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Bosonization and generalized Mandelstam soliton operators. (English) Zbl 1191.81151

Summary: The generalized massive Thirring model (GMT) with three fermion species is bosonized in the context of the functional integral and operator formulations and shown to be equivalent to a generalized sine-Gordon model (GSG) with three interacting soliton species. The generalized Mandelstam soliton operators are constructed and the fermion-boson mapping is established through a set of generalized bosonization rules in a quotient positive-definite Hilbert space of states. Each fermion species is mapped to its corresponding soliton in the spirit of particle/soliton duality of Abelian bosonization. In the semi-classical limit one recovers the so-called \(SU(3)\) affine Toda model coupled to matter fields (ATM) from which the classical GSG and GMT models were recently derived in the literature. The intermediate ATM-like effective action possesses some spinors resembling the higher grading fields of the ATM theory which have non-zero chirality. These fields are shown to disappear from the physical spectrum, thus providing a bag-model-like confinement mechanism and leading to the appearance of massive fermions (solitons). The ordinary MT/SG duality turns out to be related to each \(SU(2)\) sub-group. The higher rank Lie algebra extension is also discussed.

MSC:

81T10 Model quantum field theories
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References:

[1] M. Stone, Bosonization, 1st edition (World Scientific, Singapore 1994)
[2] E. Abdalla, M.C.B. Abdalla, K.D. Rothe, Non-perturvative methods in two-dimensional quantum field theory, 2nd edition (World Scientific, Singapore 2001) · Zbl 0983.81037
[3] S. Coleman, Phys. Rev. D 11, 2088 (1975); S. Mandelstam, Phys. Rev. D 11, 3026 (1975) · doi:10.1103/PhysRevD.11.2088
[4] J. Acosta, H. Blas, J. Math. Phys. 43, 1916 (2002); H. Blas, Generalized sine-Gordon and massive Thirring models, to appear in Progress in Soliton Research (Nova Science Publishers, 2004) · Zbl 1059.81158 · doi:10.1063/1.1454186
[5] H. Blas, JHEP 0311, 054 (2003) · doi:10.1088/1126-6708/2003/11/054
[6] C.M. Naón, Phys. Rev. D 31, 2035 (1985) · doi:10.1103/PhysRevD.31.2035
[7] M.B. Halpern, Phys. Rev. D 12, 1684 (1975); Phys. Rev. D 13, 337 (1976) · doi:10.1103/PhysRevD.12.1684
[8] T. Banks, D. Horn, H. Neuberger, Nucl. Phys. B 108, 119 (1976) · doi:10.1016/0550-3213(76)90127-9
[9] E. Witten, Commun. Math. Phys. 92, 455 (1984) · Zbl 0536.58012 · doi:10.1007/BF01215276
[10] Q.-Han Park, H.J. Shin, Nucl. Phys. B 506, 537 (1997) · Zbl 0925.81077 · doi:10.1016/S0550-3213(97)00539-7
[11] L.V. Belvedere, R.L.P.G. Amaral, Phys. Rev. D 62, 065009 (2000); L.V. Belvedere, J. Phys. A 33, 2755 (2000) · doi:10.1103/PhysRevD.62.065009
[12] H. Blas, Nucl. Phys. B 596, 471 (2001); see also hep-th/0005037 · Zbl 0972.81168 · doi:10.1016/S0550-3213(00)00734-3
[13] H. Blas, L.A. Ferreira, Nucl. Phys. B 571, 607 (2000) · Zbl 0947.81033 · doi:10.1016/S0550-3213(00)00015-8
[14] H. Blas, B.M. Pimentel, Annals Phys. 282, 67 (2000) · Zbl 1112.81336 · doi:10.1006/aphy.1999.5995
[15] A.G. Bueno, L.A. Ferreira, A.V. Razumov, Nucl. Phys. B 626, 463 (2002) · Zbl 0985.81116 · doi:10.1016/S0550-3213(02)00015-9
[16] L.A. Ferreira, J.-L. Gervais, J. Sánchez Guillen, M.V. Saveliev, Nucl. Phys. B 470, 236 (1996) · Zbl 1003.81552 · doi:10.1016/0550-3213(96)00146-0
[17] H. Blas, Phys. Rev. D 66, 127701 (2002); see also hep-th/0005130 · doi:10.1103/PhysRevD.66.127701
[18] S. Brazovskii, J. Phys. IV 10, 169 (2000); also in cond-mat/0006355; A.J. Heeger, S. Kivelson, J.R. Schrieffer, W. -P. Wu, Rev. Mod. Phys. 60, 782 (1988) · doi:10.1051/jp4:2000318
[19] D.G. Barci, L. Moriconi, Nucl. Phys. B 438, 522 (1995) · Zbl 1052.81690 · doi:10.1016/0550-3213(95)00023-L
[20] R. Jackiw, C. Rebbi, Phys. Rev. D 13, 3398 (1976); J. Goldstone, F. Wilczek, Phys. Rev. Lett. 47, 986 (1981); J.A. Mignaco, M.A. Rego Monteiro, Phys. Rev. D 31, 3251 (1985) · doi:10.1103/PhysRevD.13.3398
[21] R. Rajaraman, Solitons and instantons (North-Holland, Amsterdam 1982) · Zbl 0493.35074
[22] M.A. Lohe, Phys. Rev. D 52, 3643 (1995); M.A. Lohe, C.A. Hurst, Phys. Rev. D 37, 1094 (1988) · doi:10.1103/PhysRevD.52.3643
[23] A.M. Polyakov, P.B. Wiegman, Phys. Lett. B 131, 121 (1983); B 141, 224 (1984) · doi:10.1016/0370-2693(83)91104-8
[24] E. Witten, Nucl. Phys. B 145, 110 (1978) · doi:10.1016/0550-3213(78)90416-9
[25] Y. Frishman, J. Sonnenschein, Phys. Rep. 223, 309 (1993) · doi:10.1016/0370-1573(93)90145-4
[26] V. Juricic, B. Sazdovic, Eur. Phys. J. C 32, 443 (2004) · Zbl 1099.81516 · doi:10.1140/epjc/s2003-01401-4
[27] M.I. Eides, Phys. Lett. B 153, 157 (1985) · doi:10.1016/0370-2693(85)91419-4
[28] H. Blas, invited paper for Progress in Boson Research (Nova Science Publishers, 2005)
[29] R.K. Kaul, R. Rajaraman, Int. J. Mod. Phys. A 8, 1815 (1993) · doi:10.1142/S0217751X9300076X
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