P,T-invariant system of Chern-Simons fields: Pseudoclassical model and hidden symmetries

Nuclear Physics B

Volumn 512, Issue 1-2, 1998, Pages 295-319

  Nirov, Khazret S ^a,d   Plyushchay, Mikhail S ^b,c  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b FEDERAL UNIVERSITY OF JUIZ DE FORA   (Brazil)

^c INSTITUTE FOR HIGH ENERGY PHYSICS   (Russian Federation)

^d INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

Author keywords

Chern Simons gauge fields; Discrete and continuous symmetries; Parameter quantization; Pseudoclassical mechanics; Supersymmetry

Indexed keywords

EID: 0032536238     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(97)00746-3     Document Type: Article

References (78)

1. [1] R. Jackiw and S. Templeton, Phys. Rev. D 23 (1981) 2291; J. Schonfeld, Nucl. Phys. B 185 (1981) 157; W. Siegel, Nucl. Phys. B 156 (1979) 135; S. Deser, R. Jackiw and S. Templeton, Phys. Rev. Lett. 48 (1982) 975; Ann. Phys. 140 (1982) 372.
2. [1] R. Jackiw and S. Templeton, Phys. Rev. D 23 (1981) 2291; J. Schonfeld, Nucl. Phys. B 185 (1981) 157; W. Siegel, Nucl. Phys. B 156 (1979) 135; S. Deser, R. Jackiw and S. Templeton, Phys. Rev. Lett. 48 (1982) 975; Ann. Phys. 140 (1982) 372.
3. [1] R. Jackiw and S. Templeton, Phys. Rev. D 23 (1981) 2291; J. Schonfeld, Nucl. Phys. B 185 (1981) 157; W. Siegel, Nucl. Phys. B 156 (1979) 135; S. Deser, R. Jackiw and S. Templeton, Phys. Rev. Lett. 48 (1982) 975; Ann. Phys. 140 (1982) 372.
4. [1] R. Jackiw and S. Templeton, Phys. Rev. D 23 (1981) 2291; J. Schonfeld, Nucl. Phys. B 185 (1981) 157; W. Siegel, Nucl. Phys. B 156 (1979) 135; S. Deser, R. Jackiw and S. Templeton, Phys. Rev. Lett. 48 (1982) 975; Ann. Phys. 140 (1982) 372.
5. [1] R. Jackiw and S. Templeton, Phys. Rev. D 23 (1981) 2291; J. Schonfeld, Nucl. Phys. B 185 (1981) 157; W. Siegel, Nucl. Phys. B 156 (1979) 135; S. Deser, R. Jackiw and S. Templeton, Phys. Rev. Lett. 48 (1982) 975; Ann. Phys. 140 (1982) 372.
6. [2] R. Jackiw and C. Rebbi, Phys. Rev. Lett. 37 (1976) 172; R. Jackiw, Rev. Mod. Phys. 52 (1980) 661; S. Deser, M. Duff and C. Isham, Phys. Lett. 93 B (1980) 419.
7. [2] R. Jackiw and C. Rebbi, Phys. Rev. Lett. 37 (1976) 172; R. Jackiw, Rev. Mod. Phys. 52 (1980) 661; S. Deser, M. Duff and C. Isham, Phys. Lett. 93 B (1980) 419.
8. [2] R. Jackiw and C. Rebbi, Phys. Rev. Lett. 37 (1976) 172; R. Jackiw, Rev. Mod. Phys. 52 (1980) 661; S. Deser, M. Duff and C. Isham, Phys. Lett. 93 B (1980) 419.
9. [3] S.M. Girvin and A.H. MacDonald, Phys. Rev. Lett. 58 (1987) 1252; S. Girvin and R. Prange (eds.), The Quantum Hall Effect (Springer, Berlin, 1987); Z. Zhang, T. Hansson and S. Kivelson, Phys. Rev. Lett. 62 (1989) 82 (E), 980; N. Read, Phys. Rev. Lett. 62 (1989) 86.
10. [3] S.M. Girvin and A.H. MacDonald, Phys. Rev. Lett. 58 (1987) 1252; S. Girvin and R. Prange (eds.), The Quantum Hall Effect (Springer, Berlin, 1987); Z. Zhang, T. Hansson and S. Kivelson, Phys. Rev. Lett. 62 (1989) 82 (E), 980; N. Read, Phys. Rev. Lett. 62 (1989) 86.
