Chiral bag model for the nucleon

Physics Report

Volumn 277, Issue 2-3, 1996, Pages 65-188

  Hosaka, Atsushi ^a   Toki, Hiroshi ^b  

^a NUMAZU COLLEGE OF TECHNOLOGY   (Japan)

^b OSAKA UNIVERSITY   (Japan)

Author keywords

Bags; Chiral symmetries; Nucleon structure; Skyrmions

Indexed keywords

EID: 0030525260     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0370-1573(96)00013-0     Document Type: Review

References (242)

1. [1] M. Gell-Mann and Y. Ne'eman, The Eightfold Way (Benjamin, New York, 1964).
2. [2] G. Zweig, CERN Report no. 8182/TH 401.
3. [3] D. Gross and F. Wilczek, Phys. Rev. Lett. 26 (1973) 1343.
4. [4] H.D. Politzer, Phys. Rev. Lett. 26 (1973) 1346; Phys. Reports C 14 (1974) 130.
5. [4] H.D. Politzer, Phys. Rev. Lett. 26 (1973) 1346; Phys. Reports C 14 (1974) 130.
6. [5] S. Okubo, Phys. Lett. 5 (1963) 163; G. Zweig, CERN Report no. 8419/TH 412; J. Iizuka, Prog. Theor. Phys. Suppl. 37-38 (1966) 21.
7. [5] S. Okubo, Phys. Lett. 5 (1963) 163; G. Zweig, CERN Report no. 8419/TH 412; J. Iizuka, Prog. Theor. Phys. Suppl. 37-38 (1966) 21.
8. [5] S. Okubo, Phys. Lett. 5 (1963) 163; G. Zweig, CERN Report no. 8419/TH 412; J. Iizuka, Prog. Theor. Phys. Suppl. 37-38 (1966) 21.
9. [6] J. Kokkedee, The Quark Model (Benjamin, New York. 1969); F.E. Close, An Introduction to Quarks and Partons (Academic Press, London, 1979).
10. [6] J. Kokkedee, The Quark Model (Benjamin, New York. 1969); F.E. Close, An Introduction to Quarks and Partons (Academic Press, London, 1979).
11. [7] N. Isgur and G. Karl, Phys. Lett. 72B (1977) 109; Phys. Lett. 74B (1978) 353; Phys. Rev. D 18 (1978) 4187; Phys. Rev. D 20 (1979) 1191.
12. [7] N. Isgur and G. Karl, Phys. Lett. 72B (1977) 109; Phys. Lett. 74B (1978) 353; Phys. Rev. D 18 (1978) 4187; Phys. Rev. D 20 (1979) 1191.
13. [7] N. Isgur and G. Karl, Phys. Lett. 72B (1977) 109; Phys. Lett. 74B (1978) 353; Phys. Rev. D 18 (1978) 4187; Phys. Rev. D 20 (1979) 1191.
14. [7] N. Isgur and G. Karl, Phys. Lett. 72B (1977) 109; Phys. Lett. 74B (1978) 353; Phys. Rev. D 18 (1978) 4187; Phys. Rev. D 20 (1979) 1191.
15. [8] A. Chodos, R.L Jaffe, K. Johnson, C.B. Thorn and V. Wesskopf, Phys. Rev. D 9 (1974) 3471;
16. A. Chodos, R.L Jaffe, K. Johnson and C.B. Thorn, Phys. Rev. D 10 (1974) 2559;
17. T. DeGrand, R.L. Jaffe, K. Johnson and J. Kiskis, Phys. Rev. D 12 (1975) 2060.
18. [9] T.H.R. Skyrme, Proc. R. Soc. London A260 (1961) 127; Nucl. Phys. 31 (1962) 556.
19. [9] T.H.R. Skyrme, Proc. R. Soc. London A260 (1961) 127; Nucl. Phys. 31 (1962) 556.
20. [10] N.K. Pak and H.C. Tze, Ann. Phys. 117 (1979) 164.
21. [11] A.D. Jackson and M. Rho, Phys. Rev. Lett. 51 (1983) 751.
22. [12] G.S. Adkins, C.R. Nappi and E. Witten, Nucl. Phys. B228 (1984) 552.
23. [13] I. Zahed and G. E. Brown, Phys. Reports 142 (1986) 1.
24. [14] Selected papers, with commentary, of Tony Hilton Royle Skyrme, ed. G.E. Brown (World Scientific, Singapore, 1994).
25. [15] T. Inoue and T. Maskawa, Prog. Theor. Phys. 54 (1975) 1833.
26. [16] A. Chodos and C.B. Thorn, Phys. Rev. D 12 (1975) 2733.
27. [17] A.W. Thomas, Adv. Nucl. Phys. 13 (1984) 1.
28. [18] F. Myhrer, Int. Rev. Nucl. Phys. 1 (1984) 325.
29. [19] G.E. Brown and M. Rho, Phys. Lett. B 82 (1979) 177; V. Vento, M. Rho, E.M. Nyman, J.H. Jun and G.E. Brown, Nucl. Phys. A 345 (1980) 413.
30. [19] G.E. Brown and M. Rho, Phys. Lett. B 82 (1979) 177; V. Vento, M. Rho, E.M. Nyman, J.H. Jun and G.E. Brown, Nucl. Phys. A 345 (1980) 413.
31. [20] S. Coleman, Aspects of Symmetry (Cambrige University Press, Cambrige, 1985).
32. [21] R. Rajaraman, Solitons and Instantons (North-Holland, Amsterdam, 1982).
33. [22] M. Rho, Phys. Reports 240 (1994) 1.
34. [23] S. Nadkarni, H.B. Nielsen and I. Zahed, Nucl. Phys. B253 (1985) 308; H.B. Nielsen, in: Skyrmions and Anomalies, eds. M. Jezabek and M. Praszalowicz (World Scientific, Sngapore, 1987).
