Charged representations of the infinite Fermi and Clifford algebras. (English) Zbl 1115.81039

Galina, E.; Kaplan, A.; Saal, L.

Lett. Math. Phys. 72, No. 1, 65-77 (2005).

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

Keywords:

spinors; CAR algebra; non-Fock representations

References:

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