Indirect CP-violation in the neutral kaon system beyond leading logarithms and related topics

I describe in detail the calculation of the coefficients eta_3 and eta_1 of the low-energy Delta S=2 -hamiltonian describing K^0-K^0-bar-mixing in the next-to-leading order of renormalization group improved (RG) perturbation theory. First a general introduction into the application of the operator expansion and of RG methods to weak processes is presented. This includes the RG formalism for Green's functions with two operator insertions. Second I discuss the elimination of unphysical operators with emphasis on evanescent operators. Then the two-loop calculations needed for eta_3 and eta_1 are shown and finally the implications on the phenomenology of epsilon_K and the K_L-K_S mass difference are discussed. The results of this thesis have been published separately, but they are explained in more detail here