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The lattice gauge theory approach to quantum chromodynamics

John B. Kogut

John B. Kogut

  • Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801

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Rev. Mod. Phys. 55, 775 – Published 1 July, 1983

DOI: https://doi.org/10.1103/RevModPhys.55.775

Abstract

The author reviews in a pedagogical fashion some of the recent developments in lattice quantum chromodynamics. This review emphasizes explicit examples and illustrations rather than general proofs and analyses. It begins with a discussion of the heavy-quark potential in continuum quantum chromodynamics. Asymptotic freedom and renormalization-group improved perturbation theory are discussed. A simple dielectric model of confinement is considered as an intuitive guide to the vacuum of non-Abelian gauge theories. Next, the Euclidean form of lattice gauge theory is introduced, and an assortment of calculational methods are reviewed. These include high-temperature expansions, duality, Monte Carlo computer simulations, and weak coupling expansions. A Λ- parameter calculation for asymptotically free-spin models is presented. The Hamiltonian formulation of lattice gauge theory is presented and is illustrated in the context of flux tube dynamics. Roughening transitions, Casimir forces, and the restoration of rotational symmetry are discussed. Mechanisms of confinement in lattice theories are illustrated in the two-dimensional electrodynamics of the planar model and the U(1) gauge theory in four dimensions. Generalized actions for SU(2) gauge theories and the relevance of monopoles and strings to crossover phenomena are considered. A brief discussion of the continuity of fields and topological charge in asymptotically free lattice models is presented. The final major topic of this review concerns lattice fermions. The species doubling problem and its relation to chiral symmetry are illustrated. Staggered Euclidean fermion methods are discussed in detail, with an emphasis on species counting, remnants of chiral symmetry, Block spin variables, and the axial anomaly. Numerical methods for including fermions in computer simulations are considered. Jacobi and Gauss-Siedel inversion methods to obtain the fermion propagator in a background gauge field are reviewed. Langevin, pseudofermion Monte Carlo methods, and random walk methods are discussed, as are proposals for including the fermion determinant in computer simulations. Finally, spontaneous chiral symmetry breaking in lattice models is discussed. The review ends with brief remarks about present research directions.

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References (121)