35. [23] S. Nadkarni, H.B. Nielsen and I. Zahed, Nucl. Phys. B253 (1985) 308; H.B. Nielsen, in: Skyrmions and Anomalies, eds. M. Jezabek and M. Praszalowicz (World Scientific, Sngapore, 1987).
36. [24] G. 't Hooft, Nucl. Phys. B 72 (1974) 461; Nucl. Phys. B 75 (1974) 461.
37. [24] G. 't Hooft, Nucl. Phys. B 72 (1974) 461; Nucl. Phys. B 75 (1974) 461.
38. [25] E. Witten, Nucl. Phys. B 160 (1979) 57.
39. [26] E. Witten, Nucl. Phys. B 223 (1983) 422; 433.
40. [27] R. Dashen and A.V. Manohar, Phys. Lett. B 315 (1993) 425; 438.
41. [28] E. Jenkins, Phys. Lett. B 315 (1993) 431; 441.
42. [29] R. Dashen, E. Jenkins and A.V. Manohar, Phys. Rev. D 49 (1994) 4713.
43. [30] R. Dashen, E. Jenkins and A.V. Manohar, Phys. Rev. D51 (1995) 3697.
44. [31] M.A. Luty and J. March-Russell, Nucl. Phys. B426 (1994) 71;
45. M.A. Luty, Phys. Rev. D 51 (1995) 2322.
46. [32] N. Dorey, J. Hughes and M.P. Mattis, Phys. Rev. Lett. 73 (1994) 1211.
47. [33] A.V. Manohar, Phys. Lett. B 336 (1994) 502.
48. [34] N. Dorey and M.P. Mattis, Phys. Rev. D 52 (1995) 2891.
49. [35] G.E. Brown and M. Rho, Comments Part. Nucl. Phys. 18 (1988) 1.
50. [36] A. Hosaka and H. Toki, Prog. Theor. Phys. Suppl. 109 (1992) 137.
51. [37] C.G. Calan and I. Klebanov, Nucl. Phys. B 262 (1985) 365; C.G. Callan, K. Hornbostel and I. Klebanov, Phys. Lett. B 202 (1988) 269.
52. [37] C.G. Calan and I. Klebanov, Nucl. Phys. B 262 (1985) 365; C.G. Callan, K. Hornbostel and I. Klebanov, Phys. Lett. B 202 (1988) 269.
53. [38] G.E. Brown, A.D. Jackson, R. Rho and V. Vento, Phys. Lett. B 140 (1984) 285.
54. [39] A. Hosaka and H. Toki, Phys. Lett. B 167 (1986) 153.
55. [40] M. Rho, A.S. Goldharber and G.E. Brown, Phys. Rev. Lett. 51 (1983) 747.
56. [41] J. Goldstone and R.L. Jaffe, Phys. Rev. Lett. 51 (1983) 1518.
57. [42] M.B. Paranjape and G.W. Semenoff, Phys. Lett. B 132 (1983) 369.
58. [43] L. Vepstas, A.D. Jackson and A.S. Goldharber, Phys. Lett. B 140 (1984) 280.
59. [44] P.J. Mulders, Phys. Rev. D 30 (1984) 1073.
60. [45] I. Zahed, A. Wirzba and U.-G. Meissner, Ann. Phys. 165 (1985) 406.
61. [46] K.J. Heller, M. Jezabek and M.A. Nowak, Phys. Lett. B 166 (1986) 101.
62. [47] D.E. Kahana, A.D. Jackson and Ripka, Nucl. Phys. A 459 (1986) 663.
63. [48] A.D. Jackson, D.E. Kahana, L. Vepstas, H. Verschelde and E. Wüst, Nucl. Phys. A 462 (1987) 661.
64. [49] D.E. Kahana and J. Milana, Nucl. Phys. A 468 (1987) 493.
65. [50] K. Kusaka and H. Toki, Nucl. Phys. A 477 (1988) 596.
66. [51] P. Ring and P. Shuck, The Nuclear Many Body Problem (Springer, New York, 1980).
67. [52] B.-Y. Park and M. Rho, Z. Phys A 331 (1988) 151; Z. Phys. 473.
68. [52] B.-Y. Park and M. Rho, Z. Phys A 331 (1988) 151; Z. Phys. 473.
69. [53] M. Golberger and S. Treimann, Phys. Rev. 110 (1958) 1178.
70. [54] A. Hosaka and H. Toki, Phys. Lett. B322 (1993) 1.
71. [55] A. Hosaka and H. Toki, Phys. Lett. B343 (1995) 1.
72. [56] J.J. Sakurai, Currents and mesons (Chicago Univ. Press, Chicago, 1969).
73. [57] M. Bando, T. Kugo, K. Yamawaki, S. Uehara and Yanagida, Phys. Rev. Lett. 54 (1985) 1215; M. Bando, T. Kugo and K. Yamawaki, Prog. Theor. Phys. 73 (1985) 1541.
74. [57] M. Bando, T. Kugo, K. Yamawaki, S. Uehara and Yanagida, Phys. Rev. Lett. 54 (1985) 1215; M. Bando, T. Kugo and K. Yamawaki, Prog. Theor. Phys. 73 (1985) 1541.
75. [58] M. Bando, T. Kugo and K. Yamawaki, Phys. Reports 164 (1988) 217.
76. [59] E.G.C. Stueckelberg, Helv. Acta. Phys. 14 (1941) 51.
77. [60] K. Yamawaki, Phys. Rev. D 35 (1987) 412.
78. [61] M. Wakamatsu and W. Wese, Z. Phys. A 311 (1988) 173.