11. [3] S.M. Girvin and A.H. MacDonald, Phys. Rev. Lett. 58 (1987) 1252; S. Girvin and R. Prange (eds.), The Quantum Hall Effect (Springer, Berlin, 1987); Z. Zhang, T. Hansson and S. Kivelson, Phys. Rev. Lett. 62 (1989) 82 (E), 980; N. Read, Phys. Rev. Lett. 62 (1989) 86.
12. [3] S.M. Girvin and A.H. MacDonald, Phys. Rev. Lett. 58 (1987) 1252; S. Girvin and R. Prange (eds.), The Quantum Hall Effect (Springer, Berlin, 1987); Z. Zhang, T. Hansson and S. Kivelson, Phys. Rev. Lett. 62 (1989) 82 (E), 980; N. Read, Phys. Rev. Lett. 62 (1989) 86.
13. [4] A. Polyakov, Mod. Phys. Lett. A 3 (1988) 325; Y.-H. Chen, F. Wilczek, E. Witten and B. Halperin, Int. J. Mod. Phys. B 3 (1989) 1001; F. Wilczek, Fractional Statistics and Anyon Superconductivity (World Scientific, Singapore, 1990).
14. [4] A. Polyakov, Mod. Phys. Lett. A 3 (1988) 325; Y.-H. Chen, F. Wilczek, E. Witten and B. Halperin, Int. J. Mod. Phys. B 3 (1989) 1001; F. Wilczek, Fractional Statistics and Anyon Superconductivity (World Scientific, Singapore, 1990).
15. [4] A. Polyakov, Mod. Phys. Lett. A 3 (1988) 325; Y.-H. Chen, F. Wilczek, E. Witten and B. Halperin, Int. J. Mod. Phys. B 3 (1989) 1001; F. Wilczek, Fractional Statistics and Anyon Superconductivity (World Scientific, Singapore, 1990).
16. [5] S. Weinberg, in Understanding the Fundamental Interactions, ed. A. Zichichi (Plenum, New York, 1978); A. Linde, Rep. Prog. Phys. 42 (1979) 389; Phys. Lett. 96 B (1980) 289; D.J. Gross, R.D. Pisarski and L.G. Yaffe, Rev. Mod. Phys. 53 (1981) 43; A.M. Polyakov, Nucl. Phys. B 120 (1977) 429; E. Witten, Nucl. Phys. B 149 (1979) 285.
17. [5] S. Weinberg, in Understanding the Fundamental Interactions, ed. A. Zichichi (Plenum, New York, 1978); A. Linde, Rep. Prog. Phys. 42 (1979) 389; Phys. Lett. 96 B (1980) 289; D.J. Gross, R.D. Pisarski and L.G. Yaffe, Rev. Mod. Phys. 53 (1981) 43; A.M. Polyakov, Nucl. Phys. B 120 (1977) 429; E. Witten, Nucl. Phys. B 149 (1979) 285.
18. [5] S. Weinberg, in Understanding the Fundamental Interactions, ed. A. Zichichi (Plenum, New York, 1978); A. Linde, Rep. Prog. Phys. 42 (1979) 389; Phys. Lett. 96 B (1980) 289; D.J. Gross, R.D. Pisarski and L.G. Yaffe, Rev. Mod. Phys. 53 (1981) 43; A.M. Polyakov, Nucl. Phys. B 120 (1977) 429; E. Witten, Nucl. Phys. B 149 (1979) 285.
19. [5] S. Weinberg, in Understanding the Fundamental Interactions, ed. A. Zichichi (Plenum, New York, 1978); A. Linde, Rep. Prog. Phys. 42 (1979) 389; Phys. Lett. 96 B (1980) 289; D.J. Gross, R.D. Pisarski and L.G. Yaffe, Rev. Mod. Phys. 53 (1981) 43; A.M. Polyakov, Nucl. Phys. B 120 (1977) 429; E. Witten, Nucl. Phys. B 149 (1979) 285.
20. [5] S. Weinberg, in Understanding the Fundamental Interactions, ed. A. Zichichi (Plenum, New York, 1978); A. Linde, Rep. Prog. Phys. 42 (1979) 389; Phys. Lett. 96 B (1980) 289; D.J. Gross, R.D. Pisarski and L.G. Yaffe, Rev. Mod. Phys. 53 (1981) 43; A.M. Polyakov, Nucl. Phys. B 120 (1977) 429; E. Witten, Nucl. Phys. B 149 (1979) 285.
