Relativistic quantum mechanics of the hydrogen atom as the weak-field limit of a nonlinear theory

The effect of nonlinear terms in the Dirac equation is investigated, in the case of the hydrogen atom. It is found that the change in the energy is of order ⁶ for a very large range of values of the coupling constant of the dominant term. It is shown that a nonlinear classical field theory has a quantumlike behavior near the linear limit. This implies the existence of a close relation between linearization and quantization. A classical stable model of the hydrogen atom is presented. Some consequences are discussed.