Towards a Particle Theory in Two Dimensions

Iso, S, Dimitra Karabali A, BUNJI SAKITA

Based on the observation that a particle motion in one dimension maps to a two-dimensional motion of a charged particle in a uniform magnetic field, constrained in the lowest Landau level, we formulate a system of one-dimen- sional nonrelativistic fermions by using a Chern-Simons field theory in 2+1 dimensions. Using a hydrodynamical formulation we obtain a two-dimensional droplet picture of one-dimensional fermions. The dynamics involved is that of the boundary between a uniform density of particles and vortices. We use the sharp boundary approximation. In the case of well separated boundaries we derive the one-dimensional collective field Hamiltonian. Symmetries of the theory are also discussed as properties of curves in two dimensions.

Gianluca Stefanucci

G. Rivlis

Philip C. E. Stamp

It is shown how quasi-particle quantum numbers may be defined and calculated for interacting Fermi systems in 2 and 3 dimensions. Exact results are given for charged and neutral Fermi systems, both normal and superfluid, in 3 dimensions, and for Cherns-Simons implementations of anion theories in 2 dimensions. The latter is applied to the fractional Hall effect. In all cases, the local quasi-particle quantum numbers vary continuously with interactions and/or temperature.

Chih-Chun Chang, Richard M. Friedberg

The standard perturbation theory for repulsive bosons breaks down at finite temperature in two dimensions because of the vanishing of both the Bose-Einstein condensate (at finite temperature) and the t matrix at long wavelengths and zero particle density. By adopting polar coordinates and using a running coupling constant, we circumvent the above two difficulties. The resulting theory is more straightforward than an earlier one of Popov which depends on an artificial division of momentum space. It can also be applied to three dimensions.