We propose a finite Chern-Simons matrix model on the plane as an effective description of fractional quantum Hall fluids of finite extent. The quantization of the inverse filling fraction and of theâ€¦ (More)

We consider the quantum mechanics of a particle on a noncommutative plane. The case of a charged particle in a magnetic field (the Landau problem) with a harmonic oscillator potential is solved.â€¦ (More)

We propose a unitary matrix Chern-Simons model representing fractional quantum Hall fluids of finite extent on the cylinder. A mapping between the states of the two systems is established. Standardâ€¦ (More)

The effect of non-commutativity on electromagnetic waves violates Lorentz invariance: in the presence of a background magnetic induction field b, the velocity for propagation transverse to b differsâ€¦ (More)

The spectrum and partition function of a model consisting of SU(n) spins positioned at the equilibrium positions of a classical Calogero model and interacting through inverseâ€“square exchange areâ€¦ (More)

We derive nonperturbative classical solutions of noncommutative U(1) gauge theory, with or without a Higgs field, representing static magnetic flux tubes with arbitrary cross-section. The fields areâ€¦ (More)

We consider U(N) and SU(N) gauge theory on the sphere. We express the problem in terms of a matrix element of N free fermions on a circle. This allows us to find an alternative way to show Wittenâ€™sâ€¦ (More)

We present a finite dimensional matrix model associated to the noncommutative Chern-Simons theory, obtained by inserting a Wilson line. For a specific choice of the representation of the Wilson lineâ€¦ (More)

We show that the coefficient of the three-dimensional Chern-Simons action on the noncommutative plane must be quantized. Similar considerations apply in other dimensions as well.

We review the canonical theory for perfect fluids, in Eulerian and Lagrangian formulations. The theory is related to a description of extended structures in higher dimensions. Internal symmetry andâ€¦ (More)