Noncommutative Space-Time of the Relativistic Equations with a Coulomb Potential Using Seiberg-Witten Map

• Published in: Журнал математической физики, анализа, геометрии
• Date: 2016
• Main Author: Zaim, S.
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2016
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/140560
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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.