Some applications of non-Hermitian operators in quantum mechanics and quantum field theory

Due to the possibility of rephrasing it in terms of Lie-admissible algebras, some work done in the past in collaboration with A. Agodi, M. Baldo and V. S. Olkhvsky is here reported. Such work led to the introduction of non-Hermitian operators in (classical and relativistic) quantum theory. We deal in particular with: (i) the association of unstable states (decaying "Resonances") with the eigenvectors of non-Hermitian Hamiltonians; (ii) the problem of the four-position operators for relativistic spin-zero particles.