Comment on "Solitons and excitations in the duality-based matrix model"

It is shown that a method for constructing exact multi-solitonic solutions of the coupled BPS equations in the duality-based generalization of the hermitean matrix model, which was put forward in a recent paper, is not correct.Comment: 5 pages, no figures, JHEP-style, submitted to JHE

Example of q-deformed Field Theory

The non-relativistic Chern-Simons theory with the single-valued anyonic field is proposed as an example of q-deformed field theory. The corresponding q-deformed algebra interpolating between bosons and fermions,both in position and momentum spaces, is analyzed.A possible generalization to a space with an arbitrary dimension is suggested.Comment: 13 pages,LaTe

Multi-vortex solution in the Sutherland model

We consider the large-$N$ Sutherland model in the Hamiltonian collective-field approach based on the $1/N$ 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

Solitons in the Calogero model for distinguishable particles

We consider a large $- N,$ two-family Calogero model in the Hamiltonian, collective-field approach. The Bogomol'nyi limit appears and the corresponding solutions are given by the static-soliton configurations. Solitons from different families are localized at the same place. They behave like a paired hole and lump on the top of the uniform vacuum condensates, depending on the values of the coupling strengths. When the number of particles in the first family is much larger than that of the second family, the hole solution goes to the vortex profile already found in the one-family Calogero model.Comment: 14 pages, no figures, late

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

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)

Anyons as quon particles

The momentum operator representation of nonrelativistic anyons is developed in the Chern - Simons formulation of fractional statistics. The connection between anyons and the q-deformed bosonic algebra is established.Comment: 10 pages,Late