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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.
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
Full Text: DOI
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