79. [62] A. Hosaka, H. Toki and W. Weise, Z. Phys. A 332 (1989) 97.
80. [63] A. Hosaka, H. Toki and W. Weise, Nucl. Phys. A 506 (1990) 501.
81. [64] A. Hosaka, Nucl. Phys. A 546 (1992) 493.
82. [65] T. Cook and B. Sakita, J. Math. Phys. 8 (1967) 708.
83. [66] J.-L. Gervais and B. Sakita, Phys. Rev. Lett. 52 (1984) 87; Phys. Rev. D 30 (1984) 1795.
84. [66] J.-L. Gervais and B. Sakita, Phys. Rev. Lett. 52 (1984) 87; Phys. Rev. D 30 (1984) 1795.
85. [67] A. Hosaka and N.R. Walet, Phys. Lett. B 358 (1995) 184.
86. [68] A. Hosaka and H. Toki, Z. Phys. A 330 (1988) 111.
87. [69] S. Nawa, R. Tamagaki T. Tatsumi and S. Yoro, Prog. Theor. Phys. 84 (1990) 44; 1170.
88. [70] E. Wüst, G.E. Brown and A.D. Jackson, Nucl. Phys. A 468 (1987) 450.
89. [71] P.N. Bogoliubov, Ann. Inst. Henri Poincaré, 8 (1967) 163.
90. [72] E. Shuryak, Phys. Rep. 61 (1980) 71; 115 (1984) 151.
91. [72] E. Shuryak, Phys. Rep. 61 (1980) 71; 115 (1984) 151.
92. [73] T. Hatsuda and T. Kunihiro, Phys. Rep. 247 (1994) 221.
93. [74] M. Oka and S. Takeuchi, Phys. Rev. Lett. 63 (1989) 1780;
94. S. Takeuchi and M. Oka, Phys. Rev. Lett. 66 (1991) 1271.
95. [75] R. Machleidt, K. Holinde and C. Elster, Phys. Reports 149 (1987) 1.
96. [76] M. Lacombe et al., Phys. Rev. C21 (1980) 861.
97. [77] Mesons in Nuclei, eds. M. Rho and D.W. Wilkinson (North-Holland, Amsterdam, 1979).
98. [78] M. Rho, Ann. Rev. Nucl. Part. Sci. 34 (1984) 531.
99. [79] For discussions on non-linear representations, see, for example, Ref. [58].
100. [80] I. Hulthage, F. Myhrer and Z. Xu, Nucl. Phys. A364 (1981) 322.
101. [81] R. Jackiw and C. Rebbi, Phys. Rev. D 13 (1976) 3398.
102. [82] A.J. Niemi and G.W. Semenoff, Phys. Reports 135 (1986) 99.
103. [83] V.I. Sanyuk, J. Mod. Phys. A7 (1992) 1; See also Ref. [14].
104. [84] T.H.R. Skyrme, Proc. Roy. Soc. London A247 (1958) 260.
105. [85] S. Coleman, Phys. Rev. D11 (1975) 2088; Mandelshtam, Phys. Rev. D11 (1975) 3026.
106. [85] S. Coleman, Phys. Rev. D11 (1975) 2088; Mandelshtam, Phys. Rev. D11 (1975) 3026.
107. [86] J. Goldstone and F. Wilczek, Phys. Rev. Lett. 47 (1981) 986; A.P. Balachandran et al., Phys. Rev. D 27 (1981) 1153; S. Kahana and G. Ripka, Nucl. Phys. A 429 (1984) 462.
108. [86] J. Goldstone and F. Wilczek, Phys. Rev. Lett. 47 (1981) 986; A.P. Balachandran et al., Phys. Rev. D 27 (1981) 1153; S. Kahana and G. Ripka, Nucl. Phys. A 429 (1984) 462.
109. [86] J. Goldstone and F. Wilczek, Phys. Rev. Lett. 47 (1981) 986; A.P. Balachandran et al., Phys. Rev. D 27 (1981) 1153; S. Kahana and G. Ripka, Nucl. Phys. A 429 (1984) 462.
110. [87] N.S. Manton, Proc. LMS Symp. on Geometry of low dimensional manifolds (Durham, 1989).
111. [88] M. Wakamatsu, Phys. Lett. B 349 (1995) 204; Preprint, Osaka University (1995).
112. [89] G.E. Brown, M. Rho and W. Weise, Nucl. Phys. A 454 (1986) 669.
113. [90] E. Braaten, S. Townsend and L. Carson, Phys. Lett. B 235 (1990) 147.
114. [91] R. Edmonds, Angular Momentum (Princeton University Press, Princeton, 1975).
115. [92] H.B.G. Casimir, Proc. Kon. Ned, Akad, Wetenschap. B 51 (1948) 793.
116. [93] C. Itzykson and J.-B. Zuber, Quantum Field Theory (MacGraw Hill, New York, 1980).
117. [94] K.A. Milton, L.L. DeReed and J. Schwinger, Ann. Phys. 115 (1978) 388; K.A. Milton, Phys. Rev. D 22 (1980) 1441; D 25 (1982) 3441; Ann. Phys. 150 (1983) 432.
118. [94] K.A. Milton, L.L. DeReed and J. Schwinger, Ann. Phys. 115 (1978) 388; K.A. Milton, Phys. Rev. D 22 (1980) 1441; D 25 (1982) 3441; Ann. Phys. 150 (1983) 432.
119. [94] K.A. Milton, L.L. DeReed and J. Schwinger, Ann. Phys. 115 (1978) 388; K.A. Milton, Phys. Rev. D 22 (1980) 1441; D 25 (1982) 3441; Ann. Phys. 150 (1983) 432.
