Renormalization: The observable-state model

The usual mathematical formalism of quantum field theory is not rigorous because it contains divergences that can only be renormalized by nonrigorous mathematical methods. So we present a method of subtraction of divergences using the formalism of decoherence. This is achieved by replacing the standard renormalization method by a projector on a well defined Hilbert subspace. In this way a list of problems of the standard formalism disappears while the physical results of quantum field theory remain valid. From its own nature, this formalism can be also used in nonrenormalizable theories.