Magnetic moment effects from time-space non-commutativity in the Dirac equation for Hydrogen atom

In this work we study the effect of time-space non-commutativity on the hydrogen atom. Our goal is to solve the Dirac equation for the coulomb potential in a non-commutative time-space up to first order in the non-commutativity parameter using the Seiberg-Witten maps and the Moyal product. We thus find the non-commutative modification of the energy levels of hydrogen atom and show that the non-commutativity is the source of magnetic moment. Comparing the results with experimental values from spectroscopy, we get the bound on non-commutativity parameter at the level of (0.1 TeV)(-2).