120. [94] K.A. Milton, L.L. DeReed and J. Schwinger, Ann. Phys. 115 (1978) 388; K.A. Milton, Phys. Rev. D 22 (1980) 1441; D 25 (1982) 3441; Ann. Phys. 150 (1983) 432.
121. [95] C.M. Bender and P. Hayes, Phys. Rev. D14 (1976) 2622.
122. [96] L. Vepstas and A.D. Jackson, Phys. Reports, 187 (1990) 109.
123. [97] J.D. Bjorken and S.D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965).
124. [98] T.H. Hanson and R.L. Jaffe, Phys. Rev. D 28 (1983) 882.
125. [99] U. Ascher, J. Christiansen and R.D. Russell, ACM Trans. Math. Software 7 (1981) 209.
126. [100] G.S. Adkins, in: Chiral Solitons, ed. K.F. Liu (World Scientific, Singapore, 1987).
127. [101] A.V. Manohar, Nucl. Phys. B 248 (1984) 19.
128. [102] A. Hosaka and H. Toki, Phys. Lett. B 188 (1987) 301;
129. A. Hosaka, Prog. Theor. Phys. 78 (1987) 857.
130. [103] T.H.R. Skyrme, J. Math. Phys.12 (1971) 1735.
131. [104] S.G. Rajeev, Phys. Rev. D 29 (1984) 2944; J. Wudka, Nucls. Phys. B 259 (1985) 689.
132. [104] S.G. Rajeev, Phys. Rev. D 29 (1984) 2944; J. Wudka, Nucls. Phys. B 259 (1985) 689.
133. [105] A. Kamlah, Z. Phys. 216 (1968) 52.
134. [106] H. Weigel, R. Alkofer and H. Reinhardt, Nucl. Phys. A 582 (1995) 484.
135. [107] A. Hosaka, Phys. Lett. B 207 (1988) 249.
136. [108] E. Wüst, L. Vepstas, A.D. Jackson, Phys. Lett. B 173 (1986) 217.
137. [109] A. Hosaka, K. Kusaka, H. Takashita and H. Toki, Prog. Theor. Phys. 76 (1986) 315.
138. [110] See, for example, Refs. [20,58].
139. [111] R.L. Jaffe, Lectures at the 1979 Erice summer school, Ettore Majorana; or in: Pointlike Structures Inside and Outside Hadrons, ed. A. Zichichi (Plenum, New York, 1982) p. 99.
140. [112] M. Wakamatsu and T. Watabe, Phys. Lett. B 312 (1993) 184.
141. [113] M. Wakamatsu, Phys. Lett. B 331 (1994) 425.
142. [114] Chr.V. Christov, K. Goeke and P.V. Pobylitsa, Phys. Rev. C 52 (1995) 425.
143. [115] J. Ashman et al., Phys. Lett. B 206 (1988) 264; Nucl. Phys. B 328 (1989) 1; B. Adeva et al., Phys. Lett. B 302 (1993) 533; P.L. Anthony et al., Phys. Rev. Lett. 17 (1993) 959; K. Abe et al., Phys. Rev. Lett. 75 (1995) 25.
144. [115] J. Ashman et al., Phys. Lett. B 206 (1988) 264; Nucl. Phys. B 328 (1989) 1; B. Adeva et al., Phys. Lett. B 302 (1993) 533; P.L. Anthony et al., Phys. Rev. Lett. 17 (1993) 959; K. Abe et al., Phys. Rev. Lett. 75 (1995) 25.
145. [115] J. Ashman et al., Phys. Lett. B 206 (1988) 264; Nucl. Phys. B 328 (1989) 1; B. Adeva et al., Phys. Lett. B 302 (1993) 533; P.L. Anthony et al., Phys. Rev. Lett. 17 (1993) 959; K. Abe et al., Phys. Rev. Lett. 75 (1995) 25.
146. [115] J. Ashman et al., Phys. Lett. B 206 (1988) 264; Nucl. Phys. B 328 (1989) 1; B. Adeva et al., Phys. Lett. B 302 (1993) 533; P.L. Anthony et al., Phys. Rev. Lett. 17 (1993) 959; K. Abe et al., Phys. Rev. Lett. 75 (1995) 25.
147. [115] J. Ashman et al., Phys. Lett. B 206 (1988) 264; Nucl. Phys. B 328 (1989) 1; B. Adeva et al., Phys. Lett. B 302 (1993) 533; P.L. Anthony et al., Phys. Rev. Lett. 17 (1993) 959; K. Abe et al., Phys. Rev. Lett. 75 (1995) 25.
148. [116] G. Alterelli and G.G. Ross, Phys. Lett. B 212 (1988) 391; R.D. Carlitz, J.C. Collins and A.H. Mueller, Phys. Lett. B 214 (1988) 229.
149. [116] G. Alterelli and G.G. Ross, Phys. Lett. B 212 (1988) 391; R.D. Carlitz, J.C. Collins and A.H. Mueller, Phys. Lett. B 214 (1988) 229.
150. [117] Xiangdong Ji, Plenary talk presented at Baryons '95, hep-ph/9510362.
151. [118] Z. Ryzak, Phys. Lett. B 217 (1989) 325; B 224 (1989) 450; T.D. Cohen and M.K. Bernajee, Phys. Lett. B 230 (1989) 129.
152. [118] Z. Ryzak, Phys. Lett. B 217 (1989) 325; B 224 (1989) 450; T.D. Cohen and M.K. Bernajee, Phys. Lett. B 230 (1989) 129.
153. [118] Z. Ryzak, Phys. Lett. B 217 (1989) 325; B 224 (1989) 450; T.D. Cohen and M.K. Bernajee, Phys. Lett. B 230 (1989) 129.
154. [119] M. Rho, G.E. Brown and B.-Y. Park, Phys. Rev. C 39 (1989) 1173.