21. [5] S. Weinberg, in Understanding the Fundamental Interactions, ed. A. Zichichi (Plenum, New York, 1978); A. Linde, Rep. Prog. Phys. 42 (1979) 389; Phys. Lett. 96 B (1980) 289; D.J. Gross, R.D. Pisarski and L.G. Yaffe, Rev. Mod. Phys. 53 (1981) 43; A.M. Polyakov, Nucl. Phys. B 120 (1977) 429; E. Witten, Nucl. Phys. B 149 (1979) 285.
22. [6] J.G. Bednorz and A.K. Müller, Z. Phys. B 64 (1986) 189; M. Rasolt, T. Edis and Z. Tesanovic, Phys. Rev. Lett. 66 (1989) 2927; Q. Li et al., Phys. Rev. Lett. 64 (1990) 3086; D.H. Lowndes, D.P. Norton and J.D. Budai, Phys. Rev. Lett. 65 (1990) 1160.
23. [6] J.G. Bednorz and A.K. Müller, Z. Phys. B 64 (1986) 189; M. Rasolt, T. Edis and Z. Tesanovic, Phys. Rev. Lett. 66 (1989) 2927; Q. Li et al., Phys. Rev. Lett. 64 (1990) 3086; D.H. Lowndes, D.P. Norton and J.D. Budai, Phys. Rev. Lett. 65 (1990) 1160.
24. [6] J.G. Bednorz and A.K. Müller, Z. Phys. B 64 (1986) 189; M. Rasolt, T. Edis and Z. Tesanovic, Phys. Rev. Lett. 66 (1989) 2927; Q. Li et al., Phys. Rev. Lett. 64 (1990) 3086; D.H. Lowndes, D.P. Norton and J.D. Budai, Phys. Rev. Lett. 65 (1990) 1160.
25. [6] J.G. Bednorz and A.K. Müller, Z. Phys. B 64 (1986) 189; M. Rasolt, T. Edis and Z. Tesanovic, Phys. Rev. Lett. 66 (1989) 2927; Q. Li et al., Phys. Rev. Lett. 64 (1990) 3086; D.H. Lowndes, D.P. Norton and J.D. Budai, Phys. Rev. Lett. 65 (1990) 1160.
26. [7] P.K. Townsend, K. Pilch and P. van Nieuwenhuizen, Phys. Lett. B 136 (1984) 38.
27. [8] S. Deser and R. Jackiw, Phys. Lett. B 139 (1984) 371.
28. [9] X.G. Wen and A. Zee, Phys. Rev. Lett. 62 (1989) 2873.
29. [10] See, for example, A. Mathai, Y. Gim, R.C. Black, A. Amar and F.C. Wellstood, Phys. Rev. Lett. 74 (1995) 4523.
30. [11] A.N. Redlich, Phys. Rev. Lett. 52 (1984) 18;
31. Phys. Rev. D 29 (1984) 2366.
32. [12] J. Lykken, J. Sonnenschein and N. Weiss, Phys. Rev. D 42 (1990) 2161; N.E. Mavromatos, University of Oxford Preprint OUT-90-04P (1990).
33. [12] J. Lykken, J. Sonnenschein and N. Weiss, Phys. Rev. D 42 (1990) 2161; N.E. Mavromatos, University of Oxford Preprint OUT-90-04P (1990).
34. [13] A. Kovner and B. Rosenstein, Phys. Rev. B 42 (1990) 4748; G.W. Semenoff and N. Weiss, Phys. Lett. B 250 (1990) 117; N. Dorey and N.E. Mavromatos, Phys. Lett. B 250 (1990) 107; Nucl. Phys. B 386 (1992) 614.
35. [13] A. Kovner and B. Rosenstein, Phys. Rev. B 42 (1990) 4748; G.W. Semenoff and N. Weiss, Phys. Lett. B 250 (1990) 117; N. Dorey and N.E. Mavromatos, Phys. Lett. B 250 (1990) 107; Nucl. Phys. B 386 (1992) 614.
36. [13] A. Kovner and B. Rosenstein, Phys. Rev. B 42 (1990) 4748; G.W. Semenoff and N. Weiss, Phys. Lett. B 250 (1990) 117; N. Dorey and N.E. Mavromatos, Phys. Lett. B 250 (1990) 107; Nucl. Phys. B 386 (1992) 614.
