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The present and future of lattice QCD

  • T. DeGrand
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 409)

Abstract

These lectures provide an introduction to lattice methods for nonperturbative studies of Quantum Chromodynamics. I give a brief introduction to the subject, then discuss areas of current interest: spectroscopy, matrix elements, and the physics of high temperature QCD.

Keywords

Wave Function Lattice Spacing Quark Mass Wilson Loop Wilson Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Wilson, K.: Phys. Rev. D 10 (1974) 2445Google Scholar
  2. 2.
    Elitzur, S.: Phys. Rev. D 12 (1975) 3978Google Scholar
  3. 3.
    This particular formulation of the problem was shown to me by Toussaint, D.Google Scholar
  4. 4.
    See the discussion by Flensberg, M., and Peterson, C.: Nucl. Phys. B283 (1987) 141Google Scholar
  5. 5.
    A good reference for strong coupling expansions is Drouffe, J.M., Itzykson, C.: Phys. Rept. 38C (1978) 133Google Scholar
  6. 6.
    Golterman, M., Smit, J.: Nucl. Phys. B255 (1985) 328Google Scholar
  7. 7.
    Andersen, H.C.: J. Chem. Phys. 72 (1980) 2384; Duane, S.: Nucl. Phys. B257 (1985) 652; Duane, S., Kogut, K.: Phys. Rev. Lett. 55 (1985) 2774; Gottlieb, S., Liu, W., Toussaint, A.D., Renken, R., Sugar, R.: Phys. Rev. D 35 (1987) 2531Google Scholar
  8. 8.
    Duane, S., Kennedy, A., Pendleton, B., Roweth, D.: Phys. Lett. 194B (1987) 271Google Scholar
  9. 9.
    Brown, F., Woch, T.: Phys. Rev. Lett. 58 (1987) 2394; Creutz, M.: Phys. Rev. D 36 (1987) 55 For a review, see Adler, S.: in the Proceedings of the 1988 Symposium on Lattice Field Theory, Kronfeld, A., Mackenzie, P.: eds., Nucl. Phys. B (Proc. Suppl.) 9(1989)Google Scholar
  10. 10.
    This discussion is stolen from Lepage, G.P.: in “From Actions to Answers-Proceedings of the 1989 Theoretical Advanced Summer Institute in Particle Physics,” DeGrand, T., Toussaint, D.: eds., (World, 1990)Google Scholar
  11. 11.
    Bitar, K.M., et al.: in preparation.Google Scholar
  12. 12.
    For a good introduction to error analysis see Toussaint, D.: in “From Actions to Answers-Proceedings of the 1989 Theoretical Advanced Summer Institute in Particle Physics,” DeGrand, T., Toussaint, D.: eds., (World, 1990)Google Scholar
  13. 13.
    A good gauge fixing algorithm is overrelaxation and is described in Mandula, J.E., Ogilvie, M.C.: Phys. Lett. 248B (1990) 156Google Scholar
  14. 14.
    Marinari, E.: in the Proceedings of the 1988 Symposium on Lattice Field Theory, Kronfeld, A., Mackenzie, P.: eds., Nucl. Phys. B (Proc. Suppl) 9 (1989) 209; Bacilieri, P., et al.: Phys. Lett. 214B (1988) 115Google Scholar
  15. 15.
    Gusken, S., et al.: Phys. Lett. 227B (1989) 266; Gusken, S.: Nucl. Phys. B (Proc. Suppl) 17 (1989) 361Google Scholar
  16. 16.
    Gupta, R., Baillie, C., Brickner, R., Kilcup, G., Patel, A., Sharpe, S.: Phys. Rev. D 44 (1991) 3272Google Scholar
  17. 17.
    Bitar, K.M., et al.: Phys. Rev. Lett. 65 (1990) 2106, Phys. Rev. D 42 (1990) 3794Google Scholar
  18. 18.
