Wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics
While Wigner functions forming phase space representation of quantum states is a well-known fact, their construction for noncommutative quantum mechanics (NCQM) remains relatively lesser known, in particular with respect to gauge dependencies. This paper deals with the construction of Wigner functio...
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| Format: | Article |
| Language: | English |
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EDP Sciences, Springer Verlag
2017
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| Online Access: | http://psasir.upm.edu.my/id/eprint/63718/1/Wigner%20functions%20for%20gauge%20equivalence%20classes%20of%20unitary%20irreducible%20representations%20of%20noncommutative%20quantum%20mechanics.pdf |
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| author | Chowdhury, S. Hasibul Hassan Zainuddin, Hishamuddin |
| author_facet | Chowdhury, S. Hasibul Hassan Zainuddin, Hishamuddin |
| author_sort | Chowdhury, S. Hasibul Hassan |
| collection | UPM |
| description | While Wigner functions forming phase space representation of quantum states is a well-known fact, their construction for noncommutative quantum mechanics (NCQM) remains relatively lesser known, in particular with respect to gauge dependencies. This paper deals with the construction of Wigner functions of NCQM for a system of 2-degrees of freedom using 2-parameter families of gauge equivalence classes of unitary irreducible representations (UIRs) of the Lie group G NC which has been identified as the kinematical symmetry group of NCQM in an earlier paper. This general construction of Wigner functions for NCQM, in turn, yields the special cases of Landau and symmetric gauges of NCQM. |
| first_indexed | 2024-03-06T09:45:14Z |
| format | Article |
| id | upm.eprints-63718 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:45:14Z |
| publishDate | 2017 |
| publisher | EDP Sciences, Springer Verlag |
| record_format | dspace |
| spelling | upm.eprints-637182018-11-30T03:34:23Z http://psasir.upm.edu.my/id/eprint/63718/ Wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics Chowdhury, S. Hasibul Hassan Zainuddin, Hishamuddin While Wigner functions forming phase space representation of quantum states is a well-known fact, their construction for noncommutative quantum mechanics (NCQM) remains relatively lesser known, in particular with respect to gauge dependencies. This paper deals with the construction of Wigner functions of NCQM for a system of 2-degrees of freedom using 2-parameter families of gauge equivalence classes of unitary irreducible representations (UIRs) of the Lie group G NC which has been identified as the kinematical symmetry group of NCQM in an earlier paper. This general construction of Wigner functions for NCQM, in turn, yields the special cases of Landau and symmetric gauges of NCQM. EDP Sciences, Springer Verlag 2017-07 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/63718/1/Wigner%20functions%20for%20gauge%20equivalence%20classes%20of%20unitary%20irreducible%20representations%20of%20noncommutative%20quantum%20mechanics.pdf Chowdhury, S. Hasibul Hassan and Zainuddin, Hishamuddin (2017) Wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics. The European Physical Journal Special Topics, 226 (10). 2359 - 2374. ISSN 1951-6355; ESSN: 1951-6401 10.1140/epjst/e2017-70066-8 |
| spellingShingle | Chowdhury, S. Hasibul Hassan Zainuddin, Hishamuddin Wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics |
| title | Wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics |
| title_full | Wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics |
| title_fullStr | Wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics |
| title_full_unstemmed | Wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics |
| title_short | Wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics |
| title_sort | wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics |
| url | http://psasir.upm.edu.my/id/eprint/63718/1/Wigner%20functions%20for%20gauge%20equivalence%20classes%20of%20unitary%20irreducible%20representations%20of%20noncommutative%20quantum%20mechanics.pdf |
| work_keys_str_mv | AT chowdhuryshasibulhassan wignerfunctionsforgaugeequivalenceclassesofunitaryirreduciblerepresentationsofnoncommutativequantummechanics AT zainuddinhishamuddin wignerfunctionsforgaugeequivalenceclassesofunitaryirreduciblerepresentationsofnoncommutativequantummechanics |