Non-perturbative

In physics, such functions arise for phenomena which are impossible to understand by perturbation theory, at any finite order.

[1] A concrete, physical example is given by the Schwinger effect,[2] whereby a strong electric field may spontaneously decay into electron-positron pairs.

For not too strong fields, the rate per unit volume of this process is given by, which cannot be expanded in a Taylor series in the electric charge

In theoretical physics, a non-perturbative solution is one that cannot be described in terms of perturbations about some simple background, such as empty space.

For this reason, non-perturbative solutions and theories yield insights into areas and subjects that perturbative methods cannot reveal.