155. [120] A. Hosaka and W. Weise, Phys. Lett. B 232 (1989) 232.
156. [121] H. Hogaasen and F. Myhrer, Phys. Lett B 214 (1988) 123.
157. [122] H. Hogaasen and F. Myhrer, Z. Phys. C68 (1995) 625.
158. [123] H. Dreiner, J. Ellis and R.A. Flores, Phys. Lett. B 221 (1989) 167.
159. [124] D.I. Diakonov, V.Yu. Petrov and P.V. Povilitsa, Nucl. Phys. B 306 (1988) 809; D.I. Diakonov, V.Yu. Petrov and M. Praszalowicz, Nucl. Phys. B 323 (1989) 53;
160. [124] D.I. Diakonov, V.Yu. Petrov and P.V. Povilitsa, Nucl. Phys. B 306 (1988) 809; D.I. Diakonov, V.Yu. Petrov and M. Praszalowicz, Nucl. Phys. B 323 (1989) 53;
161. M. Wakamatsu and H. Yoshiki, Nucl. Phys. A 524 (1991) 561; T. Watabe and H. Toki, Prog. Theor. Phys. 87 (1992) 651; Th. Meissner, E. Ruiz Arriola, F. Grummer, H. Mavromatis and K. Goeke, Phys. Lett. B 214 (1988) 312; Th. Meissner, E. Ruiz Arriola and K. Goeke, Phys. Lett. B 27 (1989) 296; Th. Meissner and K. Goeke, Nucl. Phys. A 524 (1991) 719.
162. M. Wakamatsu and H. Yoshiki, Nucl. Phys. A 524 (1991) 561; T. Watabe and H. Toki, Prog. Theor. Phys. 87 (1992) 651; Th. Meissner, E. Ruiz Arriola, F. Grummer, H. Mavromatis and K. Goeke, Phys. Lett. B 214 (1988) 312; Th. Meissner, E. Ruiz Arriola and K. Goeke, Phys. Lett. B 27 (1989) 296; Th. Meissner and K. Goeke, Nucl. Phys. A 524 (1991) 719.
163. M. Wakamatsu and H. Yoshiki, Nucl. Phys. A 524 (1991) 561; T. Watabe and H. Toki, Prog. Theor. Phys. 87 (1992) 651; Th. Meissner, E. Ruiz Arriola, F. Grummer, H. Mavromatis and K. Goeke, Phys. Lett. B 214 (1988) 312; Th. Meissner, E. Ruiz Arriola and K. Goeke, Phys. Lett. B 27 (1989) 296; Th. Meissner and K. Goeke, Nucl. Phys. A 524 (1991) 719.
164. M. Wakamatsu and H. Yoshiki, Nucl. Phys. A 524 (1991) 561; T. Watabe and H. Toki, Prog. Theor. Phys. 87 (1992) 651; Th. Meissner, E. Ruiz Arriola, F. Grummer, H. Mavromatis and K. Goeke, Phys. Lett. B 214 (1988) 312; Th. Meissner, E. Ruiz Arriola and K. Goeke, Phys. Lett. B 27 (1989) 296; Th. Meissner and K. Goeke, Nucl. Phys. A 524 (1991) 719.
165. M. Wakamatsu and H. Yoshiki, Nucl. Phys. A 524 (1991) 561; T. Watabe and H. Toki, Prog. Theor. Phys. 87 (1992) 651; Th. Meissner, E. Ruiz Arriola, F. Grummer, H. Mavromatis and K. Goeke, Phys. Lett. B 214 (1988) 312; Th. Meissner, E. Ruiz Arriola and K. Goeke, Phys. Lett. B 27 (1989) 296; Th. Meissner and K. Goeke, Nucl. Phys. A 524 (1991) 719.
166. [125] J. Schechter and H. Weigel, preprints hep-ph/9410320; hep-ph/9410321.
167. [126] Handbook of mathematical functions, eds. M. Abramowitz and I.A. Stegun (Dover, New York, 1970).
168. [127] V. Vento, Phys. Lett. B 107 (1981) 5.
169. [128] G.S. Adkins and C.R. Nappi, Phys. Lett. B 137 (1984) 251.
170. [129] S. Yoro and T. Tatsumi, Prog. Theor. Phys. 78 (1987) 1392.
171. [130] D. Klabucar and G.E. Brown, Nucl. Phys. A 454 (1986) 589.
172. [131] U.-G. Meissner, Phys. Reports 161 (1988) 213.
173. [132] H. Takashita, S. Yoro and H. Toki, Nucl. Phys. A 485 (1988) 589.
174. [133] A. Dhar, R. Shanker and S.R. Wadia, Phys. Rev. D 31 (1985) 3256; D. Ebert and H. Reinhardt, Nucl. Phys. B 271 (1986) 188.
175. [133] A. Dhar, R. Shanker and S.R. Wadia, Phys. Rev. D 31 (1985) 3256; D. Ebert and H. Reinhardt, Nucl. Phys. B 271 (1986) 188.
176. [134] S. Weinberg, Phys. Rev. Lett. 18 (1967) 507.
177. [135] K. Kawarabayashi and M. Suzuki, Phys. Rev. Lett. 16 (1966) 255; Riazuddin and Fayyazuddin, Phys. Rev. 147 (1966) 1071.
178. [135] K. Kawarabayashi and M. Suzuki, Phys. Rev. Lett. 16 (1966) 255; Riazuddin and Fayyazuddin, Phys. Rev. 147 (1966) 1071.
179. [136] Z.F. Ezawa and T. Yanagida, Phys. Rev. D 33 (1986) 247.
180. [137] O. Kaymakcalan, S. Rajeev and J. Schechter, Phys. Rev. D 30 (1984) 594.
181. [138] C. Schüren, E. Ruiz Arriola and K. Goeke, Phys. Lett. B 287 (1992) 283.
