Khalfin's Theorem and neutral mesons subsystem

We analyze the proof of the Khalfin Theorem for neutral meson complex. The consequences of this Theorem are discussed: using this Theorem we find, 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. The Properties of time evolution governed by a time--independent effective Hamiltonian acting in the neutral mesons subspace of states are considered. By means of the Khalfin's Theorem we show that if such Hamiltonian is time--independent then the evolution operator for the total system containing neutral meson complex can not be a unitary operator. Within a given specific model we examine numerically the Khalfin's Theorem. We show for this model in a graphic form how the Khalfin's Theorem works. We also show for this model how the difference of the mentioned diagonal matrix elements of the effective Hamiltonian varies in time.

K. Urbanowski · 2007