Schrödinger fields on the plane with <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mo>[</mo><mi mathvariant="normal">U</mi><mn></mn><mo>(</mo><mn>1</mn><mo>)</mo><mo>]</mo></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span> Chern-Simons interactions and generalized self-dual solitons

Chanju Kim; Choonkyu Lee; Pyungwon Ko; Bum-Hoon Lee; Hyunsoo Min

doi:10.1103/PhysRevD.48.1821

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Schrödinger fields on the plane with ${[U (1)]}^{N}$ Chern-Simons interactions and generalized self-dual solitons

Chanju Kim and Choonkyu Lee

Pyungwon Ko and Bum-Hoon Lee^*

Hyunsoo Min

Department of Physics and Center for Theoretical Physics, Seoul National University, Seoul 151-742, Korea

School of Physics and Astronomy, University of Minnesota, Minnesota 55455

Department of Physics, Seoul City University, Seoul 130-743, Korea

^*Permanent address: Department of Physics, Hanyang University, Seoul 133-791, Korea.

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Phys. Rev. D 48, 1821 – Published 15 August, 1993

DOI: https://doi.org/10.1103/PhysRevD.48.1821

Abstract

A general nonrelativistic field theory on the plane with couplings to an arbitrary number of Abelian Chern-Simons gauge fields is considered. Elementary excitations of the system are shown to exhibit fractional and mutual statistics. We identify the self-dual systems for which certain classical and quantal aspects of the theory can be studied in a much simplified mathematical setting. Then, specializing to the general self-dual system with two Chern-Simons gauge fields (and nonvanishing mutual statistics parameter), we present a systematic analysis for the static vortexlike classical solutions, with or without a uniform background magnetic field. Relativistic generalizations are also discussed briefly.

References (30)

