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

DOI10.15407/MAG12.04.359zbMATH Open1365.81075arXiv1301.7297OpenAlexW2963822195MaRDI QIDQ2981273

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Publication date: 8 May 2017

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Abstract: We present an important contribution to the non-commutative 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 non-commutativity parameter using the Seiberg-Witten maps. We thus find the non-commutative modification of the energy levels and by comparing with the the current experimental results on the Lamb shift of the 2P level to extract a bound on the parameter of non-commutativity, we show that the fundamental length ($sqrtTheta$) is compatible with the value of the electroweak length scale ($l$). Phenomenologically, this effectively confirms the presence of gravity at this level.

Full work available at URL: https://arxiv.org/abs/1301.7297

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