Abstract
We investigate the positive energy representations (also called highest weight representations) of the gauge groupC ∞ (T v,G 0),G 0 being a compact simple Lie group, and discuss their unitarity, using the technique of Verma modules constructed from generalized loop algebras (a simple generalization of Kac-Moody affine Lie algebras). We show that the unitarity of the representation imposes severa restrictions in it. In particular, we show, as a part of a more general result, that the gauge group does not admit faithful unitary positive energy representations.
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References
Kac, V.,Infinite-Dimensional Lie Algebras, Cambridge University Press (1985).
Kac, AV. and Jakobsen, AH.,Lecture Notes in Physics 226, 1–20 (1985).
Albeverio, AS., Høegh-Krohn, AR., and Testard, AD.,J. Funct. Anal. 41, 378–396 (1981).
Høegh-Krohn, R. and Torresani, B., Preprint, CPT Marseille, in preparation.
Torresani, B., ‘Representations projectives des groupes de transformations de jauge locales’, Thesis, CPT Marseille, preprint CPT-86/P.1893.
Bars, I., in Lepowskyet al. (eds.),Vertex Operators in Mathematics and Physics, MSRI publications 3 (1983), p. 373.
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Torresani, B. Unitary positive energy representations of the gauge group. Lett Math Phys 13, 7–15 (1987). https://doi.org/10.1007/BF00570762
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DOI: https://doi.org/10.1007/BF00570762