J. M. Leinaas and J. Myrheim, Nuovo Cimento 37, B 1 (1977) G. Goldin, R. Menikoff, and D. Sharp, J. Math. Phys. 21, 650 (1980) F. Wilczek, Phys. Rev. Lett. 48, 1144 (1982) ibid.49, 957 (1982)
R. Jackiw and S. Templeton, Phys. Rev. D 23, 2291 (1981) J. Schonfeld, Nucl. Phys. B185, 157 (1981) S. Deser, R. Jackiw, and S. Templeton, Ann. Phys. (N.Y.) 140, 372 (1982) D. Arovas, J. Schrieffer, F. Wilczek, and A. Zee, Nucl. Phys. B251, 117 (1985) C. R. Hagen, Ann. Phys. (N.Y.) 157, 342 (1984)
S. M. Girvin and A. H. MacDonald, Phys. Rev. Lett. 58, 1252 (1987) S. C. Zhang, T. Hansson, and S. Kivelson, ibid. 62, 82 (1989) N. Read, Phys. Rep. 62, 85 (1989)
X. G. Wen and A. Zee, Nucl. Phys. B15, 135 (1990) Phys. Rev. B 44, 274(1991) ibid.46, 2290 (1992) B. Blok and X. G. Wen, ibid. 43, 8337 (1991) J. Fröhlich and A. Zee, Nucl. Phys. B364, 517 (1991) D. Wesolowski, Y. Hosotani, and C.-L. Ho, Report No. UMN-TH-1128/93 (unpublished)
F. Wilczek, Phys. Rev. Lett. 69, 132 (1992) C. R. Hagen, ibid. 68, 3821 (1992)
Z. F. Ezawa and A. Iwazaki, Int. J. Mod. Phys. B 6, 3205 (1992)
C. Ting, Int. J. Mod. Phys. B6, 3155 (1992)
Y. Aharonov and A. Casher, Phys. Rev. A 19, 2461 (1979)
S. M. Girvin, A. H. MacDonald, M. Fisher, S. J. Rey, and J. Sethna, Phys. Rev. Lett. 65, 1671 (1990) M. Y. Choi, C. Lee, and J. Lee, Phys. Rev. B 46, 1489 (1992)
R. Jackiw and S.-Y. Pi, Phys. Rev. Lett. 64, 2969 (1990)
R. Jackiw and S.-Y. Pi, Phys. Rev. D 42, 3500 (1990)
G. Dunne, R. Jackiw, S.-Y. Pi, and C. Trugenberger, Phys. Rev. D 43, 1332 (1991)
G. Dunne, Commun. Math. Phys. 150, 519 (1992)
C.-L. Ho and Y. Hosotani, Int. J. Mod. Phys. A 7, 5797 (1992)
A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971)
Y. Aharonov and A. Casher, Phys. Rev. Lett. 53, 319 (1984)
Z. F. Ezawa, M. Hotta, and A. Iwazaki, Phys. Rev. D 44, 452 (1991) G. Dunne and C. Trugenberger (private communication) S. L. Sondhi and S. A. Kivelson, Phys. Rev. B 46, 13319 (1992)
M. Toda, Prog. Theor. Phys. (Suppl.) 45, 174 (1970) Phys. Rep. 18, 1 (1975)
A. Leznov and M. Savaliev, Lett. Math. Phys. 3, 489 (1979) Commun. Math. Phys. 74, 111 (1980) B. Konstant, Adv. Math. 34, 195 (1979)
S. K. Kim, K. S. Soh, and J. H. Yee, Phys. Rev. D 42, 4139 (1990)
S. K. Kim, W. Namgung, K. S. Soh, and J. H. Yee, Phys. Rev. D 46, 1882 (1992)
S. K. Kim and H.-S. Min, Phys. Lett. B 281, 81 (1992) Y. Kim and K. Lee, Report No. CU-TP-574, 1992 (unpublished)
C. Kim, Phys. Rev. D 47, 673 (1993)
J. Hong, Y. Kim, and P.-Y. Pac, Phys. Rev. Lett. 64, 2230 (1990) R. Jackiw and E. Weinberg, ibid. 64, 2234 (1990)
R. Jackiw, K. Lee, and E. Weinberg, Phys. Rev. D 42, 3488 (1990)
R. Wang, Commun. Math. Phys. 137, 587 (1991) J. Spruck and Yisong Yang, ibid. 149, 361 (1992)
T. Vachaspati and A. Achùcarro, Phys. Rev. D 44, 3067 (1991) M. Hindmarsh, Phys. Rev. Lett. 68, 1263 (1992) G. W. Gibbons, M. E. Ortiz, F. Ruiz, and T. M. Samols, Nucl. Phys. B385, 127 (1992)
E. B. Bogomol'nyi, Yad. Fiz. 24, 861 (1976) [Sov. J. Nucl. Phys. 24, 449 (1976)]
L. S. Brown, R. D. Carlitz, and C. Lee, Phys. Rev. D 16, 417 (1977) E. J. Weinberg, ibid. 19, 3008 (1979) ibid.24, 2669 (1981)
K. Kiskis, Phys. Rev. D 15, 2329 (1977) M. Ansourian, Phys. Lett. 70B, 301 (1977) D. Boyanovsky and R. Blankenbecler, Phys. Rev. D 31, 3234 (1985)

[c1] J. M. Leinaas and J. Myrheim, Nuovo Cimento 37, B 1 (1977) G. Goldin, R. Menikoff, and D. Sharp, J. Math. Phys. 21, 650 (1980) F. Wilczek, Phys. Rev. Lett. 48, 1144 (1982) ibid.49, 957 (1982)

[c2] R. Jackiw and S. Templeton, Phys. Rev. D 23, 2291 (1981) J. Schonfeld, Nucl. Phys. B185, 157 (1981) S. Deser, R. Jackiw, and S. Templeton, Ann. Phys. (N.Y.) 140, 372 (1982) D. Arovas, J. Schrieffer, F. Wilczek, and A. Zee, Nucl. Phys. B251, 117 (1985) C. R. Hagen, Ann. Phys. (N.Y.) 157, 342 (1984)

[c3] S. M. Girvin and A. H. MacDonald, Phys. Rev. Lett. 58, 1252 (1987) S. C. Zhang, T. Hansson, and S. Kivelson, ibid. 62, 82 (1989) N. Read, Phys. Rep. 62, 85 (1989)

[c4] X. G. Wen and A. Zee, Nucl. Phys. B15, 135 (1990) Phys. Rev. B 44, 274(1991) ibid.46, 2290 (1992) B. Blok and X. G. Wen, ibid. 43, 8337 (1991) J. Fröhlich and A. Zee, Nucl. Phys. B364, 517 (1991) D. Wesolowski, Y. Hosotani, and C.-L. Ho, Report No. UMN-TH-1128/93 (unpublished)

[c5] F. Wilczek, Phys. Rev. Lett. 69, 132 (1992) C. R. Hagen, ibid. 68, 3821 (1992)