37. [13] A. Kovner and B. Rosenstein, Phys. Rev. B 42 (1990) 4748; G.W. Semenoff and N. Weiss, Phys. Lett. B 250 (1990) 117; N. Dorey and N.E. Mavromatos, Phys. Lett. B 250 (1990) 107; Nucl. Phys. B 386 (1992) 614.
38. [14] G. Grignani, M. Plyushchay and P. Sodano, Nucl. Phys. B 464 (1996) 189.
39. [15] J.L. Cortés, M.S. Plyushchay and L. Velázquez, Phys. Lett. B 306 (1993) 34.
40. [16] J.L. Martin, Proc. R. Soc. London A 251 (1959) 536.
41. [17] F.A. Berezin and M.S Marinov, JETP Lett. 21 (1975) 678; Ann. Phys. 104 (1977) 336.
42. [17] F.A. Berezin and M.S Marinov, JETP Lett. 21 (1975) 678; Ann. Phys. 104 (1977) 336.
43. [18] R. Casalbuoni, Nuovo Cimento A 33 (1976) 369; A. Barducci, R. Casalbuoni and L. Lusanna, Nuovo Cimento A 35 (1976) 377.
44. [18] R. Casalbuoni, Nuovo Cimento A 33 (1976) 369; A. Barducci, R. Casalbuoni and L. Lusanna, Nuovo Cimento A 35 (1976) 377.
45. [19] L. Brink, S. Deser, B. Zumino, P. DiVecchia and P. Howe, Phys. Lett. B 64 (1976) 435; L. Brink, P. DiVecchia and P.S. Howe, Nucl. Phys. B 118 (1977) 76.
46. [19] L. Brink, S. Deser, B. Zumino, P. DiVecchia and P. Howe, Phys. Lett. B 64 (1976) 435; L. Brink, P. DiVecchia and P.S. Howe, Nucl. Phys. B 118 (1977) 76.
47. [20] G.W. Gibbons, R.H. Rietdijk and J.W. van Holten, Nucl. Phys. B 404 (1993) 42; J.W. van Holten, Phys. Lett. B 342 (1995) 47.
48. [20] G.W. Gibbons, R.H. Rietdijk and J.W. van Holten, Nucl. Phys. B 404 (1993) 42; J.W. van Holten, Phys. Lett. B 342 (1995) 47.
49. [21] M. Tanimoto, Nucl. Phys. B 442 (1995) 549.
50. [22] F. De Jonghe, A.J. Macfarlane, K. Peelers and J.W. van Holten, Phys. Lett. B 359 (1995) 114.
51. [23] P.A.M. Dirac, Proc. R Soc. London A 133 (1931) 60; R. Jackiw, Ann. Phys. 129 (1980) 183; E. D'Hoker and L. Vinet, Phys. Lett. 137 B (1984) 72.
52. [23] P.A.M. Dirac, Proc. R Soc. London A 133 (1931) 60; R. Jackiw, Ann. Phys. 129 (1980) 183; E. D'Hoker and L. Vinet, Phys. Lett. 137 B (1984) 72.
53. [23] P.A.M. Dirac, Proc. R Soc. London A 133 (1931) 60; R. Jackiw, Ann. Phys. 129 (1980) 183; E. D'Hoker and L. Vinet, Phys. Lett. 137 B (1984) 72.
54. [24] C.A. Galvao and C. Teitelboim, J. Math. Phys. 21 (1980) 1863; M. Henneaux and C. Teitelboim, Ann. Phys. (N.Y.) 143 (1982) 127; K. Sundermeyer, Lecture Notes in Physics 169 (Springer, Berlin, 1982); M. Henneaux and C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton, 1992).
55. [24] C.A. Galvao and C. Teitelboim, J. Math. Phys. 21 (1980) 1863; M. Henneaux and C. Teitelboim, Ann. Phys. (N.Y.) 143 (1982) 127; K. Sundermeyer, Lecture Notes in Physics 169 (Springer, Berlin, 1982); M. Henneaux and C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton, 1992).
56. [24] C.A. Galvao and C. Teitelboim, J. Math. Phys. 21 (1980) 1863; M. Henneaux and C. Teitelboim, Ann. Phys. (N.Y.) 143 (1982) 127; K. Sundermeyer, Lecture Notes in Physics 169 (Springer, Berlin, 1982); M. Henneaux and C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton, 1992).
