- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Reviews of Modern Physics

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

The Nambu—Jona-Lasinio model of quantum chromodynamics

S. P. Klevansky

S. P. Klevansky

  • Institut für Theoretische Physik, 6900 Heidelberg, Federal Republic of Germany

PDF

Rev. Mod. Phys. 64, 649 – Published 1 July, 1992

DOI: https://doi.org/10.1103/RevModPhys.64.649

Abstract

The Nambu—Jona-Lasinio model is reviewed in its flavor SU(2) and SU(3) versions applied to quarks. The dynamical generation of quark masses is demonstrated as a feature of chiral symmetry breaking. One finds that the associated meson spectra, as well as the meson static properties, can be well described. Current-algebra results, which arise as a consequence of symmetry considerations, automatically hold for this model and are explicitly demonstrated to do so. These include the Goldberger-Treiman and Gell-Mann-Oakes-Renner relations. Effects of finite temperature, finite chemical potential, and strong Maxwell and chromoelectromagnetic fields on the dynamically generated quark mass and the meson spectra are discussed. The alternative procedure of bosonization to obtain an effective Lagrange density in mesonic degrees of freedom, using the derivative expansion, is also presented. The current status in relating the results of this model to that of chiral perturbation theory is critically examined.

View figure in article

References (143)

  1. Adami, C., and G. E. Brown, 1990, SUNY preprint NTG90-38
  2. Amendolia, S. R., et al., 1984, Phys. Lett. B 146, 116
  3. Amendolia, S. R., M. Arik, et al., 1986, Nucl. Phys. B 277, 168
  4. Amendolia, S. R., G. Batignani, et al., 1986, Phys. Lett. B 178, 435
  5. Antipov, Y. M., et al., 1985, Z. Phys. C 26, 496
  6. Asakawa, M., and K. Yazaki, 1989, Nucl. Phys. A 504, 668
  7. Bardeen, W. A., C. T. Hill, and M. Lindner, 1990, Phys. Rev. D 41, 1647
  8. Bernard, V., 1986, Phys. Rev. D 34, 1601
  9. Bernard, V., 1987, Phys. Lett. 198, 93
  10. Bernard, V., R. L. Jaffe, and U.-G. Meissner, 1988, Nucl. Phys. B 308, 753
  11. Bernard, V., and U.-G. Meissner, 1988a, Phys. Rev. D 38, 1551
  12. Bernard, V., and U.-G. Meissner, 1988b, Phys. Rev. Lett. 61, 2296
  13. Bernard, V., and U.-G. Meissner, 1988c, Nucl. Phys. A 489, 647
  14. Bernard, V., U.-G. Meissner, and I. Zahed, 1987a, Phys. Rev. D 36, 819
  15. Bernard, V., U.-G. Meissner, and I. Zahed, 1987b, Phys. Rev. Lett. 59, 966
  16. Bernard, V., and D. Vautherin, 1989, Phys. Rev. D 40, 1615
  17. Blin, A. W., B. Hiller, and J. da Providência, 1990, Phys. Lett. B 241, 1
  18. Blin, A. W., B. Hiller, and M. Schaden, 1988, Z. Phys. A 331, 75
  19. Brodsky, S. J., and J. R. Primack, 1969, Ann. Phys. (N.Y.) 52, 315
  20. Buchmüller, W., 1984, Lectures presented at the International School of Exotic Atoms, Erice
