Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-11-04
Int.J.Mod.Phys. A11 (1996) 3363-3378
Physics
High Energy Physics
High Energy Physics - Theory
17 pages, LaTeX, 1 Figure included as a compressed uuencoded postscript file
Scientific paper
The dynamical system of a point particle constrained on a torus is quantized \`a la Dirac with two kinds of coordinate systems respectively; the Cartesian and toric coordinate systems. In the Cartesian coordinate system, it is difficult to express momentum operators in coordinate representation owing to the complication in structure of the commutation relations between canonical variables. In the toric coordinate system, the commutation relations have a simple form and their solutions in coordinate representation are easily obtained with, furthermore, two quantum Hamiltonians turning up. A problem comes out when the coordinate system is transformed, after quantization, from the Cartesian to the toric coordinate system.
Ishikawa Sumio
Miyazaki Toshiyuki
Yamamoto Kaichi
Yamanobe Motowo
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