A nonperturbative treatment of how Born-Infeld nonlinear electrostatics shifts the energy levels of the hydrogen atom. The electrostatic potential of two true point charges is characterized as the unique minimizer of a Born-Infeld action functional (equivalently the solution of a nonlinear quasilinear elliptic PDE), real analytic away from the charges. For regularized sources the displacement field expands as a convergent power series in the Born-Infeld parameter beta whose leading term is the Coulomb field, justifying a leading-order Coulomb approximation for the interparticle potential; this potential is then fed into the Schrodinger equation to compute beta-dependent corrections to the hydrogen spectrum, with the analogous exactly solvable Bopp-Lande-Thomas-Podolsky theory supporting the same conclusions.
A reply (solicited by PRL, published only on arXiv) defending the authors' nonperturbative calculation of Born-Infeld effects on the Schrodinger spectrum of the hydrogen atom against a comment by Smo…