182. [139] R. Alkofer, H. Reinhardt, H. Weigel and U. Zückert, Phys. Lett. B 298 (1993) 132.
183. [140] A. Arima and F. Iachello, Adv. Nucl. Phys. 13 139 (1984).
184. [141] R.D. Amado, R. Bijker and M. Oka, Phys. Rev. Lett. 58 (1987) 654.
185. [142] M. Oka, R. Bijker, A. Bulgac and R.D. Amado, Phys. Rev. C 36 (1987) 1727.
186. [143] M. Ademollo and R. Gatto, Phys. Rev. Lett. 13 (1964) 264.
187. [144] G.E. Brown and W. Weise, Phys. Reports 27 (1976) 1.
188. [145] M. Wakamatsu, Phys. Lett. B 232 (1989) 251.
189. [146] R. Johnson et al., Phys. Rev. D 42 (1990) 2998.
190. [147] J.D. Breit and C.R. Nappi, Phys. Rev. Lett. 53 (1984) 889; A. Hayashi et al., Phys. Lett. B 149 (1984) 5; I. Zahed, U.-G. Meissner and U.S. Kaulfuss, Nucl. Phys. A 426 (1984) 525; U.B. Kaulfus and U.-G. Meissner, Phys. Lett. B 154 (1985) 193; K.F. Liu, J.S. Zang and G.R.E. Black, Phys. Rev. D 30 (1984) 2015; M.P. Mattis and M.E. Peskin, Phys. Rev. D 32 (1985) 58; M.P. Mattis, SLAC-0291, Feb. 1986, Ph.D. Thesis.
191. [147] J.D. Breit and C.R. Nappi, Phys. Rev. Lett. 53 (1984) 889; A. Hayashi et al., Phys. Lett. B 149 (1984) 5; I. Zahed, U.-G. Meissner and U.S. Kaulfuss, Nucl. Phys. A 426 (1984) 525; U.B. Kaulfus and U.-G. Meissner, Phys. Lett. B 154 (1985) 193; K.F. Liu, J.S. Zang and G.R.E. Black, Phys. Rev. D 30 (1984) 2015; M.P. Mattis and M.E. Peskin, Phys. Rev. D 32 (1985) 58; M.P. Mattis, SLAC-0291, Feb. 1986, Ph.D. Thesis.
192. [147] J.D. Breit and C.R. Nappi, Phys. Rev. Lett. 53 (1984) 889; A. Hayashi et al., Phys. Lett. B 149 (1984) 5; I. Zahed, U.-G. Meissner and U.S. Kaulfuss, Nucl. Phys. A 426 (1984) 525; U.B. Kaulfus and U.-G. Meissner, Phys. Lett. B 154 (1985) 193; K.F. Liu, J.S. Zang and G.R.E. Black, Phys. Rev. D 30 (1984) 2015; M.P. Mattis and M.E. Peskin, Phys. Rev. D 32 (1985) 58; M.P. Mattis, SLAC-0291, Feb. 1986, Ph.D. Thesis.
193. [147] J.D. Breit and C.R. Nappi, Phys. Rev. Lett. 53 (1984) 889; A. Hayashi et al., Phys. Lett. B 149 (1984) 5; I. Zahed, U.-G. Meissner and U.S. Kaulfuss, Nucl. Phys. A 426 (1984) 525; U.B. Kaulfus and U.-G. Meissner, Phys. Lett. B 154 (1985) 193; K.F. Liu, J.S. Zang and G.R.E. Black, Phys. Rev. D 30 (1984) 2015; M.P. Mattis and M.E. Peskin, Phys. Rev. D 32 (1985) 58; M.P. Mattis, SLAC-0291, Feb. 1986, Ph.D. Thesis.
194. [147] J.D. Breit and C.R. Nappi, Phys. Rev. Lett. 53 (1984) 889; A. Hayashi et al., Phys. Lett. B 149 (1984) 5; I. Zahed, U.-G. Meissner and U.S. Kaulfuss, Nucl. Phys. A 426 (1984) 525; U.B. Kaulfus and U.-G. Meissner, Phys. Lett. B 154 (1985) 193; K.F. Liu, J.S. Zang and G.R.E. Black, Phys. Rev. D 30 (1984) 2015; M.P. Mattis and M.E. Peskin, Phys. Rev. D 32 (1985) 58; M.P. Mattis, SLAC-0291, Feb. 1986, Ph.D. Thesis.
195. [147] J.D. Breit and C.R. Nappi, Phys. Rev. Lett. 53 (1984) 889; A. Hayashi et al., Phys. Lett. B 149 (1984) 5; I. Zahed, U.-G. Meissner and U.S. Kaulfuss, Nucl. Phys. A 426 (1984) 525; U.B. Kaulfus and U.-G. Meissner, Phys. Lett. B 154 (1985) 193; K.F. Liu, J.S. Zang and G.R.E. Black, Phys. Rev. D 30 (1984) 2015; M.P. Mattis and M.E. Peskin, Phys. Rev. D 32 (1985) 58; M.P. Mattis, SLAC-0291, Feb. 1986, Ph.D. Thesis.
196. [147] J.D. Breit and C.R. Nappi, Phys. Rev. Lett. 53 (1984) 889; A. Hayashi et al., Phys. Lett. B 149 (1984) 5; I. Zahed, U.-G. Meissner and U.S. Kaulfuss, Nucl. Phys. A 426 (1984) 525; U.B. Kaulfus and U.-G. Meissner, Phys. Lett. B 154 (1985) 193; K.F. Liu, J.S. Zang and G.R.E. Black, Phys. Rev. D 30 (1984) 2015; M.P. Mattis and M.E. Peskin, Phys. Rev. D 32 (1985) 58; M.P. Mattis, SLAC-0291, Feb. 1986, Ph.D. Thesis.