    Gupta, R., Guralnik, G., Kilcup, G., Sharpe, S.: Phys. Rev. D 43 (1991) 2003Google Scholar
  19. 19.
    Kronfeld, A.: in the Proceedings of the 1988 Symposium on Lattice Field Theory, Kronfeld, A.,Mackenzie, P. eds., Nucl. Phys. B (Proc. Suppl.) 9 (1989)Google Scholar
  20. 20.
    Compare Falcioni, M., Paciello, M., Parisi, G., Taglienti, B.: Nucl. Phys. B251 (1985) 624; Teper, M.: Phys. Lett. 183B (1987) 345; Phys. Lett. 185B (1987) 121; DeGrand, T.: Phys. Rev. D 36 (1987) 176Google Scholar
  21. 21.
    Velikson B.,Weingarten, D.: Nucl. Phys. B249 (1985) 433Google Scholar
  22. 22.
    Gottlieb, S.: in “Advances in Lattice Gauge Theory,” Duke D., Owens, J.: eds. (World Scientific, 1985)Google Scholar
  23. 23.
    Chu, M. C., Lassia, M., Negele, J.W.: Nucl. Phys. 8360 (1991) 31Google Scholar
  24. 24.
    Brodsky, S., Lepage, G.P.: Phys. Lett. 878 (1979) 359; Phys. Rev. D 22 (1980) 2157Google Scholar
  25. 25.
    Weingarten, D.,Petcher, D.: Phys. Lett. 998 (1981) 333; Hamber, H., Parisi, G.: Phys. Rev. Lett. 47 (1981) 1792Google Scholar
  26. 26.
    Brown, F., et al.: Phys. Rev. Lett. 67 (1991) 1062Google Scholar
  27. 27.
    Bitar, K., et al.: in the Proceedings of Lattice '90, U. Heller, A. Kennedy and S. Sanielevici, eds. Nucl. Phys. B (Pros. Suppl) 20 (1991) 362Google Scholar
  28. 28.
    Gottlieb, S., Liu, W., Toussaint, D., Renken, R., Sugar, R.: Phys. Rev. D 38 (1988) 2245Google Scholar
  29. 29.
    Fukugita, M., Mino, H., Okawa, M., Ukawa, A.: preprint KEK-TH-271 (1990)Google Scholar
  30. 30.
    Bacilieri, P., et al.: Nucl. Phys. 8343 (1990) 228; Cabasino, S., et al.: Phys. Lett. 258B (1991) 202Google Scholar
  31. 31.
    Bacilieri, P., et al.: Nucl. Phys. 8317 (1989) 509; Cabasino, S., et al.: Phys. Lett. 258B (1991) 195Google Scholar
  32. 32.
    Thacker, B., Lepage, G.P.: Phys. Rev. D 43 (1991) 196Google Scholar
  33. 33.
    Kokkedee, J.: “The Quark Model,” (W. A. Benjamin, New York, 1969)Google Scholar
  34. 34.
    Hecht, M., DeGrand, T.: Phys. Lett. B, in pressGoogle Scholar
  35. 35.
    Svetitsky, B.: Phys. Rep. 132 (1986) 1Google Scholar
  36. 36.
    Svetitsky, B., Yaffe, L.: Phys. Rev. D 26 (1982) 963, Nucl. Phys. B210 (1982) 423Google Scholar
  37. 37.
    Pisarski, R., Wilczek, F.: Phys. Rev. D 29 (1984) 338Google Scholar
  38. 38.
    Bernard, C., DeGrand, T., DeTar, C., Gottlieb, S., Krasnitz, A., Ogilvie, M.C., Sugar, R.L., Toussaint, D.: University of California, Santa Barbara report UCSB TH-91-52 (1991)Google Scholar
  39. 39.
    Brown, F., et al.: Phys. Rev. Lett. 65 (1990) 2491Google Scholar
  40. 40.
    Gottlieb, S.: Nucl. Physics B (Proc. Suppl.) 20 (1991) 247Google Scholar
  41. 41.
    Kennedy, A.D., Kuti, J., Meyer, S., Pendleton, B.J.: Phys. Rev. Lett. 54 (1985) 87; Gottlieb, S.A., Kuti, J., Toussaint, D., Kennedy, A.D., Meyer, S., Pendleton, B.J., Sugar, R.L.: Phys. Rev. Lett. 55 (1985) 1958Google Scholar
  42. 42.
    Bacilieri, P., et al.: Nucl. Phys. B343 (1990) 228; Cabasino, S., et al.: Nucl. Physics B (Proc. Suppl.) 20 (1991) 399; Gupta, R., et al.: Phys. Rev. D 43 (1991) 2003; Bitar, K.M., et al.: Nucl. Physics B (Proc. Suppl.) 20 (1991) 362Google Scholar
