Gribov copies in the minimal landau gauge: The influence on gluon and ghost propagators

Nuclear Physics B

Volumn 508, Issue 1-2, 1997, Pages 353-370

  Cucchieri, Attilio ^a,b  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b BIELEFELD UNIVERSITY   (Germany)

Author keywords

Gluon and ghost propagators; Gribov copies; Landau gauge; Lattice gauge theory

Indexed keywords

EID: 0031584018     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(97)80016-8     Document Type: Article

References (61)

1. [1] V.N. Gribov, Nucl. Phys. B 139 (1978) 1.
2. [2] G.C. Rossi, Nucl. Phys. B (Proc. Suppl.) 53 (1997) 3.
3. [3] E. Marinari, C. Parrinello and R. Ricci, Nucl. Phys. B 362 (1991) 487.
4. [4] Ph. de Forcrand et al., Nucl. Phys. B (Proc. Suppl.) 20 (1991) 194; J.E. Mandula and M.C. Ogilvie, Phys. Rev. D 41 (1990) 2586; LE. Hetrick et al., Nucl. Phys, B (Proc. Suppl.) 26 (1992) 432; A. Nakamura and M. Mizutani, Vistas in Astronomy 37 (1993) 305.
5. [4] Ph. de Forcrand et al., Nucl. Phys. B (Proc. Suppl.) 20 (1991) 194; J.E. Mandula and M.C. Ogilvie, Phys. Rev. D 41 (1990) 2586; LE. Hetrick et al., Nucl. Phys, B (Proc. Suppl.) 26 (1992) 432; A. Nakamura and M. Mizutani, Vistas in Astronomy 37 (1993) 305.
6. [4] Ph. de Forcrand et al., Nucl. Phys. B (Proc. Suppl.) 20 (1991) 194; J.E. Mandula and M.C. Ogilvie, Phys. Rev. D 41 (1990) 2586; LE. Hetrick et al., Nucl. Phys, B (Proc. Suppl.) 26 (1992) 432; A. Nakamura and M. Mizutani, Vistas in Astronomy 37 (1993) 305.
7. [4] Ph. de Forcrand et al., Nucl. Phys. B (Proc. Suppl.) 20 (1991) 194; J.E. Mandula and M.C. Ogilvie, Phys. Rev. D 41 (1990) 2586; LE. Hetrick et al., Nucl. Phys, B (Proc. Suppl.) 26 (1992) 432; A. Nakamura and M. Mizutani, Vistas in Astronomy 37 (1993) 305.
8. [5] Ph. de Forcrand and J.E. Hetrick, Nucl. Phys. B (Proc. Suppl.) 42 (1995) 861.
9. [6] P. Marenzoni and P. Rossi, Phys. Lett. B 311 (1993) 219.
10. [7] K.G. Wilson, Recent Developments in Gauge Theories Proc. NATO Advanced Study Institute (Cargése, 1979), ed. G. 't Hooft et al. (Plenum, New York-London, 1980).
11. [8] J.E. Mandula and M. Ogilvie, Phys. Lett. B185 (1987) 127.
12. [9] S. Hioki et al., Phys. Lett. B 271 (1991) 201.
13. [10] M.L. Paciello et al., Phys, Lett. B 289 (1992) 405; M.L. Paciello et al., Phys. Lett. B 341 (1994) 341; L. Conti et al., Phys. Lett. B 373 (1996) 164.
14. [10] M.L. Paciello et al., Phys, Lett. B 289 (1992) 405; M.L. Paciello et al., Phys. Lett. B 341 (1994) 341; L. Conti et al., Phys. Lett. B 373 (1996) 164.
15. [10] M.L. Paciello et al., Phys, Lett. B 289 (1992) 405; M.L. Paciello et al., Phys. Lett. B 341 (1994) 341; L. Conti et al., Phys. Lett. B 373 (1996) 164.
16. [11] U.M. Heller, F Karsch and J. Rank, Phys. Lett. B 355 (1995) 511.
17. [12] G.S. Bali et al., Nucl. Phys. B (Proc, Suppl.) 42 (1995) 852.
18. [13] G.S. Bali et al., Phys. Rev. D 54 (1996) 2863.
19. [14] A. Nakamura and M. Plewnia, Phys. Lett. B 255 (1991) 274; V.G. Bornyakov et al., Nucl. Phys. B (Proc. Suppl.) 34 (1994) 802.
20. [14] A. Nakamura and M. Plewnia, Phys. Lett. B 255 (1991) 274; V.G. Bornyakov et al., Nucl. Phys. B (Proc. Suppl.) 34 (1994) 802.
21. [15] L. Del Debbio et al., Nucl. Phys. B (Proc. Suppl.) 53 (1997) 141.
22. [16] R. Gupta et al., Phys. Rev. D 36 (1987) 2813; P. Marenzoni et al., Phys. Lett. B 318 (1993) 511; C. Bernard, C. Parrinello and A. Soni, Phys. Rev. D 49 (1994) 1585; P. Marenzoni, G. Martinelli and N. Stella, Nucl. Phys. B455 (1995) 339.
