On kinetic expansion in scalar-field theory

Summary

The kinetic expansion is the expansion in the degrees of the kinetic term$\partial ^2$. The leading order of this expansion is the static ultralocal approximation, exactly solvable for the scalar-field theory with polynomial interaction at the level of Green's functions. The strong-coupling expansion is closely related with the kinetic expansion. However, the latter has a more complicated combinatorial structure, allowing to relate it with the perturbation theory. In the present paper, a way to sum over the kinetic expansion is proposed, underlying which is the self-consistent expansion in the bilocal source via the Legendre transformation. The self-consistent kinetic expansion allows to solve two principal problems concerning the strong-coupling expansion; the interpretation problem and that of the ultraviolet cut-off removal (renormalization).