  21. Casher, A., H. Neuberger, and S. Nussinov, 1979, Phys. Rev. D 20, 179
  22. Chakrabarti, A., and B. Hu, 1976, Phys. Rev. D 13, 2347
  23. Cheng, T.-P., and L.-F. Li, 1984, Gauge Theory of Elementary Particle Physics (Clarendon, Oxford)
  24. Christ, N. H., 1991, Nucl. Phys. A 527, 539
  25. Clark, T. E., S. T. Love, and W. A. Bardeen, 1990, Phys. Lett. B 237, 235
  26. Claudson, M., A. Yildiz, and P. H. Cox, 1980, Phys. Rev. D 22, 2022
  27. Cox, P. H., and A. Yildiz, 1985, Phys. Rev. D 32, 819
  28. da Providência, J., M. C. Ruivo, and C. A. de Sousa, 1987, Phys. Rev. D 36, 1882
  29. Dolan, L., and R. Jackiw, 1974, Phys. Rev. D 9, 3320
  30. Dumbrais, O., 1983, Nucl. Phys. B 216, 277
  31. Ebert, D., 1985, Z. Phys. 28, 433
  32. Ebert, D., and H. Reinhardt, 1986, Nucl. Phys. B 271, 188
  33. Ebert, D., and M. K. Volkov, 1983, Z. Phys. C 16, 305
  34. Eguchi, T., 1976, Phys. Rev. D 14, 2755
  35. Eguchi, T., and H. Sugawara, 1974, Phys. Rev. D 10, 4257
  36. Ericson, T. E. O., and J. Hüfner, 1973, Nucl. Phys. B 57, 604
  37. Fetter, A. L., and J. D. Walecka, 1971, Quantum Theory of Many Particle Systems (McGraw-Hill, New York)
  38. Feynman, R., 1950, Phys. Rev. 80, 440
  39. Finger, J. R., and J. E. Mandula, 1982, Nucl. Phys. B 199, 168
  40. Gasser, J., 1981, Ann. Phys. (N.Y.) 136, 62
  41. Gasser, J., and H. Leutwyler, 1982, Phys. Rep. 87, 77
  42. Gasser, J., and H. Leutwyler, 1984, Ann. Phys. (N.Y.) 158, 142
  43. Gasser, J., and H. Leutwyler, 1985, Nucl. Phys. B 250, 465
  44. Gasser, J., and H. Leutwyler, 1987, Phys. Lett. B 184, 83
  45. Gasser, J., H. Leutwyler, and M. E. Sainio, 1991, Phys. Lett. B 253, 252
  46. Gatoff, G., A. K. Kerman, and T. Matsui, 1987, Phys. Rev. D 36, 114
  47. Gell-Mann, M., R. Oakes, and B. Renner, 1968, Phys. Rev. 175, 2195
  48. Gerber, P., and H. Leutwyler, 1989, Nucl. Phys. B 321, 387
  49. Giacomo, A. D., M. Maggiore, and S. Olejník, 1990, Nucl. Phys. B 347, 441
  50. Gilman, F. J., and R. Kauffman, 1987, Phys. Rev. D 36, 2761
  51. Ginzburg, V. L., and L. D. Landau, 1950, Zh. Eksp. Teor. Fiz. 20, 1064 Men of Physics: L. D. Landau, Vol. 1, p. 138 (Pergamon, Oxford, 1965)
  52. Göckler, M., R. Horsley, and E. Laermann, 1990, Nucl. Phys. B 334, 527
  53. Goldberger, M. L., and S. B. Treiman, 1958, Phys. Rev. 110, 1178
  54. Goldstone, J., 1961, Nuovo Cimento 19, 154
  55. Goldstone, J., A. Salam, and S. Weinberg, 1962, Phys. Rev. 127, 965
  56. Gor'kov, L. P., 1959, Zh. Eksp. Teor. Fiz. 36, 1918 [Sov. Phys. JETP 9, 1364 (1959)]
  57. Hansson, T. H., M. Prakash, and I. Zahed, 1990, Nucl. Phys. B 335, 67
  58. Hatsuda, T., 1988, Phys. Lett. B 213, 361
  59. Hatsuda, T., and T. Kunihiro, 1984, Phys. Lett. B 145, 7
  60. Hatsuda, T., and T. Kunihiro, 1985a, Prog. Theor. Phys. 74, 765
  61. Hatsuda, T., and T. Kunihiro, 1985b, Phys. Rev. Lett. 55, 158
