Two dimensional plane, modified symplectic structure and quantization
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 s...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Malaysian Institute of Physics (IFM)
2018
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/74350/ http://psasir.upm.edu.my/id/eprint/74350/1/Two%20dimensional%20plane%2C%20modified%20symplectic%20structure%20and%20quantization.pdf |
| _version_ | 1848857483053891584 |
|---|---|
| author | Umar, Mohd Faudzi Mohd Shah, Nurisya Zainuddin, Hishamuddin |
| author_facet | Umar, Mohd Faudzi Mohd Shah, Nurisya Zainuddin, Hishamuddin |
| author_sort | Umar, Mohd Faudzi |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-15T11:58:16Z |
| format | Article |
| id | upm-74350 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T11:58:16Z |
| publishDate | 2018 |
| publisher | Malaysian Institute of Physics (IFM) |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-743502020-03-27T06:13:50Z http://psasir.upm.edu.my/id/eprint/74350/ Two dimensional plane, modified symplectic structure and quantization Umar, Mohd Faudzi Mohd Shah, Nurisya Zainuddin, Hishamuddin 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. Malaysian Institute of Physics (IFM) 2018 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/74350/1/Two%20dimensional%20plane%2C%20modified%20symplectic%20structure%20and%20quantization.pdf 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 http://ifm.org.my/jurnal-fizik-malaysia |
| spellingShingle | Umar, Mohd Faudzi Mohd Shah, Nurisya Zainuddin, Hishamuddin Two dimensional plane, modified symplectic structure and quantization |
| title | Two dimensional plane, modified symplectic structure and quantization |
| title_full | Two dimensional plane, modified symplectic structure and quantization |
| title_fullStr | Two dimensional plane, modified symplectic structure and quantization |
| title_full_unstemmed | Two dimensional plane, modified symplectic structure and quantization |
| title_short | Two dimensional plane, modified symplectic structure and quantization |
| title_sort | two dimensional plane, modified symplectic structure and quantization |
| url | http://psasir.upm.edu.my/id/eprint/74350/ http://psasir.upm.edu.my/id/eprint/74350/ http://psasir.upm.edu.my/id/eprint/74350/1/Two%20dimensional%20plane%2C%20modified%20symplectic%20structure%20and%20quantization.pdf |