Non-commutative harmonic oscillator in magnetic field and continuous limit.

The spectra of a charged harmonic oscillator minimally coupled to a perpendicular magnetic field in the non-commutative plane are studied by using the path integral formulation. We get the spectra in a mapping-independent way. Interestingly, we find that the spectra have no continuous limit when the dimensionless parameter tends to zero. In order to get a finite result, a truncation is inevitable. Finally, we give a reasonable explanation of truncation from the constrained theory point of view. [ABSTRACT FROM AUTHOR]