×

Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory. (English) Zbl 0479.17003


MSC:

17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
22E70 Applications of Lie groups to the sciences; explicit representations
81T08 Constructive quantum field theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Banks, T.; Horn, D.; Neuberger, H., Bosonization of the \(SU (N)\) Thirring models, Nucl. Phys. B, 108, 119-129 (1976)
[2] Bardakci, K.; Halpern, M. B., New dual quark models, Phys. Rev. D, 3, 2493-2506 (1971)
[3] Bateman, H., The \(k\)-function, a particular case of the confluent hypergeometric function, Trans. Amer. Math. Soc., 33, 817-831 (1931) · JFM 57.0426.03
[4] Bateman, H.; Erdelyi, A., (Higher transcendental functions, Vol. 1 (1953), Mc Graw-Hill: Mc Graw-Hill New York/Toronto/London)
[5] Bourbaki, N., Groupes et algebras de Lie (1975), Herman: Herman Paris, Chaps. 7, 8 · Zbl 0329.17002
[6] Coleman, S., Quantum sine-Gordon equation as the massive Thirring model, Phys. Rev. D, 11, 2088-2097 (1975)
[7] Dashen, R.; Frishman, Y., Four-fermion interactions and scale invriance, Phys. Rev. D, 11, 2781-2802 (1975)
[8] Feingold, A.; Lepowsky, J., The Weyl-Kac character formula and power series identities, Adv. in Math., 29, 271-309 (1978) · Zbl 0391.17009
[9] Frenkel, I. B., Spinor representation of affine Lie algebras, (Proc. Nat. Acad. Sci. USA, 77 (1980)), 6303-6306 · Zbl 0451.17004
[10] Frenkel, I. B.; Kac, V. G., Basic representations of affine Lie algebras and dual resonance models, Invent. Math., 62, 23-66 (1980) · Zbl 0493.17010
[11] I. B. Frenkel and V. G. Kac; I. B. Frenkel and V. G. Kac · Zbl 0493.17010
[12] Frenkel, I. B.; Reiman, A. G.; Semenov-Tjan-S̆anskii, M. A., Graded Lie algebras and completely integrable dynamical systems, Sov. Math. Dokl, 20, 811-814 (1979) · Zbl 0437.58008
[13] Garland, H., The arithmetic theory of loop algebras, J. Algebra, 53, 480-551 (1978) · Zbl 0383.17012
[14] Glimm, J.; Jaffe, A., (DeWitt, C.; Stora, R., Quantum Field Models in Statistical Mechanics and Quantum Field Theory. Quantum Field Models in Statistical Mechanics and Quantum Field Theory, Les Houches, 1970 (1971), Gordon & Breach: Gordon & Breach New York), 1-108 · Zbl 0191.27101
[15] Halpern, M. B., Quantum “solitons” which are \(SU (N)\) fermions, Phys. Rev. D, 12, 1684-1699 (1975)
[16] Kac, V. G., Infinite-dimensional Lie algebras and Dedekind’s η-function, J. Funct. Anal. Appl., 8, 68-70 (1974) · Zbl 0299.17005
[17] Kac, V. G., Infinite dimensional algebras, Dedekind’s η-function, classical Möbius function and the very strange formula, Adv. in Math., 30, 85-136 (1978) · Zbl 0391.17010
[18] V. G. Kac, D. A. Kazhdan, J. Lepowsky and R. L. WilsonAdv. in Math.; V. G. Kac, D. A. Kazhdan, J. Lepowsky and R. L. WilsonAdv. in Math.
[19] Kogut, J.; Susskind, L., How quark confinement solves the η − 3π problem, Phys. Rev. D, 11, 3594-3610 (1975)
[20] Lepowsky, J.; Wilson, R. L., Construction of the affine Lie algebra \(A_l^{(1)}\), Commun. Math. Phys., 62, 43-53 (1978) · Zbl 0388.17006
[21] Mandelstam, S., Dual-resonance models, Phys. Rep. Sect. C, 13, 259-353 (1974)
[22] Mandelstam, S., Soliton operators for the quantized sine-Gordon equation, Phys. Rev D, 11, 3026-3030 (1974)
[23] Mikhailov, A. V.; Olshanetsky, M. A.; Perelomov, A. M., Two dimensional generalized Toda lattice, preprint, Commun. Math. Phys., 79, 473-488 (1981) · Zbl 0491.35061
[24] Shankar, R., Some novel features of the Gross-Neveu model, Phys. Lett. B, 92, 333-336 (1980)
[25] Takhtadzhyan, L. A., Exact theory of propagation of ultrashort optical pulses in two-level media, Sov. Phys. JETP, 39, 228-233 (1975)
[26] Witten, E., Some properties of the \((\̄gyψ)\(^2\) model in two dimensions, Nucl. Phys. B, 142, 285-300 (1978)
[27] Segal, G., Unitary representations of some infinite dimensional groups, Commun. Math. Phys., 80, 301-342 (1981) · Zbl 0495.22017
[28] Kac, V. G.; Peterson, D. H., Spin and wedge representations of infinite-dimensional Lie algebras and groups, (Proc. Nat. Acad. Sci. USA, 78 (1981)), 3308-3312 · Zbl 0469.22016
[29] Date, E.; Jimbo, M.; Kashiwara, M.; Miwa, T., Transformation groups for soliton equations, RIMS preprints, ((1981)), 356-362
[30] Drinfeld, V. G.; Sokolov, V. V., Korteweg-de-Vries type equations and simple Lie algebras, Sov. Math. Dokl. ANSSSR, 258, 11-16 (1981), (Russian)
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.