui,et al.  Infrared Features of Unquenched Lattice Landau Gauge QCD , 2006 .

[5]  P. J. Silva,et al.  Just how different are SU(2) and SU(3) Landau-gauge propagators in the IR regime? , 2007, 0705.3367.

[6]  Critical slowing-down in SU(2) Landau gauge-fixing algorithms , 1995, hep-lat/9511020.

[7]  Christian S. Fischer.  Infrared properties of QCD from Dyson-Schwinger equations , 2006 .

[8]  L. Smekal,et al.  Comparing SU(2) to SU(3) gluodynamics on large lattices , 2007, 0710.1982.

[9]  V. N. Gribov,et al.  Quantization of non-Abelian gauge theories , 1978 .

[10]  A. C. Aguilar,et al.  Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations , 2008, 0802.1870.

[11]  S. Furui,et al.  Effects of the quark field on the ghost propagator of lattice Landau gauge QCD , 2006, hep-lat/0602027.

[12]  LATTICE GAUGE-FIXING FOR GENERIC COVARIANT GAUGES , 1996, hep-lat/9605032.

[13]  A. C. Aguilar,et al.  Infrared finite ghost propagator in the Feynman gauge , 2007, 0712.0780.

[14]  Numerical study of the fundamental modular region in the minimal Landau gauge , 1997, hep-lat/9711024.

[15]  Reinhard Alkofer,et al.  The infrared behaviour of QCD Green's functions ☆: Confinement, dynamical symmetry breaking, and hadrons as relativistic bound states , 2000 .

[16]  A. C. Aguilar,et al.  A dynamical gluon mass solution in a coupled system of the Schwinger-Dyson equations , 2004, hep-ph/0408254.

[17]  Landau gauge ghost and gluon propagators and the Faddeev-Popov operator spectrum , 2005, hep-lat/0511053.

[18]  A. Cucchieri,et al.  Constraints on the infrared behavior of the gluon propagator in Yang-Mills theories. , 2007, Physical review letters.

[19]  A. Cucchieri,et al.  Numerical study of the ghost-gluon vertex in Landau gauge , 2004 .

[21]  Lattice gauge fixing for parameter dependent covariant gauges , 1999, hep-lat/9911038.

[22]  M. L. Paciello,et al.  Problems on Lattice Gauge Fixing , 2001, hep-lat/0104012.

[23]  Lorenz von Smekal,et al.  A Solution to Coupled Dyson-Schwinger Equations for Gluons and Ghosts in Landau Gauge , 1997, hep-ph/9707327.

[24]  Renormalizability of the critical limit of lattice gauge theory by BRS invariance , 1993 .

[25]  Lattice Gauge Theory in Two Spacetime Dimensions , 1979 .

[26]  Christoph Lerche,et al.  Infrared exponent for gluon and ghost propagation in Landau gauge QCD , 2002 .

[27]  F. Rademakers,et al.  ROOT — An object oriented data analysis framework , 1997 .

[28]  Exploratory study of three-point Green's functions in Landau-gauge Yang-Mills theory , 2006, hep-lat/0605011.

[29]  Markus Q. Huber,et al.  The infrared behavior of Landau gauge Yang–Mills theory in d=2, 3 and 4 dimensions , 2007, 0705.3809.

[30]  H. Gies,et al.  Quark confinement from colour confinement , 2007, 0708.2413.

[31]  Daniel F Litim,et al.  Infrared behavior and fixed points in Landau-gauge QCD. , 2004, Physical review letters.

[32]  D. Zwanziger.  Time-independent stochastic quantization, Dyson-Schwinger equations, and infrared critical exponents in QCD , 2002, hep-th/0206053.

[33]  John Ellis,et al.  Int. J. Mod. Phys. , 2005 .

[34]  Quark confinement: the hard problem of hadron physics , 2006, hep-ph/0610365.

[35]  Lorenz von Smekal,et al.  The Infrared Behavior of QCD Green's Functions , 2000 .

[36]  Unquenching effects in the quark and gluon propagator , 2007, 0705.4129.

[37]  Infrared properties of propagators in Landau-gauge pure Yang-Mills theory at finite temperature , 2007, hep-lat/0702022.

[38]  D. Zwanziger.  Fundamental modular region, Boltzmann factor and area law in lattice theory , 1994 .

[39]  A. Denner,et al.  Gauge Theories of the Strong and Electroweak Interaction , 2001 .

[40]  Nonperturbative Faddeev-Popov formula and the infrared limit of QCD , 2003, hep-ph/0303028.

[41]  Daniel Zwanziger.  Nonperturbative Landau gauge and infrared critical exponents in QCD , 2002 .

[42]  Propagators and running coupling from SU(2) lattice gauge theory , 2003, hep-lat/0312036.

[43]  A. Maas.  Two- and three-point Green's functions in two-dimensional Landau-gauge Yang-Mills theory , 2007, 0704.0722.

[44]  A. Schiller,et al.  Towards the infrared limit in SU(3) Landau gauge lattice gluodynamics , 2005, hep-lat/0506007.

[45]  A. Yaouanc,et al.  IR finiteness of the ghost dressing function from numerical resolution of the ghost SD equation , 2008, 0801.2721.

[46]  Critical slowing-down in SU(2) Landau-gauge-fixing algorithms at β=∞ , 2003, hep-lat/0301019.

[47]  Lorenz von Smekal,et al.  INFRARED BEHAVIOR OF GLUON AND GHOST PROPAGATORS IN LANDAU GAUGE QCD , 1997 .

[48]  J. Micheli,et al.  On the IR behaviour of the Landau-gauge ghost propagator , 2008, 0803.2161.

[49]  Christian S. Fischer,et al.  Vertex functions and infrared fixed point in Landau gauge SU(N) Yang-Mills theory , 2005 .