The $\star$-value Equation and Wigner Distributions in Noncommutative Heisenberg algebras

Research paper by Marcos Rosenbaum, J. David Vergara

Indexed on: 13 May '05Published on: 13 May '05Published in: High Energy Physics - Theory


We consider the quantum mechanical equivalence of the Seiberg-Witten map in the context of the Weyl-Wigner-Groenewold-Moyal phase-space formalism in order to construct a quantum mechanics over noncommutative Heisenberg algebras. The formalism is then applied to the exactly soluble Landau and harmonic oscillator problems in the 2-dimensional noncommutative phase-space plane, in order to derive their correct energy spectra and corresponding Wigner distributions. We compare our results with others that have previously appeared in the literature.