Semiperturbative

Semiperturbative refers to a class of methods in physics and applied mathematics that blend perturbative expansions with nonperturbative information. In a semiperturbative approach, one or more aspects of a problem are treated with a perturbative expansion in a small parameter (for example a coupling constant or a ratio of scales), while essential features are supplied by nonperturbative input. This combination aims to extend the reach of perturbation theory into regimes where purely perturbative methods would be unreliable.

Semiperturbative methods are common in quantum field theory, quantum mechanics, and many-body physics. For instance, high-energy processes may be described by perturbation theory, while bound states, confinement effects, or strong-coupling phenomena require nonperturbative input such as lattice results, instanton contributions, or effective field theories with nonperturbative matching. Hybrid techniques also appear as resummations that incorporate infinitely many perturbative terms or as semiclassical approaches anchored by exact or numerical nonperturbative data.

The approach emphasizes controlled approximations and error assessment, but its success depends on the quality of the nonperturbative input and the regime of validity of the perturbative pieces. It is distinct from fully perturbative methods and from fully nonperturbative techniques; rather, it sits between them to capture a broader range of physical behavior.

Related topics include perturbation theory, nonperturbative methods, resummation, lattice gauge theory, and effective field theory.