197. [148] G.E. Brown, J.D. Durso and M.B. Johnson, Nucl. Phys. A 397 (1983) 447; Nucl. Phys. A 454 (1986) 669; L. Tomio and Y. Nogami, Phys. Rev. D 31 (1985) 2813; N. Yamanishi, A. Suzuki and Y. Takahashi, Prog. Theor. Phys. 73 (1985) 1198.
198. [148] G.E. Brown, J.D. Durso and M.B. Johnson, Nucl. Phys. A 397 (1983) 447; Nucl. Phys. A 454 (1986) 669; L. Tomio and Y. Nogami, Phys. Rev. D 31 (1985) 2813; N. Yamanishi, A. Suzuki and Y. Takahashi, Prog. Theor. Phys. 73 (1985) 1198.
199. [148] G.E. Brown, J.D. Durso and M.B. Johnson, Nucl. Phys. A 397 (1983) 447; Nucl. Phys. A 454 (1986) 669; L. Tomio and Y. Nogami, Phys. Rev. D 31 (1985) 2813; N. Yamanishi, A. Suzuki and Y. Takahashi, Prog. Theor. Phys. 73 (1985) 1198.
200. [148] G.E. Brown, J.D. Durso and M.B. Johnson, Nucl. Phys. A 397 (1983) 447; Nucl. Phys. A 454 (1986) 669; L. Tomio and Y. Nogami, Phys. Rev. D 31 (1985) 2813; N. Yamanishi, A. Suzuki and Y. Takahashi, Prog. Theor. Phys. 73 (1985) 1198.
201. [149] H. Toki, J. Dey and M. Dey, Phys. Lett. B 133 (1983) 20.
202. [150] T. Hatsuda, Nucl. Phys. A 458 (1986) 583.
203. [151] G.E. Brown, H.Q. Song, R.K. Su and K.F. Lie, Nucl. Phys. A 458 (1986) 573.
204. [152] For example, L.I. Schiff, Quantum mechanics (McGraw-Hill, New York, 1970).
205. [153] A. Jackson, A.D. Jackson, V. Pasquier, Nucl. Phys. A 432 (1985) 567; R. VinMau et al., Phys. Lett. B 150 (1985) 259; H. Yabu and K. Ando , Prog. Theor. Phys. 74 (1985) 31.
206. [153] A. Jackson, A.D. Jackson, V. Pasquier, Nucl. Phys. A 432 (1985) 567; R. VinMau et al., Phys. Lett. B 150 (1985) 259; H. Yabu and K. Ando , Prog. Theor. Phys. 74 (1985) 31.
207. [153] A. Jackson, A.D. Jackson, V. Pasquier, Nucl. Phys. A 432 (1985) 567; R. VinMau et al., Phys. Lett. B 150 (1985) 259; H. Yabu and K. Ando , Prog. Theor. Phys. 74 (1985) 31.
208. [154] N.S. Manton, Phys. Lett. B 192 (1987) 177; J.J.M. Verbaaschot, Phys. Lett. B 195 (1987) 235; V.B. Kopeliovich and B.E. Stern, JETP Lett. 45 (1987) 203; E. Braaten and L. Carson, Phys. Rev. D 38 (1988) 3525.
209. [154] N.S. Manton, Phys. Lett. B 192 (1987) 177; J.J.M. Verbaaschot, Phys. Lett. B 195 (1987) 235; V.B. Kopeliovich and B.E. Stern, JETP Lett. 45 (1987) 203; E. Braaten and L. Carson, Phys. Rev. D 38 (1988) 3525.
210. [154] N.S. Manton, Phys. Lett. B 192 (1987) 177; J.J.M. Verbaaschot, Phys. Lett. B 195 (1987) 235; V.B. Kopeliovich and B.E. Stern, JETP Lett. 45 (1987) 203; E. Braaten and L. Carson, Phys. Rev. D 38 (1988) 3525.
211. [154] N.S. Manton, Phys. Lett. B 192 (1987) 177; J.J.M. Verbaaschot, Phys. Lett. B 195 (1987) 235; V.B. Kopeliovich and B.E. Stern, JETP Lett. 45 (1987) 203; E. Braaten and L. Carson, Phys. Rev. D 38 (1988) 3525.
212. [155] J.J.M. Verbaarschot, T.S. Walhaut, J. Wambach and H.W. Wyld, Nucl. Phys. A 468 (1987) 520.
213. [156] A. Hosaka, S.M. Griffies, M. Oka and R.D. Amado, Phys. Lett. B 251 (1990) 1; A. Hosaka, M. Oka and R.D. Amado, Nucl. Phys. A 530 (1991) 507; M. Oka and A. Hosaka, Ann. Rev. Nucl. Part. Sci. 42 (1992) 333.
214. [156] A. Hosaka, S.M. Griffies, M. Oka and R.D. Amado, Phys. Lett. B 251 (1990) 1; A. Hosaka, M. Oka and R.D. Amado, Nucl. Phys. A 530 (1991) 507; M. Oka and A. Hosaka, Ann. Rev. Nucl. Part. Sci. 42 (1992) 333.
215. [156] A. Hosaka, S.M. Griffies, M. Oka and R.D. Amado, Phys. Lett. B 251 (1990) 1; A. Hosaka, M. Oka and R.D. Amado, Nucl. Phys. A 530 (1991) 507; M. Oka and A. Hosaka, Ann. Rev. Nucl. Part. Sci. 42 (1992) 333.
216. [157] M.F. Atiyah and N.S. Manton, Phys. Lett. B 222 (1989) 438; N.S. Manton, Proc. LMS Symp. Geometry of low dimensional manifolds (Durham, 1989); M.F. Atiyah and N.S. Manton, Commun. Math. Phys. 153 (1993) 391.
