×
Tarantello, Gabriella

Multiple condensate solutions for the Chern-Simons-Higgs theory. (English) Zbl 0863.58081

J. Math. Phys. 37, No. 8, 3769-3796 (1996).
Summary: We study the existence of condensate solutions for the Chern-Simons-Higgs model with the choice of a potential field where both the symmetric and asymmetric vacua occur as ground states [see J. Hong, Y. Kim and P. Y. Pac, Phys. Rev. Lett. 64, No. 19, 2230-2233 (1990) and R. Jackiw and E. J. Weinberg, ibid., 2234-2237 (1990)]. We show that if the Chern-Simons coupling parameter \(k\) is above a critical value, no such solutions can exist, while for \(k>0\) below this critical value there exist at least two condensate solutions carrying the same quantized energy, as well as electric and magnetic charge. This multiplicity result accounts for the two vacua states present in the model. In fact, as \(k\to 0^+\) it is shown that the two solutions found “bifurcate” from the asymmetric and symmetric vacuum states, respectively.

Cited in 2 Reviews
Cited in 169 Documents

MSC:

58Z05 Applications of global analysis to the sciences
81T13 Yang-Mills and other gauge theories in quantum field theory

Keywords:

condensate solutions; Chern-Simons-Higgs model
Cite Review PDF
Full Text: DOI

References:

[1] DOI: 10.1007/BF01239028 · Zbl 0651.58044 · doi:10.1007/BF01239028
[2] DOI: 10.1007/BF01217803 · Zbl 0819.58045 · doi:10.1007/BF01217803
[3] DOI: 10.1103/PhysRevD.44.441 · doi:10.1103/PhysRevD.44.441
[4] DOI: 10.1103/PhysRevLett.62.2785 · doi:10.1103/PhysRevLett.62.2785
[5] DOI: 10.1016/0550-3213(90)90292-L · doi:10.1016/0550-3213(90)90292-L
[6] Polychronakos A., AM. Phys. 203 pp 231– (1990)
[7] DOI: 10.1016/0370-2693(90)90419-7 · doi:10.1016/0370-2693(90)90419-7
[8] DOI: 10.1103/PhysRevLett.64.2230 · Zbl 1014.58500 · doi:10.1103/PhysRevLett.64.2230
[9] DOI: 10.1103/PhysRevLett.64.2234 · Zbl 1050.81595 · doi:10.1103/PhysRevLett.64.2234
[10] DOI: 10.1007/BF01197552 · Zbl 0451.35101 · doi:10.1007/BF01197552
[11] DOI: 10.1007/BF01212709 · Zbl 0448.58029 · doi:10.1007/BF01212709
[12] DOI: 10.1007/BF02100279 · Zbl 0733.58009 · doi:10.1007/BF02100279
[13] DOI: 10.1007/BF02097630 · Zbl 0760.53063 · doi:10.1007/BF02097630
[14] DOI: 10.1103/PhysRevD.42.3488 · doi:10.1103/PhysRevD.42.3488
[15] DOI: 10.1016/0550-3213(79)90595-9 · doi:10.1016/0550-3213(79)90595-9
[16] Bogomol’nyi E. B., Sov. J. Nucl. Phys. 24 pp 449– (1976)
[17] DOI: 10.1007/BF02099262 · Zbl 0745.76001 · doi:10.1007/BF02099262
[18] DOI: 10.1002/cpa.3160460103 · Zbl 0811.76002 · doi:10.1002/cpa.3160460103
[19] DOI: 10.1016/0022-1236(79)90052-1 · Zbl 0411.46019 · doi:10.1016/0022-1236(79)90052-1
[20] Brezis H., CR. Acad. Sci. Paris, serie 1 317 pp 465– (1993)
[21] DOI: 10.1016/0022-1236(73)90051-7 · Zbl 0273.49063 · doi:10.1016/0022-1236(73)90051-7
[22] Suzuki T., Ann. I.H.P. Analyse Nonlin. 9 (4) pp 367– (1992)
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.