Alternative descriptions of physical systems based on perturbation theory

In quantum physics, the perturbation theory up to some finite order in the coupling constant contains a nonpositive-definite scalar product of physical wave functions or a nonunitary evolution of states. It cannot therefore be considered a consistent theory describing reality. This problem can be solved by modifying the scalar product of wave functions and the multiplication of dynamical variables. The obtained solutions can be used for an alternative description of quantum physical systems that agrees with experiment within the prescribed accuracy.