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Systems of neutral interacting mesons are investigated, concerning inparticular the validity of their description by an effective hamiltonian.First, I study its connection to quantum field theory and show that thespectrum of such systems cannot be reduced in general to the one of a singleconstant effective mass matrix. Choosing nevertheless to work in this customaryformalism, one then faces several ways to diagonalize a complex matrix, whichlead to different eigenvalues and eigenvectors. Last, and it is the mainsubject of this work, because K0 and its charge conjugate K0bar are alsoconnected, in quantum field theory, by hermitian conjugation, any constanteffective mass matrix is defined, in this basis, up to arbitrary diagonalantisymmetric terms; I use this freedom to deform the mass matrix in variousways and study the consequences on its spectrum. Emphasis is put on the role ofdiscrete symmetries throughout the paper. That the degeneracy of theeigenvalues of the full renormalized mass matrix can be a sufficient conditionfor the outcome of CP violation is outlined in an appendix. In the whole work,the dual formalism of |in> and <out| states and bi-orthogonal basis, suitablefor non-normal matrices, is used.Comment: 29 pages, LaTeX, 1 postscript log

ABOUT NEUTRAL KAONS AND SIMILAR SYSTEMS: FROM QUANTUM FIELD THEORY TO EFFECTIVE MASS MATRICES