  1. Balian, R., J. M. Drouffe, and C. Itzykson, 1975a, Phys. Rev. D 11, 2098
  2. Balian, R., J. M. Drouffe, and C. Itzykson, 1975b, Phys. Rev. D 11, 2104
  3. Banks, T., J. Kogut, and R. Myerson, 1977, Nucl. Phys. B 129, 493
  4. Banks, T., J. Kogut, and L. Susskind, 1976, Phys. Rev. D 13, 1043
  5. Berg, B., and M. Lüscher, 1981, Nucl. Phys. B 190 [FS3], 412
  6. Bhanot, G., and M. Creutz, 1981, Phys. Rev. D 24, 3212
  7. Bhanot, G.M. CreutzBinder, K., editor, 1979, Monte Carlo Methods in Statistical Physics (Springer, New York)
  8. Bjorken, J., and S. Drell, 1964, Relativistic Quantum Mechanics (McGraw-Hill, New York)
  9. Blairon, J.-M., R. Brout, F. Englert, and J. Greensite, 1980, Universite Libre de Buxelles preprint, September
  10. Brower, R., D. Kessler, and H. Levine, 1981, Phys. Rev. Lett. 47, 621
  11. Cabibbo, N., and E. Marinari, 1982, University of Rome preprint No. 301, June 21
  12. Callan, C., 1970, Phys. Rev. D 2, 1541
  13. Casher, A., 1979, Phys. Lett. B 83, 395
  14. Casher, A., J. Kogut, and L. Susskind, 1974, Phys. Rev. D 10, 732
  15. Coleman, S., 1975, Phys. Rev. D 11, 2088
  16. Coleman, S., 1976, private communication
  17. Coleman, S., and D. J. Gross, 1973, Phys. Rev. Lett. 31, 851
  18. Coleman, S., and E. Witten, 1980, Phys. Rev. Lett. 45, 100
  19. Cornwell, J., R. Jackiw, and E. Tomboulis, 1974, Phys. Rev. D 10, 2428
  20. Creutz, M., 1977, Phys. Rev. D 15, 1128
  21. Creutz, M., 1980a, Phys. Rev. D 21, 2308
  22. Creutz, M., 1980b, Phys. Rev. Lett. 45, 313
  23. d'Adda, A., M. Lüscher, and P. Di Vecchia, 1978, Nucl. Phys. B 146, 63
  24. Dashen, R., and D. J. Gross, 1981, Phys. Rev. D 23, 2340
  25. David, F., 1980, Phys. Lett. B 96, 371
  26. DeGrand, T. A., and D. Toussaint, 1980, Phys. Rev. D 22, 2478
  27. DeWitt, B. S., 1967, Phys. Rev. 162, 1195
  28. Drell, S. D., M. Weinstein, and S. Yankielowicz, 1976, Phys. Rev. D 14, 487
  29. Duncan, A., R. Roskies, and H. Vaidya, 1982, University of Pittsburgh preprint PITT-82-6
  30. Eguchi, T., and H. Kawai, 1982, Phys. Rev. Lett. 48, 1063
  31. Eichenherr, H., 1978, Nucl. Phys. B 146, 214
  32. Elitzur, S., 1975, Phys. Rev. D 12, 3978
  33. Fetter, A. L., and J. D. Walecka, 1971, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York)
  34. Fischler, W., 1977, Nucl. Phys. B 129, 157
  35. Forsythe, G. E., and R. A. Leibler, 1950, M.T.A.C. (Vol. 4), 127
  36. Fucito, R., E. Marinari, G. Parisi, and C. Rebbi, 1981, Nucl. Phys. B 180 [FS2], 369
  37. Gell-Mann, M., and F. Low, 1954, Phys. Rev. 95, 1300
  38. Gilmer, G. H., and P. Bennema, 1972, J. Appl. Phys. 43, 1347
  39. Gross, D. J., and F. Wilczek, 1973, Phys. Rev. Lett. 30, 1343
  40. Hageman, R., and A. Young, 1979, Applied Iterative Methods (Academic, New York)
  41. Halliday, G., and A. Schwimmer, 1981a, Phys. Lett. B 101, 327
  42. Halliday, G., and A. Schwimmer, 1981b, Phys. Lett. B 102, 337
  43. Hamber, H., and G. Parisi, 1981, Phys. Rev. Lett. 47, 1792
  44. Hamer, C. J., and M. N. Barber, 1980, J. Phys. A 13, L169
  45. Hamer, C. J., and M. N. Barber, 1981, J. Phys. A 14, 241
  46. Hasenfratz, A., E. Hasenfratz, and P. Hasenfratz, 1981, Nucl. Phys. B 180, 353
  47. Hasenfratz, A., and P. Hasenfratz, 1980, Phys. Lett. B 93, 165
  48. Hasenfratz, A., P. Hasenfratz, Z. Kunszt, and C. B. Lang, 1982, Phys. Lett. B 110, 289
  49. Hestenes, M. R., and E. Stiefel, 1952, J. Res. Natl. Bur. Stand. 49, 409
  50. Hughes, R., 1979, Phys. Lett. B 97, 246
  51. Itzykson, C., M. Peskin, and J.-B. Zuber, 1980, Phys. Lett. B 95, 259
  52. Jones, D. R. T., J. Kogut, and D. K. Sinclair, 1979, Phys. Rev. D 19, 1882
  53. Jose, J., L. P. Kadanoff, S. Kirkpatrick, and D. R. Nelson, 1977, Phys. Rev. B 16, 1217
  54. Kadanoff, L. P., 1977, Rev. Mod. Phys. 49, 267
  55. Kawamoto, N., and J. Smit, 1981, Nucl. Phys. B 192, 100
  56. Kogut, J., 1979, Rev. Mod. Phys. 51, 659
  57. Kogut, J., R. B. Pearson, J. L. Richardson, J. Shigemitsu, and D. K. Sinclair, 1981, Phys. Rev. D 23, 2945
  58. Kogut, J., R. B. Pearson, and J. Shigemitsu, 1979, Phys. Rev. Lett. 43, 484
  59. Kogut, J., R. B. Pearson, and J. Shigemitsu, 1980, Phys. Lett. B 98, 63
  60. Kogut, J., and J. Shigemitsu, 1981, Nucl. Phys. B 190, 365
  61. Kogut, J., and D. K. Sinclair, 1981, Phys. Rev. D 24, 1610
  62. Kogut, J., M. Stone, H. W. Wyld, W. R. Gibbs, J. Shigemitsu, S. H. Shenker, and D. K. Sinclair, 1983, Phys. Rev. Lett. 50, 393
  63. Kogut, J., M. Stone, H. W. Wyld, J. Shigemitsu, S. H. Shenker, and D. K. Sinclair, 1982, Phys. Rev. Lett. 48, 1140
