In a large variety of quantum mechanical systems, we show that the full nonperturbative expression for energy eigenvalues, containing all orders of perturbative, nonperturbative, and quasi-zero-mode terms, may be generated directly from the perturbative expansion about the perturbative vacuum, combined with a single global boundary condition. This provides a dramatic realization of the principle of “resurgence,” that the fluctuations about different semiclassical saddle points are related to one another in a precise quantitative manner. The analysis of quantum mechanics also generalizes to certain calculable regimes of quantum field theory.

• Received 19 June 2013

DOI:https://doi.org/10.1103/PhysRevD.89.041701