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Noncommutative Space-Time of the Relativistic Equations with a Coulomb Potential Using Seiberg-Witten Map
We present an important contribution to the noncommutative approach to the hydrogen atom to deal with Lamb shift corrections. This can be done by studying the Klein{Gordon and Dirac equations in a non-commutative space-time up to first-order of the noncommutativity parameter using the Seiberg-Witten...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2016
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| Series: | Журнал математической физики, анализа, геометрии |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/140560 |
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irk-123456789-1405602018-07-11T01:23:16Z Noncommutative Space-Time of the Relativistic Equations with a Coulomb Potential Using Seiberg-Witten Map Zaim, S. We present an important contribution to the noncommutative approach to the hydrogen atom to deal with Lamb shift corrections. This can be done by studying the Klein{Gordon and Dirac equations in a non-commutative space-time up to first-order of the noncommutativity parameter using the Seiberg-Witten maps. We thus find the noncommutative modification of the energy levels and by comparing with the current experimental results on the Lamb shift of the 2P level to extract a bound on the parameter of noncommutativity, we show that the fundamental length (√Θ) is compatible with the value of the electroweak length scale (l). Phenomenologically, this effectively confirms the presence of gravity at this level. 2016 Article Noncommutative Space-Time of the Relativistic Equations with a Coulomb Potential Using Seiberg-Witten Map / S. Zaim // Журнал математической физики, анализа, геометрии. — 2016. — Т. 12, № 4. — С. 359-373. — Бібліогр.: 46 назв. — англ. 1812-9471 DOI : doi.org/10.15407/mag12.04.359 Mathematics Subject Classification 2000: 81T80, 37K05, 81Q05 http://dspace.nbuv.gov.ua/handle/123456789/140560 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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English |
| description |
We present an important contribution to the noncommutative approach to the hydrogen atom to deal with Lamb shift corrections. This can be done by studying the Klein{Gordon and Dirac equations in a non-commutative space-time up to first-order of the noncommutativity parameter using the Seiberg-Witten maps. We thus find the noncommutative modification of the energy levels and by comparing with the current experimental results on the Lamb shift of the 2P level to extract a bound on the parameter of noncommutativity, we show that the fundamental length (√Θ) is compatible with the value of the electroweak length scale (l). Phenomenologically, this effectively confirms the presence of gravity at this level. |
| format |
Article |
| author |
Zaim, S. |
| spellingShingle |
Zaim, S. Noncommutative Space-Time of the Relativistic Equations with a Coulomb Potential Using Seiberg-Witten Map Журнал математической физики, анализа, геометрии |
| author_facet |
Zaim, S. |
| author_sort |
Zaim, S. |
| title |
Noncommutative Space-Time of the Relativistic Equations with a Coulomb Potential Using Seiberg-Witten Map |
| title_short |
Noncommutative Space-Time of the Relativistic Equations with a Coulomb Potential Using Seiberg-Witten Map |
| title_full |
Noncommutative Space-Time of the Relativistic Equations with a Coulomb Potential Using Seiberg-Witten Map |
| title_fullStr |
Noncommutative Space-Time of the Relativistic Equations with a Coulomb Potential Using Seiberg-Witten Map |
| title_full_unstemmed |
Noncommutative Space-Time of the Relativistic Equations with a Coulomb Potential Using Seiberg-Witten Map |
| title_sort |
noncommutative space-time of the relativistic equations with a coulomb potential using seiberg-witten map |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/140560 |
| citation_txt |
Noncommutative Space-Time of the Relativistic Equations with a Coulomb Potential Using Seiberg-Witten Map / S. Zaim // Журнал математической физики, анализа, геометрии. — 2016. — Т. 12, № 4. — С. 359-373. — Бібліогр.: 46 назв. — англ. |
| series |
Журнал математической физики, анализа, геометрии |
| work_keys_str_mv |
AT zaims noncommutativespacetimeoftherelativisticequationswithacoulombpotentialusingseibergwittenmap |
| first_indexed |
2023-10-18T21:22:55Z |
| last_indexed |
2023-10-18T21:22:55Z |
| _version_ |
1796152662481174528 |