  62. Hatsuda, T., and T. Kunihiro, 1987a, Phys. Lett. B 185, 304
  63. Hatsuda, T., and T. Kunihiro, 1987b, Phys. Lett. B 198, 126
  64. Hosaka, A., 1990, Phys. Lett. B 244, 363
  65. Huang, K., 1982, Quarks, Leptons and Gauge Fields (World Scientific, Singapore)
  66. Itzykson, C., and J.-B. Zuber, 1980, Quantum Field Theory (McGraw-Hill, New York)
  67. Jaminon, M., G. Ripka, and P. Stassart, 1989, Phys. Rev. Lett. B 227, 191
  68. Kawarabayashi, K., and M. Suzuki, 1966, Phys. Rev. Lett. 16, 255
  69. Kikkawa, K., 1976, Prog. Theor. Phys. 56, 947
  70. Klevansky, S. P., 1991, Nuovo Cimento A 104, 1035
  71. Klevansky, S. P., J. Jaenicke, and R. H. Lemmer, 1991, Phys. Rev. D 43, 3040
  72. Klevansky, S. P., and R. H. Lemmer, 1989, Phys. Rev. D 39, 3478
  73. Klevansky, S. P., and R. H. Lemmer, 1990, Z. Phys. A 336, 223
  74. Klimt, S., M. Lutz, and W. Weise, 1990, Phys. Lett. B 249, 386
  75. Klimt, S., M. Lutz, U. Vogl, and W. Weise, 1990, Nucl. Phys. A 516, 429
  76. Kocić, A., 1986, Phys. Rev. D 33, 1785
  77. Kogut, J. B., 1980, Phys. Rep. 67, 67
  78. Kogut, J. B., D. B. Sinclair, and K. C. Wang, 1991, Phys. Lett. B 263, 101
  79. Kogut, J. B., and L. Susskind, 1975, Phys. Rev. D 11, 395
  80. Kruglov, S. I., 1984, Acta Phys. Pol. B 15, 725
  81. Kruglov, S. I., 1988, Sov. J. Phys. 3, 198
  82. Kruglov, S. I., 1989a, Acta Phys. Pol. B 20, 723
  83. Kruglov, S. I., 1989b, Acta Phys. Pol. B 20, 729
  84. Kruglov, S. I., 1989c, Sov. J. Phys. 6, 413
  85. Kruglov, S. I., 1990, Acta Phys. Pol. B 21, 985
  86. Kunihiro, T., 1987, Phys. Lett. B 185, 307
  87. Kunihiro, T., 1988, Prog. Theor. Phys. 80, 34
  88. Kunihiro, T., 1989a, Genshikaku Kenkyu Summer School, Iiama (Japan) 33, No. 5, 19
  89. Kunihiro, T., 1989b, Phys. Lett. B 219, 363
  90. Kunihiro, T., 1991, Nucl. Phys. B 351, 593
  91. Kunihiro, T., and T. Hatsuda, 1988, Phys. Lett. B 206, 385
  92. Lee, T. D., 1981, Particle Physics and Introduction to Field Theory (Harwood, New York)
  93. LeYaouanc, A., et al., 1988, Phys. Rev. D 39, 924
  94. Low, F., 1975, Phys. Rev. D 12, 163
  95. Lutz, M., and W. Weise, 1990, Nucl. Phys. A 518, 156
  96. Martin, C., and D. Vautherin, 1988, Phys. Rev. D 38, 3593
  97. Mattuck, R. D., 1976, A Guide to Feynman Diagrams in the Many-body Problem (McGraw-Hill, New York)
  98. Meissner, U.-G., 1988, Phys. Rep. 161, 213
  99. Meissner, Th., F. Grümmer, and K. Goeke, 1990, Ann. Phys. (N.Y.) 202, 297
  100. Meissner, Th., E. Ruiz-Arriola, F. Grümmer, and H. Mavromatis, 1988, Phys. Lett. B 214, 312
  101. Nambu, Y., and G. Jona-Lasinio, 1961a, Phys. Rev. 122, 345
  102. Nambu, Y., and G. Jona-Lasinio, 1961b, Phys. Rev. 124, 246
  103. Olsson, M. G., and C. J. Suchyta, III, 1987, Phys. Rev. D 36, 1459
  104. Pauli, W., and F. Villars, 1949, Rev. Mod. Phys. 21, 434
  105. Pham, X.-Y., 1990, Phys. Lett. B 241, 111
