We study spontaneous bremsstrahlung emission in a highly intense laser field. In this regime the interaction with the laser field has to be treated nonperturbatively by using the relativistic formalism including Dirac-Volkov propagators, while the interaction with the Coulomb field and the bremsstrahlung radiation can be treated in first-order perturbation theory. For the intermediate electron state a fully laser-dressed propagator is used, including radiative corrections to avoid singularities on the mass shell. We find that the use of the Dirac-Volkov propagator is crucial to obtain correct numerical results. The cross section of the process is evaluated for laser intensities of order ${10}^{20}\mathrm{W}/{\mathrm{cm}}^2$ and relativistic energies of the initial electron.

We present a unified treatment, including higher-order corrections, of anharmonic oscillators of arbitrary even and odd degree. Our approach is based on a dispersion relation which takes advantage of the $\mathcal{P}\mathcal{T}$ symmetry of odd potentials for imaginary coupling parameter, and of generalized quantization conditions which take into account instanton contributions. We find a number of explicit new results, including the general behavior of large-order perturbation theory for arbitrary levels of odd anharmonic oscillators, and subleading corrections to the decay width of excited states for odd potentials, which are numerically significant.

A method for the resummation of a nonalternating divergent perturbation series is described. The procedure constitutes a generalization of the Borel-Padé method. Of crucial importance is a special integration contour in the complex plane. Nonperturbative imaginary contributions can be inferred from the purely real perturbative coefficients. A connection is drawn from the quantum field theoretic problem of resummation to divergent perturbative expansions in other areas of physics.