Derivation of QFT Dynamics

The perturbative dynamics of quantum field theories is described by a recursive expansion similar to the well known loop expansion. The equivalent formulation based on low-energy dynamics via an expansion in derivatives is well known in the literature; this is described by terms from low energy to high energy. The coefficients of these terms are presented in a simplified algebraic manner. In general, the dynamics of any bare Lagrangian, including additional higher dimension terms, is found by iteration in a discrete algorithm. Inversion of the quantized dynamics to the fundamental theory is possible.