Lorentz-violating corrections on the hydrogen spectrum induced by a nonminimal coupling

The influence of a Lorentz-violating fixed background on fermions is considered by means of a torsion-free nonminimal coupling. The nonrelativistic regime is assessed and the Lorentz-violating Hamiltonian is determined. The effect of this Hamiltonian on the hydrogen spectrum is determined to first-order evaluation (in the absence and in the presence of an external magnetic field), revealing that there appear some energy shifts that modify the fine structure of the spectrum. In the case the nonminimal coupling is torsionlike, no first order correction shows up in the absence of an external field; in the presence of an external field, a secondary Zeeman effect is implied. Such effects are then used to set up stringent bounds on the parameters of the model.