On parastatistics defined as triple operator algebras
TLDR
Parastatistics, defined as triple operator algebras represented on Fock space, are unified in a simple way using the transition number operators as discussed by the authors, expressed as a normal ordered expansion of creation and annihilation operators.Abstract:
Parastatistics, defined as triple operator algebras represented on Fock space, are unified in a simple way using the transition number operators. They are expressed as a normal ordered expansion of creation and annihilation operators. We discuss several examples of parastatistics, particularly Okubo's and Palev's parastatistics connected to many-body Wigner quantum systems and relate them to the notion of extended Haldane statistics.read more
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Jacobson generators, Fock representations and statistics of sl(n + 1)
TL;DR: Palev as discussed by the authors investigated the properties of A-statistics, related to the class A of simple Lie algebras, and proved that the Fock spaces Wp, p∈N are the simple symmetric (finite-dimensional) modules of sl(n+1).
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Bosonic realization of algebras in the Calogero model
Larisa Jonke,Stjepan Meljanac +1 more
TL;DR: In this article, an N-body Calogero model in the symmetric subspace of the positive definite Fock space has been studied and a new algebra of SN-symmetric operators represented on the Fock spaces has been constructed, and a natural orthogonal basis is found by mapping the algebra onto the Heisenberg algebra.
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Bosonic realization of algebras in the Calogero model
Larisa Jonke,Stjepan Meljanac +1 more
TL;DR: In this article, an N-body Calogero model was studied in the S_N-symmetric subspace of the positive definite Fock space, and a new algebra of S-N symmetric operators represented on the symmetric Fock spaces was constructed and a natural orthogonal basis was found by mapping the algebra onto the Heisenberg algebra.
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Exclusion statistics, operator algebras and Fock space representations
TL;DR: In this article, the authors consider operator algebras with positive definite Fock space and restrict them in a such a way that certain state vectors in Fock spaces are forbidden ab initio.
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Fock representations of the superalgebra sl(n+1|m), its quantum analogue Uq[sl(n+1|m)] and related quantum statistics
TL;DR: In this article, the Lie superalgebra sl (n + 1|m ) and its quantum analogue Uq [sl (n+1|m )] are described via creation and annihilation operators.
References
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Realizability of a model in infinite statistics
Don Zagier,Don Zagier +1 more
TL;DR: In this paper, a space with a collection of operators satisfying the q-mutator relations was studied, and it was shown that the commutator relations have a Hilbert space representation in this case.