57. [24] C.A. Galvao and C. Teitelboim, J. Math. Phys. 21 (1980) 1863; M. Henneaux and C. Teitelboim, Ann. Phys. (N.Y.) 143 (1982) 127; K. Sundermeyer, Lecture Notes in Physics 169 (Springer, Berlin, 1982); M. Henneaux and C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton, 1992).
58. [25] M.S. Plyushchay, Phys. Lett. B 236 (1990) 291.
59. [26] P.A.M. Dirac, The Principles of Quantum Mechanics (Clarendon, Oxford, 1958).
60. [27] T.F. Jordan and N. Mukunda, Phys. Rev. 132 (1963) 1842.
61. [28] M.S. Plyushchay and A.V. Razumov, Int. J. Mod. Phys. A 11 (1996) 1427.
62. [29] N.N. Bogolubov, A.A. Logunov, A.I. Oksak and I.T. Todorov, General Principles of Quantum Field Theory (Kluwer, Dordrecht, 1990).
63. [30] B. Binegar, J. Math. Phys. 23 (1982) 1511.
64. [31] J. Beckers, N. Debergh and A.G. Nikitin, Fortschr. Phys. 43 (1995) 81.
65. [32] P.P. Srivastava, Nuovo Cimento Lett. 19 (1977) 239; V.D. Gershun and V.I. Tkach, JETP Lett. 29 (1979) 320; A. Barducci and L. Lusanna, J. Phys. A 16 (1983) 1993; P.S. Howe, S. Penati, M. Pernici and P. Townsend, Phys. Lett. B 215 (1988) 555.
66. [32] P.P. Srivastava, Nuovo Cimento Lett. 19 (1977) 239; V.D. Gershun and V.I. Tkach, JETP Lett. 29 (1979) 320; A. Barducci and L. Lusanna, J. Phys. A 16 (1983) 1993; P.S. Howe, S. Penati, M. Pernici and P. Townsend, Phys. Lett. B 215 (1988) 555.
67. [32] P.P. Srivastava, Nuovo Cimento Lett. 19 (1977) 239; V.D. Gershun and V.I. Tkach, JETP Lett. 29 (1979) 320; A. Barducci and L. Lusanna, J. Phys. A 16 (1983) 1993; P.S. Howe, S. Penati, M. Pernici and P. Townsend, Phys. Lett. B 215 (1988) 555.
68. [32] P.P. Srivastava, Nuovo Cimento Lett. 19 (1977) 239; V.D. Gershun and V.I. Tkach, JETP Lett. 29 (1979) 320; A. Barducci and L. Lusanna, J. Phys. A 16 (1983) 1993; P.S. Howe, S. Penati, M. Pernici and P. Townsend, Phys. Lett. B 215 (1988) 555.
69. [33] J.L. Cortés and M.S. Plyushchay, J. Math. Phys. 35 (1994) 6049.
70. [34] W. Siegel, Phys. Lett. B 149 (1984) 157, 162, (corrected in Phys. Lett. B 151 (1985) 391, 396).
71. [34] W. Siegel, Phys. Lett. B 149 (1984) 157, 162, (corrected in Phys. Lett. B 151 (1985) 391, 396).
72. [35] E. Witten, Nucl. Phys. B 268 (1986) 253;
73. B 276 (1986) 291.
74. [36] M. de Crombrugghe and V. Rittenberg, Ann. Phys. 151 (1983) 99.
75. [37] D. Birmingham, M. Rakowski and G. Thompson, Nucl. Phys. B 329 (1989) 83; D. Birmingham and M. Rakowski, Mod. Phys. Lett. A 4 (1989) 1753; F. Delduc, F. Gieres and S.P. Sorella, Phys. Lett. B 225 (1989) 367.
76. [37] D. Birmingham, M. Rakowski and G. Thompson, Nucl. Phys. B 329 (1989) 83; D. Birmingham and M. Rakowski, Mod. Phys. Lett. A 4 (1989) 1753; F. Delduc, F. Gieres and S.P. Sorella, Phys. Lett. B 225 (1989) 367.
77. [37] D. Birmingham, M. Rakowski and G. Thompson, Nucl. Phys. B 329 (1989) 83; D. Birmingham and M. Rakowski, Mod. Phys. Lett. A 4 (1989) 1753; F. Delduc, F. Gieres and S.P. Sorella, Phys. Lett. B 225 (1989) 367.
78. [38] P.H. Damgaard and V.O. Rivelles, Phys. Lett. B 245 (1990) 48.