[c6] Z. F. Ezawa and A. Iwazaki, Int. J. Mod. Phys. B 6, 3205 (1992)

[c7] C. Ting, Int. J. Mod. Phys. B6, 3155 (1992)

[c8] Y. Aharonov and A. Casher, Phys. Rev. A 19, 2461 (1979)

[c9] S. M. Girvin, A. H. MacDonald, M. Fisher, S. J. Rey, and J. Sethna, Phys. Rev. Lett. 65, 1671 (1990) M. Y. Choi, C. Lee, and J. Lee, Phys. Rev. B 46, 1489 (1992)

[c10] R. Jackiw and S.-Y. Pi, Phys. Rev. Lett. 64, 2969 (1990)

[c11] R. Jackiw and S.-Y. Pi, Phys. Rev. D 42, 3500 (1990)

[c12] G. Dunne, R. Jackiw, S.-Y. Pi, and C. Trugenberger, Phys. Rev. D 43, 1332 (1991)

[c13] G. Dunne, Commun. Math. Phys. 150, 519 (1992)

[c14] C.-L. Ho and Y. Hosotani, Int. J. Mod. Phys. A 7, 5797 (1992)

[c15] A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971)

[c16] Y. Aharonov and A. Casher, Phys. Rev. Lett. 53, 319 (1984)

[c17] Z. F. Ezawa, M. Hotta, and A. Iwazaki, Phys. Rev. D 44, 452 (1991) G. Dunne and C. Trugenberger (private communication) S. L. Sondhi and S. A. Kivelson, Phys. Rev. B 46, 13319 (1992)

[c18] M. Toda, Prog. Theor. Phys. (Suppl.) 45, 174 (1970) Phys. Rep. 18, 1 (1975)

[c19] A. Leznov and M. Savaliev, Lett. Math. Phys. 3, 489 (1979) Commun. Math. Phys. 74, 111 (1980) B. Konstant, Adv. Math. 34, 195 (1979)

[c20] S. K. Kim, K. S. Soh, and J. H. Yee, Phys. Rev. D 42, 4139 (1990)

[c21] S. K. Kim, W. Namgung, K. S. Soh, and J. H. Yee, Phys. Rev. D 46, 1882 (1992)

[c22] S. K. Kim and H.-S. Min, Phys. Lett. B 281, 81 (1992) Y. Kim and K. Lee, Report No. CU-TP-574, 1992 (unpublished)

[c23] C. Kim, Phys. Rev. D 47, 673 (1993)

[c24] J. Hong, Y. Kim, and P.-Y. Pac, Phys. Rev. Lett. 64, 2230 (1990) R. Jackiw and E. Weinberg, ibid. 64, 2234 (1990)

[c25] R. Jackiw, K. Lee, and E. Weinberg, Phys. Rev. D 42, 3488 (1990)

[c26] R. Wang, Commun. Math. Phys. 137, 587 (1991) J. Spruck and Yisong Yang, ibid. 149, 361 (1992)

[c27] T. Vachaspati and A. Achùcarro, Phys. Rev. D 44, 3067 (1991) M. Hindmarsh, Phys. Rev. Lett. 68, 1263 (1992) G. W. Gibbons, M. E. Ortiz, F. Ruiz, and T. M. Samols, Nucl. Phys. B385, 127 (1992)

[c28] E. B. Bogomol'nyi, Yad. Fiz. 24, 861 (1976) [Sov. J. Nucl. Phys. 24, 449 (1976)]

[c29] L. S. Brown, R. D. Carlitz, and C. Lee, Phys. Rev. D 16, 417 (1977) E. J. Weinberg, ibid. 19, 3008 (1979) ibid.24, 2669 (1981)

[c30] K. Kiskis, Phys. Rev. D 15, 2329 (1977) M. Ansourian, Phys. Lett. 70B, 301 (1977) D. Boyanovsky and R. Blankenbecler, Phys. Rev. D 31, 3234 (1985)

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Schrödinger fields on the plane with ${[U (1)]}^{N}$ Chern-Simons interactions and generalized self-dual solitons

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Schrödinger fields on the plane with [U(1)]N Chern-Simons interactions and generalized self-dual solitons

Abstract

References (30)

Schrödinger fields on the plane with ${[U (1)]}^{N}$ Chern-Simons interactions and generalized self-dual solitons