2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56320We consider an easy way to get the noncommutative spacetime in Minkowski space. This corresponds to introducing a magnetic field ${\rm\bf B} = B \hat {\rm\bf k}$ 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 $Ω$ as opposed to the free-particle nature.19 pages in ReVTeX, 3 embedded eps figures, minor correction was made between eq.(50) and (51), one reference is addedHigh Energy Physics - Theorytext