2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51500The quantum correlations of scalar fields are examined as a power series in derivatives. Recursive algebraic equations are derived and determine the amplitudes; all loop integrations are performed. This recursion contains the same information as the usual loop expansion. The approach is pragmatic and generalizable to most quantum field theories.8 pages, 1 figureHigh Energy Physics - TheoryHigh Energy Physics - PhenomenologyScalar Field Theory in the Derivative Expansiontext