  43. 43.
    Gottlieb, S., Liu, W., Toussaint, D., Renken, R.L., Sugar, R.L.: Phys. Rev. Lett. 59 (1987) 1513Google Scholar
  44. 44.
    Gottlieb, S., Heller, U.M.: Kennedy, A.D., Kogut, J.B., Krasnitz, A., Liu, W., Renken, R.L., Sinclair, D.K., Sugar, R.L., Toussaint, D., Wang, K.C.: to be publishedGoogle Scholar
  45. 45.
    The HEMCGC Collaboration, Bitar, K.M., et al.: Phys. Rev. Lett. 65 (1990) 2106; Phys. Rev. D 42 (1990) 3794; Brown, F.R., Butler, F.P., Chen, H., et al.: Phys. Rev. Lett. 67 (1991) 1062Google Scholar
  46. 46.
    Born, K.D., et al.: Phys. Rev. Lett. 67 (1991) 302Google Scholar
  47. 47.
    Deng, Y.: in the Proceedings of the 1988 Symposium on Lattice Field Theory,Kronfeld, A., Mackenzie, P.: eds., (Nucl. Phys. B (Proc. Suppl.) 9 (1989),334Google Scholar
  48. 48.
    Gottlieb, S., Liu, W., Renken, R., Sugar, R., Toussaint, D.: Phys. Rev. Lett. 59 (1987) 2247; Phys. Rev. D 38 (1988) 2888Google Scholar
  49. 49.
    Karsch, F.: Nucl. Phys. B205[FS5] (1982) 285Google Scholar
  50. 50.
    DeGrand, T., DeTar, C.: Phys. Rev. D 34 (1986) 2469Google Scholar
  51. 51.
    DeTar, C., Kogut, J.: Phys. Rev. Lett. 59 (1987) 399Google Scholar
  52. 52.
    Bernard, C., et al.: preprint AZPH-TH/91-60 (1991)Google Scholar
  53. 53.
    Borgs, C.: Nucl. Phys. B261 (1991) 455; E. Manousakis and J. Polonyi, Phys. Rev. Lett. 58 (1987) 847Google Scholar
  54. 54.
    LePage, G.P., MacKenzie, P.: Nucl. Phys. B (Proc. Suppl) 20 (1991) 173Google Scholar
  55. 55.
    These techniques go back to Symanzik, K.: Nucl. Phys. B226 (1983) 187 Recently these techniques have been applied to QCD simulations of matrix elements by Martinelli, G., Sachrajda, C., Vladikas, A.: Nucl. Phys. B (Proc. Suppl) 20 (1991) 448 and Heattlie, G., Martinelli, G., Pittori, C., Rossi, G.C., Sachrajda, C.: Nucl. Phys. B352 (1991) 266Google Scholar
  56. 56.
    For a review, see Sachrajda, C.: Nucl. Phys. B (Proc. Suppl) 9 (1989) 121Google Scholar
  57. 57.
    Bernard, C., Labrenz, J., Soni, A.: contribution to Lattice '91; Labrenz, J.: private communicationGoogle Scholar
  58. 58.
    Van Royen, R., Weisskopf, V.F.: Nuovo Cim. 50 (1967) 17Google Scholar
  59. 59.
    Abada, A., et al.: preprint LERN-TH. 6271/91 and contribution to Lattice '91, Pene, O.: private communicationGoogle Scholar
  60. 60.
    Alexandrou, C., et al.: Phys. Lett. 256B (1991) 60Google Scholar
  61. 61.
    Allton, C., et al.: Nucl. Phys. B349 (1991) 598Google Scholar
  62. 62.
    Gavela, M.B., et al.: Phys. Lett. 206B (1988) 113; Maiani, L., G. Martinelli, G.: Phys. Lett. 178B (1986) 265Google Scholar
  63. 64.
    Boltzmann, L.: “Reise eines deutschen Professors in Eldorado,” in “Populáre Schriften,” ed. Broda, E.: reprinted 1979, Vieweg, F.: & Sohn, Weisbaden, and reprinted in English translation in Physics Today, January 1992, p. 44Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • T. DeGrand
    • 1
  1. 1.Department of PhysicsUniversity of ColoradoBoulder

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