Finite-energy field configuration ($E[\Phi ]<\infty$)

A finite-energy field configuration has integrable energy density after the vacuum energy has been subtracted. The boundary conditions used for a localized classical field-theory soliton require approaching a vacuum at spatial infinity. In one dimension the two ends may approach distinct scalar-field vacua; in a gauge theory the asymptotic field can have nontrivial winding even when its local energy density tends to zero.