 The Dyson series captures the effect of the discrepancy between formula_2 and the true Hamiltonian formula_3, in the form of a power series in the coupling constant "g"; it is the principal tool for making quantitative predictions from a quantum field theory.To use the Dyson series to calculate anything, one needs more than a gauge-invariant Lagrangian density; one also needs the quantization and gauge fixing prescriptions that enter into the Feynman rules of the theory.The Dyson series produces infinite integrals of various kinds when applied to the Hamiltonian of a particular QFT.