Parastatistics as Examples of the Extended Haldane Statistics

Meljanac, Stjepan; Mileković, Marijan

doi:10.1142/s0217732396003064

Cited by 5 publications

(13 citation statements)

References 9 publications

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“…Similar approach has been also considered by others authors, see [35,36,37] and [38,39]. An interesting approach to quantum statistics has been also given in [40,41]. A proposal for the general algebraic formalism for description of particle systems equipped with an arbitrary generalized statistics based on the concept of monoidal categories with duality has been given by the author in [42].…”

Section: Introductionmentioning

confidence: 85%

Remarks on quantum statistics

Marcinek

1998

AIP Conference Proceedings

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Section: Introductionmentioning

confidence: 85%

Remarks on quantum statistics

Marcinek

1998

AIP Conference Proceedings

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“…In a previous paper [16] we found that any operator algebra of creation and annihilation operators with a Fock-like representations could be described in terms of extended Haldane statistics parameters. Using this result, we described para-Fermi and para-Bose statistics as exclusion statistics of the Haldane type and calculated a few extended statistics parameters.…”

Section: Introductionmentioning

confidence: 94%

“…In this section we briefly review the definition of general multimode oscilator algebras possessing Fock-like representations and well defined number operators [16,17].…”

Section: Definition Of the Multimode Oscillator Algebras 21 Fock Spacementioning

confidence: 99%

“…From these vectors we form a hermitian matrix A (N ) (i 1 , · · · i N ) of their scalar products [16,17]. As we have already stated, the appearance of null-vectors implies corresponding relations between monomials in a † i and reduces the number of linearly independent states in π(a † i 1 · · · a † i N |0 >).…”

Section: Matrix Of Inner Products a (N ) And Statisticsmentioning

confidence: 99%

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Exclusion statistics, operator algebras and Fock space representations

Meljanac

Mileković²,

Stojić

1999

J. Phys. A: Math. Gen.

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We study exclusion statistics within the second quantized approach. We consider operator algebras with positive definite Fock space and restrict them in a such a way that certain state vectors in Fock space are forbidden ab initio. We describe three characteristic examples of such exclusion, namely exclusion on the base space which is characterized by states with specific constraint on quantum numbers belonging to base space M (e.g. Calogero-Sutherland type of exclusion statistics), exclusion in the single-oscillator Fock space , where some states in single oscillator Fock space are forbidden (e.g. the Gentile realization of exclusion statistics) and a combination of these two exclusions (e.g. Green's realization of para-Fermi statistics). For these types of exclusions we discuss extended Haldane statistics parameters g, recently introduced by two of us in Mod.Phys. Lett.A 11, 3081 (1996) AbstractWe study exclusion statistics within the second quantized approach. We consider operator algebras with positive definite Fock space and restrict them in a such a way that certain state vectors in Fock space are forbidden ab initio. We describe three characteristic examples of such exclusion, namely exclusion on the base space which is characterized by states with specific constraint on quantum numbers belonging to base space M (e.g. Calogero-Sutherland type of exclusion statistics), exclusion in the single-oscillator Fock space , where some states in single oscillator Fock space are forbidden (e.g. the Gentile realization of exclusion statistics) and a combination of these two exclusions (e.g. Green's realization of para-Fermi statistics). For these types of exclusions we discuss extended Haldane statistics parameters g, recently introduced by two of us in Mod.Phys. Lett.A 11, 3081 (1996), and associated counting rules. Within these three types of exclusions in Fock space the original Haldane exclusion statistics cannot be realized.3

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“…We discuss them in the framework of the Haldane's definition of statistics 9 . We point out that none of them is an example of the original Haldane exclusion statistics, but can be related to the so-called extended Haldane statistics 10 . For each of them we find the extended Haldane statistics parameters .…”

Section: Introductionmentioning

confidence: 99%

On Parastatistics Defined as Triple Operator Algebras

1998

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We unify parastatistics, defined as triple operator algebras represented on Fock space, in a simple way using the transition number operators. We express them 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. We relate them to the notion of extended Haldane statistics. AbstractWe unify parastatistics, defined as triple operator algebras represented on Fock space, in a simple way using the transition number operators. We express them 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. We relate them to the notion of extended Haldane statistics.

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Parastatistics as Examples of the Extended Haldane Statistics

Cited by 5 publications

References 9 publications

Remarks on quantum statistics

Remarks on quantum statistics

Exclusion statistics, operator algebras and Fock space representations

On Parastatistics Defined as Triple Operator Algebras

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