Chern-Simons theory and BCS superconductivity. (English) Zbl 0983.81120
Summary: We study the relationship between the holomorphic unitary connection of Chern-Simons theory with temporal Wilson lines and the Richardson’s exact solution of the reduced BCS Hamiltonian. We derive the integrals of motion of the BCS model, their eigenvalues and eigenvectors as a limiting case of the Chern-Simons theory.
MSC:
| 81V70 | Many-body theory; quantum Hall effect |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
References:
| [1] | Zhang, S. C.; Hansson, T. H.; Kivelson, S., Phys. Rev. Lett., 62, 82 (1988) |
| [2] | Fetter, A. L.; Hanna, C. B.; Laughlin, R. B., Phys. Rev. B, 39, 9679 (1989) |
| [3] | Bardeen, J.; Cooper, L. N.; Schrieffer, J. R., Phys. Rev., 108, 1175 (1957) · Zbl 0090.45401 |
| [4] | Ring, P.; Schuck, P., The Nuclear Many Body Problem (1980), Springer-Verlag |
| [5] | Richardson, R. W., Phys. Lett., 3, 277 (1963) · Zbl 0108.23203 |
| [6] | Richardson, R. W., Phys. Lett., 5, 82 (1963) |
| [7] | Richardson, R. W.; Sherman, N., Nucl. Phys. B, 52, 221 (1964) |
| [8] | Ralph, D. C.; Black, C. T.; Tinkham, M., Phys. Rev. Lett., 78, 4087 (1997) |
| [9] | von Delft, J.; Ralph, D. C., Phys. Rep., 345, 61 (2001) · Zbl 0978.81522 |
| [10] | Gaudin, M., J. Physique, 37, 1087 (1976) |
| [11] | Cambiaggio, M. C.; Rivas, A. M.F.; Saraceno, M., Nucl. Phys. A, 624, 157 (1997) |
| [12] | Sierra, G., Nucl. Phys. B, 572 [FS], 517 (2000) · Zbl 0947.81107 |
| [13] | Dukelsky, J.; Schuck, P., Phys. Rev. Lett., 86, 4207 (2001) |
| [14] | Amico, L.; Di Lorenzo, A.; Osterloh, A., Phys. Rev. Lett., 86, 5759 (2001) |
| [15] | Dukelsky, J.; Esebbag, C.; Schuck, P., Phys. Rev. Lett., 87, 66403 (2001) |
| [16] | Babujian, H. M., J. Phys. A, 26, 6981 (1993) · Zbl 0821.35113 |
| [17] | Babujian, H. M.; Flume, R., Mod. Phys. Lett., 9, 2029 (1994) |
| [18] | Amico, L.; Falci, G.; Fazio, R., J. Phys. A, 34, 6425-6434 (2001) · Zbl 0988.81146 |
| [19] | Zhou, H.-Q.; Links, J.; McKenzie, R. H.; Gould, M. D. |
| [20] | Delft, J.von; Poghossian, R. |
| [21] | G. Sierra, Lectures on the BCS model, Univ. of Zaragoza (May, 2001), and the NATO Advanced Research Workshop on Statistical Field Theories, Como (Italy) 18-23 June, 2001 (unpublished work); G. Sierra, Lectures on the BCS model, Univ. of Zaragoza (May, 2001), and the NATO Advanced Research Workshop on Statistical Field Theories, Como (Italy) 18-23 June, 2001 (unpublished work) |
| [22] | Richardson, R. W., J. Math. Phys., 6, 1034 (1965) |
| [23] | These papers can be found in: Travaux de Michel Gaudin, Modèles exactament résolus, Les Éditions de Physique, France, 1995; These papers can be found in: Travaux de Michel Gaudin, Modèles exactament résolus, Les Éditions de Physique, France, 1995 |
| [24] | Amico, L.; Osterloh, A. |
| [25] | Korepin, V. E., Commun. Math. Phys., 86, 391 (1982) · Zbl 0531.60096 |
| [26] | Sklyanin, E. K., Lett. Math. Phys., 47, 275 (1999) · Zbl 1055.82508 |
| [27] | Witten, E., Commun. Math. Phys., 121, 351 (1989) · Zbl 0667.57005 |
| [28] | Knizhnik, V.; Zamolodchikov, A. B., Nucl. Phys. B, 247, 83-103 (1984) · Zbl 0661.17020 |
| [29] | Bernard, D., Nucl. Phys. B, 303, 77-93 (1988) |
| [30] | G. Luzón, Ph.D. Dissertation, Zaragoza University, 1994; G. Luzón, Ph.D. Dissertation, Zaragoza University, 1994 |
| [31] | Labastida, J. M.; Ramallo, A., Phys. Lett. B, 228, 214 (1989) |
| [32] | Falceto, F.; Gawȩdzki, K., Commun. Math. Phys., 159, 549-580 (1994) · Zbl 0797.57011 |
| [33] | Falceto, F.; Gawȩdzki, K., Lett. Math. Phys., 38, 155-175 (1996) · Zbl 0854.53060 |
| [34] | Etingof, P.; Frenkel, I.; Kirillov, A., Duke Math. J., 80, 59-90 (1995) · Zbl 0848.43010 |
| [35] | Axelrod, S.; Della Pietra, S.; Witten, E., J. Diff. Geom., 33, 787 (1991) · Zbl 0697.53061 |
| [36] | Etingof, P.; Kirillov, A., Duke Math. J., 74, 585-614 (1994) · Zbl 0811.17026 |
| [37] | Felder, G.; Wieczerkowski, C., Commun. Math. Phys., 176, 133-162 (1996) · Zbl 0972.32012 |
| [38] | Felder, G.; Varchenko, A., Int. Math. Res. Notices, 5, 221-233 (1995) · Zbl 0840.17020 |
| [39] | Falceto, F.; Gawȩdzki, K., Commun. Math. Phys., 183, 267-290 (1997) · Zbl 0872.58076 |
| [40] | Gawedzki, K.; Tran-Ngoc-Bich, P., J. Math. Phys., 41, 4695-4712 (2000) · Zbl 0974.32009 |
| [41] | Bershadsky, M. A.; Ooguri, H., Commun. Math. Phys., 126, 31 (1986) |
| [42] | Dotsenko, V. S., Nucl. Phys. B, 338, 747 (1990) |
| [43] | Dotsenko, V. S., Nucl. Phys. B, 358, 547 (1990) |
| [44] | di Francesco, P.; Mathieu, P.; Sénéchal, D., Conformal Field Theory (1999), Springer-Verlag: Springer-Verlag New York |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