  64. Kogut, J., M. Stone, H. W. Wyld, J. Shigemitsu, S. H. Shenker, and D. K. Sinclair, The Scales of Chiral Symmetry Breaking in SU(2) Gauge Theory, Ohio State University preprint, to appear
  65. Kogut, J., and L. Susskind, 1974, Phys. Rev. D 9, 3501
  66. Kogut, J., and L. Susskind, 1975, Phys. Rev. D 11, 395
  67. Kosterlitz, J. M., and D. J. Thouless, J. Phys. C 6, 118
  68. Kramers, H. A., and G. H. Wannier, 1941, Phys. Rev. 60, 252
  69. Kuti, J., 1982, Phys. Rev. Lett. 49, 183
  70. Landau, L. D., and E. M. Lifschitz, 1975, Electrodynamics of Continuous Media (Pergamon, Oxford)
  71. Langevin, P. 1908, C. R. Acad. Sci. Paris 146, 530
  72. Lee, T. D., 1981, Particle Physics and Introduction to Field Theory (Harwood, New York)
  73. Lüscher, M., 1981, Nucl. Phys. B 180, 317
  74. Lüscher, M., 1981, Bern preprint BUTP-10, to appear in Commun. Math. Phys.
  75. Lüscher, M., 1982, Nucl. Phys. B 200 [FS4], 61
  76. Lüscher, M., G. Münster, and P. Weisz, 1981, Nucl. Phys. B 180 [FS2], 1
  77. Mack, G., and V. B. Petkova, 1980, Ann. Phys. (N.Y.) 125, 117
  78. Mandelstam, S., 1976, Phys. Rep. C 23, 245
  79. Marinari, E., G. Parisi, and C. Rebbi, 1981, Phys. Rev. Lett. 47, 1795
  80. Mermin, N. D., and H. Wagner, 1966, Phys. Rev. Lett. 17, 1133
  81. Metropolis, N., A. W. Rosenbluth, A. H. Teller, and E. Teller, 1953, J. Chem. Phys. 21, 1087
  82. Münster, G., 1981, Nucl. Phys. B 128 [FS2], 23
  83. Nambu, Y., and G. Jona-Lasinio, 1961, Phys. Rev. 122, 345
  84. Nauenberg, M., and B. Lautrup, 1980, Phys. Rev. Lett. 45, 1755
  85. Nielsen, H. B., and M. Ninomiya, 1981, Nucl. Phys. 185, 20
  86. Nightingale, M. P., 1976, Physica A 83, 561
  87. Osterwalder, K., and E. Seiler, 1978, Ann. Phys. (N.Y.) 110, 440
  88. Pietarinen, E., 1981, Nucl. Phys. B 190, 349
  89. Politzer, H. D., 1973, Phys. Rev. Lett. 30, 1346
  90. Polyakov, A. M., 1975a, Phys. Lett. B 59, 79
  91. Polyakov, A. M., 1975b, Phys. Lett. B 59, 82
  92. Polyakov, A. M., 1981, Phys. Lett. B 103, 207
  93. Raby, S., S. Dimopoulos, and L. Susskind, 1980, Nucl. Phys. B 169, 373
  94. Samuel, S., 1980, J. Math. Phys. 21, 1842
  95. Satz, H., 1982, Phys. Rep. 88, 321
  96. Savit, R., 1980, Rev. Mod. Phys. 52 453
  97. Scalapino, D. J., and R. L. Sugar, 1981, Phys. Rev. Lett. 46, 519
  98. Shenker, S. H., M. Stone, J. Kogut, J. Bartholomew, and J. Sloan, 1983, Chiral Symmetry Breaking in Lattice Electrodynamics, University of Chicago preprint, to appear
  99. Shenker, S., and J. Tobochnik, 1980, Phys. Rev. B 22, 4462
  100. Stack, J. D., 1983, Phys. Rev. D 27, 412
  101. Stone, M., 1982, private communication
  102. Susskind, L., 1977, "Coarse grained quantum chromodynamics," in Weak and Electromagnetic Interactions at High Energy, edited by R. Balian and C. H. Llewellyn Smith, Les Houches 29, 1976 (North-Holland, Amsterdam), p. 207
  103. Swendsen, R. H., 1978, Phys. Rev. B 18, 492
  104. Symanzik, K., 1970, Commun. Math. Phys. 49, 424
  105. Symanzik, K., 1982, in Mathematical Problems in Theoretical Physics, edited by R. Schroder, Lecture Notes in Physics, 153 (Springer, Berlin)
  106. 't Hooft, G., 1972, unpublished remarks at the Marseilles Conference on Gauge Theories
  107. 't Hooft, G., 1976, in High Energy Physics, edited by A. Zichichi, Palermo, 1976 (Editrice Compositori, Bologna)
  108. van Beijeren, H., 1975, Commun. Math. Phys. 40, 1
  109. Villain, J., 1975, J. Phys. C 36, 581
  110. Wasow, W. R., 1951, M.T.A.C. (Vol. 5), 78
  111. Weeks, J. D., G. H. Gilmer, and H. J. Leamy, 1973, Phys. Rev. Lett. 31, 549
  112. Wegner, F., 1971, J. Math. Phys. 12, 2259
  113. Weingarten, D., 1982, Phys. Lett. B 109, 57
  114. Weingarten, D., and D. Petcher, 1981, Phys. Lett. B 99, 33
  115. Wilson, K. G., 1974, Phys. Rev. D 14, 2455
  116. Wilson, K. G., 1977, in "Quarks: from paradox to myth," in New Phenomena in Subnuclear Physics, edited by A. Zichichi, Erice, 1975 (Plenum, New York), p. 13
  117. Wilson, K. G., 1980, in "Monte-Carlo calculations for the lattice gauge theory," in Recent Developments in Gauge Theories, edited by G. 't Hooft , Cargèse, 1979 (Plenum, New York), p. 363
  118. Wilson, K. G., and J. Kogut, 1974, Phys. Rev. C 12, 75
  119. Wortis, M., 1974, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, London), Vol. 3, p. 113
  120. Yaffe, L. G., and B. Svetitsky, 1982, Phys. Rev. D 26, 963
  121. Yang, C. N., and R. L. Mills, 1954, Phys. Rev. 96, 1605

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Rev. Mod. Phys. 55, 775– Published 1 July, 1983

    © 1983 American Physical Society

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