https://doi.org/10.1140/epjc/s10052-009-0950-1
Regular Article - Theoretical Physics
Non-commutative harmonic oscillator in magnetic field and continuous limit
1
Key Lab for Nanomaterials, Ministry of Education, Beijing University of Chemical Technology, Beijing, 100029, People’s Republic of China
2
Department of Physics and Electronic, School of Science, Beijing University of Chemical Technology, Beijing, 100029, People’s Republic of China
* e-mail: jingjian@mail.buct.edu.cn
Received:
21
July
2008
Revised:
19
January
2009
Published online:
11
March
2009
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.
PACS: 11.10.Ef – / 11.10.Nx –
© Springer-Verlag, 2009
