63 research outputs found
Multi-vortex solution in the Sutherland model
We consider the large- Sutherland model in the Hamiltonian
collective-field approach based on the expansion. The Bogomol'nyi limit
appears and the corresponding solutions are given by static-soliton
configurations. They exist only for \l<1, i.e. for the negative coupling
constant of the Sutherland interaction. We determine their creation energies
and show that they are unaffected by higher-order corrections. For \l=1, the
Sutherland model reduces to the free one-plaquette Kogut-Susskind model.Comment: Latex, using ioplppt.sty, 11 page
Harmonic oscillator with minimal length uncertainty relations and ladder operators
We construct creation and annihilation operators for harmonic oscillators
with minimal length uncertainty relations. We discuss a possible generalization
to a large class of deformations of cannonical commutation relations. We also
discuss dynamical symmetry of noncommutative harmonic oscillator.Comment: 8 pages, revtex4, final version, to appear in PR
Finite Chern-Simons matrix model - algebraic approach
We analyze the algebra of observables and the physical Fock space of the
finite Chern-Simons matrix model. We observe that the minimal algebra of
observables acting on that Fock space is identical to that of the Calogero
model. Our main result is the identification of the states in the l-th tower of
the Chern-Simons matrix model Fock space and the states of the Calogero model
with the interaction parameter nu=l+1. We describe quasiparticle and quasihole
states in the both models in terms of Schur functions, and discuss some
nontrivial consequences of our algebraic approach.Comment: 12pages, jhep cls, minor correction
New realizations of Lie algebra kappa-deformed Euclidean space
We study Lie algebra -deformed Euclidean space with undeformed
rotation algebra and commuting vectorlike derivatives. Infinitely
many realizations in terms of commuting coordinates are constructed and a
corresponding star product is found for each of them. The -deformed
noncommutative space of the Lie algebra type with undeformed Poincar{\'e}
algebra and with the corresponding deformed coalgebra is constructed in a
unified way.Comment: 30 pages, Latex, accepted for publication in Eur.Phys.J.C, some typos
correcte
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
Algebra of the observables in the Calogero model and in the Chern-Simons matrix model
The algebra of observables of an N-body Calogero model is represented on the
S_N-symmetric subspace of the positive definite Fock space. We discuss some
general properties of the algebra and construct four different realizations of
the dynamical symmetry algebra of the Calogero model. Using the fact that the
minimal algebra of observables is common to the Calogero model and the finite
Chern-Simons (CS) matrix model, we extend our analysis to the CS matrix model.
We point out the algebraic similarities and distinctions of these models.Comment: 24 pages, misprints corrected, reference added, final version, to
appear in PR
Collective Field Formulation of the Multispecies Calogero Model and its Duality Symmetries
We study the collective field formulation of a restricted form of the
multispecies Calogero model, in which the three-body interactions are set to
zero. We show that the resulting collective field theory is invariant under
certain duality transformations, which interchange, among other things,
particles and antiparticles, and thus generalize the well-known strong-weak
coupling duality symmetry of the ordinary Calogero model. We identify all these
dualities, which form an Abelian group, and study their consequences. We also
study the ground state and small fluctuations around it in detail, starting
with the two-species model, and then generalizing to an arbitrary number of
species.Comment: latex, 53 pages, no figures;v2-minor changes (a paragraph added
following eq. (61)
Matrix oscillator and Calogero-type models
We study a single matrix oscillator with the quadratic Hamiltonian and
deformed commutation relations. It is equivalent to the multispecies Calogero
model in one dimension, with inverse-square two-body and three-body
interactions. Specially, we have constructed a new matrix realization of the
Calogero model for identical particles, without using exchange operators. The
critical points at which singular behaviour occurs are briefly discussed.Comment: Accepted for publication in Phys.Lett.
The topological AC effect on noncommutative phase space
The Aharonov-Casher (AC) effect in non-commutative(NC) quantum mechanics is
studied. Instead of using the star product method, we use a generalization of
Bopp's shift method. After solving the Dirac equations both on noncommutative
space and noncommutative phase space by the new method, we obtain the
corrections to AC phase on NC space and NC phase space respectively.Comment: 8 pages, Latex fil
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