Two Dimensional Plane, Modified Symplectic Structure and Quantization

Publication Issue: 
Volume 39, Issue 2, 2018
Page No: 
Date Received: 
Sunday, January 28, 2018
Authors' Name: 
Mohd Faudzi Umar
Nurisya Mohd Shah
Hishamuddin Zainuddin
Authors' Affiliation and Address: 
Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, 35900 Tanjung Malim, Perak.
Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, 43400 Serdang, Selangor.
Department of Physics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor.
Noncommutative quantum mechanics on the plane has been widely studied in the literature. Here, we consider the problem using Isham's canonical group quantization scheme for which the primary object is the symmetry group that underlies the phase space. The noncommutativity of the configuration space coordinates requires us to introduce the noncommutative term in the symplectic structure of the system. This modified symplectic structure will modify the group acting on the configuration space from abelian R^2 to a nonabelian one. As a result, the canonical group obtained is a deformed Heisenberg group and the canonical commutation relation (CCR) corresponds to what is usually found in noncommutative quantum mechanics.
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