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Two dimensional plane, modified symplectic structure and quantization


Umar, Mohd Faudzi and Mohd Shah, Nurisya and Zainuddin, Hishamuddin (2018) Two dimensional plane, modified symplectic structure and quantization. Jurnal Fizik Malaysia, 39 (2). 30022 - 30026. ISSN 0128-0333; EISSN: 2590-4191


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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Official URL or Download Paper: http://ifm.org.my/jurnal-fizik-malaysia

Additional Metadata

Item Type: Article
Publisher: Malaysian Institute of Physics (IFM)
Keywords: Noncommutative quantum mechanics; Canonical group quantization; Symplectic structure
Depositing User: Ms. Nida Hidayati Ghazali
Date Deposited: 27 Mar 2020 06:13
Last Modified: 27 Mar 2020 06:13
URI: http://psasir.upm.edu.my/id/eprint/74350
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