Unitarity and real properties of the neutral meson complex

The proof of the Khalfin Theorem for neutral meson complex is analyzed. It is shown that the unitarity of the time evolution operator for the total system under considerations assures that the Khalfin's Theorem holds. The consequences of this Theorem for the neutral mesons system are discussed: it is shown, eg., that diagonal matrix elements of the exact effective Hamiltonian for the neutral meson complex can not be equal if CPT symmetry holds and CP symmetry is violated. Properties of time evolution governed by a time--independent effective Hamiltonian acting in the neutral mesons subspace of states are considered. Using the Khalfin's Theorem it is shown that if such Hamiltonian is time--independent then the evolution operator for the total system containing the neutral meson complex can not be a unitary operator. It is shown graphically for a given specific model how the Khalfin's Theorem works. It is also shown for this model how the difference of the mentioned diagonal matrix elements of the effective Hamiltonian varies in time.