23. [16] R. Gupta et al., Phys. Rev. D 36 (1987) 2813; P. Marenzoni et al., Phys. Lett. B 318 (1993) 511; C. Bernard, C. Parrinello and A. Soni, Phys. Rev. D 49 (1994) 1585; P. Marenzoni, G. Martinelli and N. Stella, Nucl. Phys. B455 (1995) 339.
24. [16] R. Gupta et al., Phys. Rev. D 36 (1987) 2813; P. Marenzoni et al., Phys. Lett. B 318 (1993) 511; C. Bernard, C. Parrinello and A. Soni, Phys. Rev. D 49 (1994) 1585; P. Marenzoni, G. Martinelli and N. Stella, Nucl. Phys. B455 (1995) 339.
25. [16] R. Gupta et al., Phys. Rev. D 36 (1987) 2813; P. Marenzoni et al., Phys. Lett. B 318 (1993) 511; C. Bernard, C. Parrinello and A. Soni, Phys. Rev. D 49 (1994) 1585; P. Marenzoni, G. Martinelli and N. Stella, Nucl. Phys. B455 (1995) 339.
26. [17] A. Nakamura et al., Gluon Propagators and Confinement, hep-lat/9506024, published in RCNP Confinement 1995; H. Aiso et al., Nucl. Phys. B (Proc. Suppt.) 53 (1997) 570; F. Gutbrod, A Study of the Gluon Propagator in SU(2) Lattice Gauge Theory, DESY-96-252 preprint.
27. [17] A. Nakamura et al., Gluon Propagators and Confinement, hep-lat/9506024, published in RCNP Confinement 1995; H. Aiso et al., Nucl. Phys. B (Proc. Suppt.) 53 (1997) 570; F. Gutbrod, A Study of the Gluon Propagator in SU(2) Lattice Gauge Theory, DESY-96-252 preprint.
28. [17] A. Nakamura et al., Gluon Propagators and Confinement, hep-lat/9506024, published in RCNP Confinement 1995; H. Aiso et al., Nucl. Phys. B (Proc. Suppt.) 53 (1997) 570; F. Gutbrod, A Study of the Gluon Propagator in SU(2) Lattice Gauge Theory, DESY-96-252 preprint.
29. [18] H. Suman and K. Schilling, Phys. Lett. B 373 (1996) 314.
30. [19] M.A. Semenov-Tyan-Shanskii and V.A. Franke, Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V.A. Steklova AN SSSR 120 (1982) 159 [English translation: J. Sov. Math. 34 (1986) 1999]; G. Dell'Antonio and D. Zwanziger, Commun. Math. Phys. 138 (1991) 291.
31. [19] M.A. Semenov-Tyan-Shanskii and V.A. Franke, Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V.A. Steklova AN SSSR 120 (1982) 159 [English translation: J. Sov. Math. 34 (1986) 1999]; G. Dell'Antonio and D. Zwanziger, Commun. Math. Phys. 138 (1991) 291.
32. [19] M.A. Semenov-Tyan-Shanskii and V.A. Franke, Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V.A. Steklova AN SSSR 120 (1982) 159 [English translation: J. Sov. Math. 34 (1986) 1999]; G. Dell'Antonio and D. Zwanziger, Commun. Math. Phys. 138 (1991) 291.
33. [20] P. van Baal, Nucl. Phys. B 369 (1992) 259; P. van Baal, Global Issues in Gauge Fixing, hep-th/9511119, published in the Proceedings of the QCD Workshop, Trento (Italy) 1995.
34. [20] P. van Baal, Nucl. Phys. B 369 (1992) 259; P. van Baal, Global Issues in Gauge Fixing, hep-th/9511119, published in the Proceedings of the QCD Workshop, Trento (Italy) 1995.
35. [21] I.M, Singer, Commun. Math. Phys. 60 (1978) 7; T.P. Killingback, Phys. Lett. B 138 (1984) 87.
36. [21] I.M, Singer, Commun. Math. Phys. 60 (1978) 7; T.P. Killingback, Phys. Lett. B 138 (1984) 87.
37. [22] D. Zwanziger, Nucl. Phys. B 364 (1991) 127.
38. [23] D. Zwanziger, Nucf. Phys. B 412 (1994) 657.
39. [24] V.K. Mitryushkin, Phys. Lett. B 390 (1997) 293.
40. [25] M. Schaden and D. Zwanziger, Horizon Condition Holds Pointwise on Finite Lattice with Free Boundary Conditions, hep-th/9410019, published in the Proceedings of the Workshop on Quantum Infrared Physics, Paris (France) 6-10 Jun 1994.
41. [26] D. Zwanziger, Phys. Lett. B 257 (1991) 168.
