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Charged representations of the infinite Fermi and Clifford algebras. (English) Zbl 1115.81039
Summary: The real and quaternionic charge conjugation operators invariant under the infinite-dimensional Clifford algebra, or compatible with the Fermi algebra, are determined. There results a maze of inequivalent irreducible charged representations, all of which are non-Fock. The representation vectors and their charges admit two interpretations besides those of spinors or states of quantum fields: as wavelets on the circle, with charge conjugations acting via ordinary complex conjugation; and as infinite-dimensional numbers, with charge conjugations acting by automorphisms.
MSC:
 81R15 Operator algebra methods applied to problems in quantum theory 15A66 Clifford algebras, spinors 46N50 Applications of functional analysis in quantum physics 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $$W$$-algebras and other current algebras and their representations
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References:
 [5] Guichardet, A. (1968). In: A. Colin (ed.). Algèbres d’observables Associées aux Relations de Commutation. · Zbl 0169.17302 [7] Galina, E., Kaplan, A. and Saal, L.: Split Clifford modules over a Hilbert space, Math. RT/0204117 (2002), 1–11. [9] Kadison, R., Ringrose, J. (1969). Fundamentals of the theory of operator algebras. Amer. Math. Soc. Ed.: 1998. · Zbl 0601.46054 [11] Lawson, H., Michelsohn, M. (1989). Spin Geometry, Princeton University Press, 1989. · Zbl 0688.57001
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