[en] The consequences of a generalized Dirac equation are discussed for the energy levels of the hydrogen atom. Apart from the usual generalizations of the Dirac equation by adding new interaction terms, the authors generalize the anticommutation rule of the Dirac matrices, which leads to spin-dependent propagation properties. Such a theory can be looked at as a model theory for testing Lorentz invariance or as an outcome of pregeometric dynamical induction schemes for space-time structure. For special examples of generalized Dirac matrices including perturbation terms with respect to the SRT Dirac matrices, the authors derive the energy level of the hydrogen atom and find a hyperfine splitting due to these perturbations. A comparison of this additional splitting with Lamb shift measurements gives us upper limits for possible perturbations, which turn out to be of measurable magnitude. Spin precession experiments give much more restrictive limits. So, it turns out that the hydrogen atom is not such a sensitive indicator for the Lorentz invariance as widely believed. 13 refs