Noncommutative Geometry and Anyonic Field Theory in the Magnetic Field

Abstract

We consider an easy way to get the noncommutative spacetime in Minkowski space. This corresponds to introducing a magnetic field $\mathbf{B}=B\hat{\mathbf{k}}$ in the plane. We construct a green's function in coordinate space which includes a Moyal phase factor. The projection to the lowest Landau level(LLL) is necessary for a simple calculation. Using this green's function and a second quantized formalism, we study the thermodynamic property of the anyons on the noncommutative geometry. It turns out that the Moyal phase factors contribute to the thermodynamic potential $\Omega$ as opposed to the free-particle nature.

arXiv comment19 pages in ReVTeX, 3 embedded eps figures, minor correction was made between eq.(50) and (51), one reference is added

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