38 research outputs found
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
Covariant realizations of kappa-deformed space
We study a Lie algebra type -deformed space with undeformed rotation
algebra and commutative vector-like Dirac derivatives in a covariant way. Space
deformation depends on an arbitrary vector. Infinitely many covariant
realizations in terms of commuting coordinates of undeformed space and their
derivatives are constructed. The corresponding coproducts and star products are
found and related in a new way. All covariant realizations are physically
equivalent. Specially, a few simple realizations are found and discussed. The
scalar fields, invariants and the notion of invariant integration is discussed
in the natural realization.Comment: 31 pages, no figures, LaTe
A New Deformed Supersymmetric Oscillator
We construct and discuss the Fock-space representation for a deformed
oscillator with "peculiar" statistics. We show that corresponding algebra
represents deformed supersymmetric oscillator.Comment: LATEX, 10 pages, no figures, to appear in Europhys.Let
On Infinite Quon Statistics and "Ambiguous" Statistics
We critically examine a recent suggestion that "ambiguous" statistics is
equivalent to infinite quon statistics and that it describes a dilute,
nonrelativistics ideal gas of extremal black holes. We show that these two
types of statistics are different and that the description of extremal black
holes in terms of "ambiguous" statistics cannot be applied.Comment: Latex, 9 pages, no figures, to appear in Mod.Phys.Lett.
Fock representations of the superalgebra sl(n+1|m), its quantum analogue U_q[sl(n+1|m)] and related quantum statistics
Fock space representations of the Lie superalgebra and of its
quantum analogue are written down. The results are based on a
description of these superalgebras via creation and annihilation operators. The
properties of the underlying statistics are shortly discussed.Comment: 12 pages, PlainTex; to appear in J. Phys. A: Math. Ge
Perturbative spectrum of Trapped Weakly Interacting Bosons in Two Dimensions
We study a trapped Bose-Einstein condensate under rotation in the limit of
weak, translational and rotational invariant two-particle interactions. We use
the perturbation-theory approach (the large-N expansion) to calculate the
ground-state energy and the excitation spectrum in the asymptotic limit where
the total number of particles N goes to infinity while keeping the total
angular momentum L finite. Calculating the probabilities of different
configurations of angular momentum in the exact eigenstates gives us a clear
view of the physical content of excitations. We briefly discuss the case of
repulsive contact interaction.Comment: Revtex, 10 pages, 1 table, to appear in Phys. Rev.
Nonpointlike Particles in Harmonic Oscillators
Quantum mechanics ordinarily describes particles as being pointlike, in the
sense that the uncertainty can, in principle, be made arbitrarily
small. It has been shown that suitable correction terms to the canonical
commutation relations induce a finite lower bound to spatial localisation.
Here, we perturbatively calculate the corrections to the energy levels of an in
this sense nonpointlike particle in isotropic harmonic oscillators. Apart from
a special case the degeneracy of the energy levels is removed.Comment: LaTeX, 9 pages, 1 figure included via epsf optio
Detailed Analysis of Proton Decay Rate in the Minimal Supersymmetric SO(10) Model
We consider the minimal supersymmetric SO(10) model, where only one {\bf 10}
and one Higgs multiplets have Yukawa couplings with matter
multiplets. This model has the high predictive power for the Yukawa coupling
matrices consistent with the experimental data of the charged fermion mass
matrices, and all the Yukawa coupling matrices are completely determined once a
few parameters in the model are fixed. This feature is essential for definite
predictions to the proton decay rate through the dimension five operators. We
analyze the proton decay rate for the dominant decay modes by including as many free parameters as possible and varying them.
There are two free parameters in the Yukawa sector, while five in the Higgsino
sector. It is found that an allowed region exists when the free parameters in
the Higgs sector are tuned so as to cancel the proton decay amplitude. The
resultant proton lifetime is proportional to and the allowed
region eventually disappears as becomes large.Comment: 15 pages, 3 figures; the version to appear in JHE
Jacobson generators, Fock representations and statistics of sl(n+1)
The properties of A-statistics, related to the class of simple Lie algebras
sl(n+1) (Palev, T.D.: Preprint JINR E17-10550 (1977); hep-th/9705032), are
further investigated. The description of each sl(n+1) is carried out via
generators and their relations, first introduced by Jacobson. The related Fock
spaces W_p (p=1,2,...) are finite-dimensional irreducible sl(n+1)-modules. The
Pauli principle of the underlying statistics is formulated. In addition the
paper contains the following new results: (a) The A-statistics are interpreted
as exclusion statistics; (b) Within each W_p operators B(p)_1^\pm, ...,
B(p)_n^\pm, proportional to the Jacobson generators, are introduced. It is
proved that in an appropriate topology the limit of B(p)_i^\pm for p going to
infinity is equal to B_i^\pm, where B_i^\pm are Bose creation and annihilation
operators; (c) It is shown that the local statistics of the degenerated
hard-core Bose models and of the related Heisenberg spin models is p=1
A-statistics.Comment: LaTeX-file, 33 page