217. [157] M.F. Atiyah and N.S. Manton, Phys. Lett. B 222 (1989) 438; N.S. Manton, Proc. LMS Symp. Geometry of low dimensional manifolds (Durham, 1989); M.F. Atiyah and N.S. Manton, Commun. Math. Phys. 153 (1993) 391.
218. [157] M.F. Atiyah and N.S. Manton, Phys. Lett. B 222 (1989) 438; N.S. Manton, Proc. LMS Symp. Geometry of low dimensional manifolds (Durham, 1989); M.F. Atiyah and N.S. Manton, Commun. Math. Phys. 153 (1993) 391.
219. [158] N.R. Walet, Nucl. Phys. A 586 (1995) 649.
220. [159] N.S. Manton, Phys. Rev. Lett. 60 (1988) 1916.
221. [160] N.R. Walet, R.D. Amado and A. Hosaka, Phys. Rev. Lett. 68 (1992) 3849.
222. [161] M. Oka and K. Yazaki, Prog. Theor. Phys. Phys. Lett. B 90 (1980) 41; Prog. Theor. Phys. 66 (1981) 556, 572; H. Toki, Z. Phys. A 294 (1980) 173.
223. [161] M. Oka and K. Yazaki, Prog. Theor. Phys. Phys. Lett. B 90 (1980) 41; Prog. Theor. Phys. 66 (1981) 556, 572; H. Toki, Z. Phys. A 294 (1980) 173.
224. [161] M. Oka and K. Yazaki, Prog. Theor. Phys. Phys. Lett. B 90 (1980) 41; Prog. Theor. Phys. 66 (1981) 556, 572; H. Toki, Z. Phys. A 294 (1980) 173.
225. [162] T.S. Walhout, Nucl. Phys. A 484 (1991) 397.
226. [163] I. Klebanov, Nucl. Phys. B 262 (1985) 133.
227. [164] A.D. Jackson and J.J.M. Verbaarschot, Nucl. Phys. A 484 (1988) 419; L. Castillejo et al., Nucl. Phys. A 501 (1989) 801.
228. [164] A.D. Jackson and J.J.M. Verbaarschot, Nucl. Phys. A 484 (1988) 419; L. Castillejo et al., Nucl. Phys. A 501 (1989) 801.
229. [165] H. Forkel et al., Nucl. Phys. A 504 (1989) 818.
230. [166] N.S. Manton and P.J. Ruback, Phys. Lett. B 181 (1986) 137; A.D. Jackson, A. Wirzba and L. Castillejo, Nucl. Phys. A 486 (1988) 634. [167] A.D. Jackson, N.S. Manton and A. Wirzba, Nucl. Phys. A 495 (1989) 499; B.A. Campbell, J. Ellis and K.A. Olive, Nucl. Phys. B 345 (1990) 57.
231. [166] N.S. Manton and P.J. Ruback, Phys. Lett. B 181 (1986) 137; A.D. Jackson, A. Wirzba and L. Castillejo, Nucl. Phys. A 486 (1988) 634. [167] A.D. Jackson, N.S. Manton and A. Wirzba, Nucl. Phys. A 495 (1989) 499; B.A. Campbell, J. Ellis and K.A. Olive, Nucl. Phys. B 345 (1990) 57.
232. [166] N.S. Manton and P.J. Ruback, Phys. Lett. B 181 (1986) 137; A.D. Jackson, A. Wirzba and L. Castillejo, Nucl. Phys. A 486 (1988) 634. [167] A.D. Jackson, N.S. Manton and A. Wirzba, Nucl. Phys. A 495 (1989) 499; B.A. Campbell, J. Ellis and K.A. Olive, Nucl. Phys. B 345 (1990) 57.
233. [166] N.S. Manton and P.J. Ruback, Phys. Lett. B 181 (1986) 137; A.D. Jackson, A. Wirzba and L. Castillejo, Nucl. Phys. A 486 (1988) 634. [167] A.D. Jackson, N.S. Manton and A. Wirzba, Nucl. Phys. A 495 (1989) 499; B.A. Campbell, J. Ellis and K.A. Olive, Nucl. Phys. B 345 (1990) 57.
234. [168] E. Guadagnini, Nucl. Phys. B 236 (1984) 35.
235. [169] H. Yabu, K. Ando, Nucl. Phys. B 301 (1988) 601.
236. [170] B.-Y. Park, D.-P. Min and M. Rho, Nucl. Phys. A 551 (1993) 657.
237. [171] G. 't Hooft, Nucl. Phys. B 190 (1981) 455; See also Under the Spell of Gauge Principle, Advanced Series in Mathematical Physics, Vol. 19 (World Scientific, Singapore, 1994).
238. [171] G. 't Hooft, Nucl. Phys. B 190 (1981) 455; See also Under the Spell of Gauge Principle, Advanced Series in Mathematical Physics, Vol. 19 (World Scientific, Singapore, 1994).
239. [172] T. Suzuki, Prog. Theor. Phys. 80 (1988) 929; 81 (1989) 752; S. Maedan and T. Suzuki, Prog. Theor. Phys. 81 (1989) 229.
240. [172] T. Suzuki, Prog. Theor. Phys. 80 (1988) 929; 81 (1989) 752; S. Maedan and T. Suzuki, Prog. Theor. Phys. 81 (1989) 229.
241. [172] T. Suzuki, Prog. Theor. Phys. 80 (1988) 929; 81 (1989) 752; S. Maedan and T. Suzuki, Prog. Theor. Phys. 81 (1989) 229.
242. [173] H. Suganuma, T. Sasaki and H. Toki, Nucl. Phys. B 435 (1995) 207.