64 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
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
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
Solitons in the Calogero-Sutherland Collective-Field Model
In the Bogomol'nyi limit of the Calogero-Sutherland collective-field model we
find static-soliton solutions. The solutions of the equations of motion are
moving solitons, having no static limit for \l>1. They describe holes and
lumps, depending on the value of the statistical parametar \l.Comment: minor correction
Homolumo Gap and Matrix Model
We discuss a dynamical matrix model by which probability distribution is
associated with Gaussian ensembles from random matrix theory. We interpret the
matrix M as a Hamiltonian representing interaction of a bosonic system with a
single fermion. We show that a system of second-quantized fermions influences
the ground state of the whole system by producing a gap between the highest
occupied eigenvalue and the lowest unoccupied eigenvalue.Comment: 8 pages, 2 figure
Poincare covariant mechanics on noncommutative space
The Dirac approach to constrained systems can be adapted to construct
relativistic invariant theories on a noncommutative (NC) space. As an example,
we propose and discuss relativistic invariant NC particle coupled to
electromagnetic field by means of the standard term . Poincare
invariance implies deformation of the free particle NC algebra in the
interaction theory. The corresponding corrections survive in the
nonrelativistic limit.Comment: 7 pages, JHEP style, final versio
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
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