5 research outputs found
Unified view of multimode algebras with Fock-like representations
A unified view of general multimode oscillator algebras with Fock-like
representations is presented.It extends a previous analysis of the single-mode
oscillator algebras.The expansion of the operators is
extended to include all normally ordered terms in creation and annihilation
operators and we analyze their action on Fock-like states.We restrict ourselves
to the algebras compatible with number operators. The connection between these
algebras and generalized statistics is analyzed.We demonstrate our approach by
considering the algebras obtainable from the generalized Jordan-Wigner
transformation, the para-Bose and para-Fermi algebras, the Govorkov
"paraquantization" algebra and generalized quon algebra.Comment: Latex, 34 pages, no figures ( accepted in Int.J.Theor.Phys.A
Parastatistics as Examples of the Extended Haldane Statistics
We show that for every algebra of creation and annihilation operators with a
Fock-like representation,one can define extended Haldane statistical parameters
in a unique way. Specially for parastatistics, we calculate extended Haldane
parameters and discuss the corresponding partition functions.Comment: Latex, 13 pages, no figures,to appear in Mod.Phys.Lett.
Calogero Model(s) and Deformed Oscillators
We briefly review some recent results concerning algebraical (oscillator)
aspects of the -body single-species and multispecies Calogero models in one
dimension. We show how these models emerge from the matrix generalization of
the harmonic oscillator Hamiltonian. We make some comments on the solvability
of these models.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
Exclusion statistics,operator algebras and Fock space representations
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), and associated counting rules. Within these three types of
exclusions in Fock space the original Haldane exclusion statistics cannot be
realized.Comment: Latex,31 pages,no figures,to appear in J.Phys.A : Math.Ge