We derive an alternative time-evolution operator for the Heisenberg picture in five rigorous ways with different starting points to confirm its validity and generality.This time-evolution operator called the generalized time-evolution operator is an analytical scattering operator that is obtained in a nonperturbative way unlike the Dyson series based on a perturbative approximation.We verify that the obtained scattering operator thoroughly preserves the Hermiticity, unitarity, causality of the scattering operator which are the basic requirements for the consistent scattering operator.It is analyzed that the Dyson series does not guarantee the Hermiticity, unitarity, causality of the scattering operator, and thus is not consistent.It is demonstrated that our formulation based on the generalized time-evolution operator does not need the Feynman diagram and renormalization and therefore there does not exist the infinity problem within the framework of the theory that we constructed.Ultimately, it is shown that the new formulation enables us to construct a consistent scattering theory which, beyond the infinity problem, satisfies all necessary requirements for the scattering operator.