Trans-series in quantum physics

Alexander Turbiner (ICN-UNAM)

RESUMEN: In a number of physically-important special situations ranging from quantum mechanics, molecular physics to field theory and string theory in addition to Taylor series in coupling constant (perturbation theory) it appears the infinite expansion in exponentially-small terms (non-perturbative expansion). This phenomenon was discovered by J Zinn-Justin (Saclay) for the ground state energy at 1981 and recently this expansion was called trans-series. The example of quartic double-well symmetric potential will be presented and influence of exponential small terms to the wavefunction will be studied in semiclassical domain.