On the Quantization of Length in Noncommutative Spaces
We consider canonical/Weyl-Moyal type noncommutative (NC) spaces with rectilinear coordinates. Motivated by the analogy of the formalism of the quantum mechanical harmonic oscillator problem in quantum phase-space with that of the canonical-type NC 2-D space, and noting that the square of length in...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Advances in High Energy Physics |
| Online Access: | http://dx.doi.org/10.1155/2022/8009789 |
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| author | Muthukumar Balasundaram Aamir Rashid |
| author_facet | Muthukumar Balasundaram Aamir Rashid |
| author_sort | Muthukumar Balasundaram |
| collection | DOAJ |
| description | We consider canonical/Weyl-Moyal type noncommutative (NC) spaces with rectilinear coordinates. Motivated by the analogy of the formalism of the quantum mechanical harmonic oscillator problem in quantum phase-space with that of the canonical-type NC 2-D space, and noting that the square of length in the latter case is analogous to the Hamiltonian in the former case, we arrive at the conclusion that the length and area are quantized in such an NC space, if the area is expressed entirely in terms of length. We extend our analysis to the 3-D case and formulate a ladder operator approach to the quantization of length in 3-D space. However, our method does not lend itself to the quantization of spacetime length in 1+1 and 2+1 Minkowski spacetimes if the noncommutativity between time and space is considered. If time is taken to commute with spatial coordinates and the noncommutativity is maintained only among the spatial coordinates in 2+1 and 3+1 dimensional spacetime, then the quantization of spatial length is possible in our approach. |
| format | Article |
| id | doaj-art-3492fa4948dd4cb08e43ce0d2d64a179 |
| institution | OA Journals |
| issn | 1687-7365 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in High Energy Physics |
| spelling | doaj-art-3492fa4948dd4cb08e43ce0d2d64a1792025-08-20T02:24:05ZengWileyAdvances in High Energy Physics1687-73652022-01-01202210.1155/2022/8009789On the Quantization of Length in Noncommutative SpacesMuthukumar Balasundaram0Aamir Rashid1Department of PhysicsDepartment of PhysicsWe consider canonical/Weyl-Moyal type noncommutative (NC) spaces with rectilinear coordinates. Motivated by the analogy of the formalism of the quantum mechanical harmonic oscillator problem in quantum phase-space with that of the canonical-type NC 2-D space, and noting that the square of length in the latter case is analogous to the Hamiltonian in the former case, we arrive at the conclusion that the length and area are quantized in such an NC space, if the area is expressed entirely in terms of length. We extend our analysis to the 3-D case and formulate a ladder operator approach to the quantization of length in 3-D space. However, our method does not lend itself to the quantization of spacetime length in 1+1 and 2+1 Minkowski spacetimes if the noncommutativity between time and space is considered. If time is taken to commute with spatial coordinates and the noncommutativity is maintained only among the spatial coordinates in 2+1 and 3+1 dimensional spacetime, then the quantization of spatial length is possible in our approach.http://dx.doi.org/10.1155/2022/8009789 |
| spellingShingle | Muthukumar Balasundaram Aamir Rashid On the Quantization of Length in Noncommutative Spaces Advances in High Energy Physics |
| title | On the Quantization of Length in Noncommutative Spaces |
| title_full | On the Quantization of Length in Noncommutative Spaces |
| title_fullStr | On the Quantization of Length in Noncommutative Spaces |
| title_full_unstemmed | On the Quantization of Length in Noncommutative Spaces |
| title_short | On the Quantization of Length in Noncommutative Spaces |
| title_sort | on the quantization of length in noncommutative spaces |
| url | http://dx.doi.org/10.1155/2022/8009789 |
| work_keys_str_mv | AT muthukumarbalasundaram onthequantizationoflengthinnoncommutativespaces AT aamirrashid onthequantizationoflengthinnoncommutativespaces |