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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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