|
HAIT Journal of Science and Engineering A Volume 3, Issue 1, pp. 153-161 © 2006 Holon Institute of Technology | |||||
| |||||
Operator ordering and continuum limit for path integrals: a toy model
Victor Kagalovsky
Sami Shamoon College of Engineering, Beer-Sheva 84100,
Israel
| email: victork@sce.ac.il Received 23 January 2006, accepted 15 February 2006
| We address the problem of continuum limit for path integrals in quantum systems where the operator ordering is ambiguous. A two-dimensional (2d) electron in a harmonic potential in the presence of a perpendicular magnetic field serves as a toy model. We, first, reorder operators in the Hamiltonian following a special ``antiordering'' procedure to obtain correct continuum limit. We use adiabatic expansion to present a propagator as a path integral for slow variables. We then show that the ``antiordering'' procedure solves the problem only in the case of projection onto the lowest Landau level. PACS: 73.20.Fz, 72.15.Rn
|