42. [27] A. Cucchieri, Numerical Results in Minimal Lattice Coulomb and Landau Gauges: Color-Coulomb Potential and Gluon and Ghost Propagators, PhD thesis, New York University (May 1996).
43. [28] F.R. Brown and T.J. Woch, Phys. Rev. Lett. 58 (1987) 2394; S.L. Adler, Nucl. Phys. B (Proc. Suppl.) 9 ( 1989) 437; U. Wolff, Nucl. Phys. B (Proc. Suppl.) 17 (1990) 93; U. Wolff, Phys. Lett. B 288 (1992) 166; U. Wolff, Int.J. Mod. Phys. C 4 (1993) 451.
44. [28] F.R. Brown and T.J. Woch, Phys. Rev. Lett. 58 (1987) 2394; S.L. Adler, Nucl. Phys. B (Proc. Suppl.) 9 ( 1989) 437; U. Wolff, Nucl. Phys. B (Proc. Suppl.) 17 (1990) 93; U. Wolff, Phys. Lett. B 288 (1992) 166; U. Wolff, Int.J. Mod. Phys. C 4 (1993) 451.
45. [28] F.R. Brown and T.J. Woch, Phys. Rev. Lett. 58 (1987) 2394; S.L. Adler, Nucl. Phys. B (Proc. Suppl.) 9 ( 1989) 437; U. Wolff, Nucl. Phys. B (Proc. Suppl.) 17 (1990) 93; U. Wolff, Phys. Lett. B 288 (1992) 166; U. Wolff, Int.J. Mod. Phys. C 4 (1993) 451.
46. [28] F.R. Brown and T.J. Woch, Phys. Rev. Lett. 58 (1987) 2394; S.L. Adler, Nucl. Phys. B (Proc. Suppl.) 9 ( 1989) 437; U. Wolff, Nucl. Phys. B (Proc. Suppl.) 17 (1990) 93; U. Wolff, Phys. Lett. B 288 (1992) 166; U. Wolff, Int.J. Mod. Phys. C 4 (1993) 451.
47. [28] F.R. Brown and T.J. Woch, Phys. Rev. Lett. 58 (1987) 2394; S.L. Adler, Nucl. Phys. B (Proc. Suppl.) 9 ( 1989) 437; U. Wolff, Nucl. Phys. B (Proc. Suppl.) 17 (1990) 93; U. Wolff, Phys. Lett. B 288 (1992) 166; U. Wolff, Int.J. Mod. Phys. C 4 (1993) 451.
48. [29] K.M. Decker and Ph. de Forcrand, Nucl. Phys. B (Proc. Suppl.) 17 (1990) 567.
49. [30] A.D. Sokal, Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms, Cours de Troisième Cycle de la Physique en Suisse Romande (Lausanne, June 1989).
50. [31] M. Lüscher et al., Nucl. Phys. B 389 (1993) 247.
51. [32] R.G. Edwards et al., Nucl. Phys. B 380 (1992) 621.
52. [33] G. de Divitiis et al., Nucl. Phys. B 437 (1995) 447.
53. [34] M. Grabenstein and K. Pinn, Phys. Rev. D 50 (1994) 6998.
54. [35] Ph. de Forcrand and R. Gupta, Nucl. Phys. B (Proc. Suppl.) 9 (1989) 516.
55. [36] A. Cucchieri and T. Mendes, Nucl. Phys. B 471 (1996) 263; A. Cucchieri and T. Mendes, Nucl. Phys. B (Proc. Suppl.) 53 (1997) 811; A. Cucchieri and T. Mendes, Critical Slowing-Down in SU(2) Landau Gauge-Fixing Algorithms (II): the Four-Dimensional Case, to be submitted to Nucl. Phys. B.
56. [36] A. Cucchieri and T. Mendes, Nucl. Phys. B 471 (1996) 263; A. Cucchieri and T. Mendes, Nucl. Phys. B (Proc. Suppl.) 53 (1997) 811; A. Cucchieri and T. Mendes, Critical Slowing-Down in SU(2) Landau Gauge-Fixing Algorithms (II): the Four-Dimensional Case, to be submitted to Nucl. Phys. B.
57. [36] A. Cucchieri and T. Mendes, Nucl. Phys. B 471 (1996) 263; A. Cucchieri and T. Mendes, Nucl. Phys. B (Proc. Suppl.) 53 (1997) 811; A. Cucchieri and T. Mendes, Critical Slowing-Down in SU(2) Landau Gauge-Fixing Algorithms (II): the Four-Dimensional Case, to be submitted to Nucl. Phys. B.
58. [37] L. von Smekal, A. Hauck and R. Alkofer, A Solution to Coupled Dyson-Schwinger Equations for Gluons and Ghosts in Landau Gauge, hep-ph/9707327.
59. [38] A. Cucchieri, Numerical Study of the Fundamental Modular Region in the Minimal Landau Gauge, in preparation.
60. [39] W.H. Press et al., Numerical Recipes (Cambridge University Press, Cambridge, 1992, second edition).
61. [40] A. Cucchieri, Infra-Red Behavior of the Gluon Propagator in Lattice Landau Gauge, submitted to Phys. Lett. B.