  106. Pokorski, S., 1989, Gauge Field Theories, Cambridge Monographs on Mathematical Physics (Cambridge University, New York), p. 329
  107. Ramond, P., 1981, Field Theory: A Modern Primer (Benjamin, London/New York)
  108. Rebbi, C., 1986, Phys. Rep. 137, 63
  109. Redlich, K., and L. Turko, 1980, Z. Phys. C 5, 201
  110. Reinders, L., J. H. Rubinstein, and S. Yazaki, 1985, Phys. Rep. 127, 2
  111. Reinhardt, H., 1990, Phys. Lett. B 244, 316
  112. Reinhardt, H., 1991, Phys. Lett. B 257, 375
  113. Riazuddin, and Fayyazuddin, 1966, Phys. Rev. 147, 1071
  114. Rosenstein, B., B. J. Warr, and S. H. Park, 1991, Phys. Rep. 205, 59
  115. Ruiz Arriola, E., 1991, Phys. Lett. B 253, 430
  116. Ruiz Arriola, E., V. Christov, and K. Goeke, 1989, Phys. Lett. B 221, 39
  117. Salam, A., and J. Strathdee, 1975, Nucl. Phys. B 90, 203
  118. Schüren, C., E. Ruiz Arriola, and K. Goeke, 1991, Bochum Preprint, RUB-TPII-07-91
  119. Schwinger, J., 1951, Phys. Rev. 82, 644
  120. Serot, B. D., and J. D. Walecka, 1986, The Relativistic Nuclear Many-Body Problem, Advances in Nuclear Physics, Vol. 16, edited by J. W. Negele and Erich Vogt (Plenum, New York/London)
  121. Skyrme, H., 1961, Proc. R. Soc. London Ser. A 260, 127
  122. Skyrme, H., 1962, Nucl. Phys. 31, 556
  123. Stephens, C. R., 1988, Ann. Phys. (N.Y.) 181, 120
  124. Suganuma, H., and T. Tatsumi, 1990, Proceedings of the Workshop on High Density Nuclear Matter, 18-21 September, KEK, Japan, edited by J. Chiba, KEK report, in press, KEK Preprint KUNS 1049
  125. Suganuma, H., and T. Tatsumi, 1991, Ann. Phys. (N.Y.) 208, 470
  126. Suzuki, M., 1963, Prog. Theor. Phys. 30, 138
  127. Takizawa, M., K. Kubodera, and F. Myhrer, 1991, Phys. Lett. B 261, 221
  128. Takizawa, M., K. Tsushima, Y. Kohyama, and K. Kubodera, 1989, Nucl. Phys. A 507, 611
  129. Tarrach, R., 1979, Z. Phys. C 2, 221
  130. 't Hooft, G., 1973, Nucl. Phys. B 62, 444
  131. 't Hooft, G., 1974, Nucl. Phys. B 74, 461
  132. 't Hooft, G., 1976a, Phys. Rev. Lett. 37, 8
  133. 't Hooft, G., 1976b, Phys. Rev. D 14, 3432
  134. Turko, L., 1981, Phys. Lett. B 104, 153
  135. Vogl, U., M. Lutz, S. Klimt, and W. Weise, 1990, Nucl. Phys. A 516, 469
  136. Vogl, U., and W. Weise, 1991, Prog. Part. Nucl. Phys. 27, 195
  137. Volkov, M. K., 1984, Ann. Phys. (N.Y.) 157, 282
  138. Volkov, M. K., 1986, Sov. J. Part. Nucl. 17, 186
  139. Weinberg, S., 1967, Phys. Rev. Lett. 18, 507
  140. Wess, J., and B. Zumino, 1979, Phys. Lett. B 37, 164
  141. Witten, E., 1979, Nucl. Phys. B 160, 57
  142. Witten, E., 1983, Nucl. Phys. B 223, 422, 433
  143. Yildiz, A., and P. H. Cox, 1980, Phys. Rev. D 22, 2022

Outline

Information

Rev. Mod. Phys. 64, 649– Published 1 July, 1992

    © 1992 American Physical Society

    Sign In to Your Journals Account

    Filter

    Filter

    Article Lookup

    Enter a citation