Non-self-adjoint operators as observables in quantum theory and nuclear physics

The aim of this paper is to show the importance and applicability of non-self-adjoint operators for description of observables both in relativistic and nonrelativistic quantum mechanics, as well as in quantum electrodynamics. The paper considers (i) a maximally Hermitian (but non-self-adjoint) time operator in nonrelativistic quantum mechanics and in quantum electrodynamics and (ii) the problem of defining the four-dimensional coordinate and momentum operators describing relativistic particles with zero spin (each of these operators contains both Hermitian and anti-Hermitian parts). Some other applications of non-selfadjoint and non-Hermitian operators in physics are analyzed as well. The paper ends with an analysis of a few cases of T -non-invariant interactions, including quantum dissipation and nuclear optical potentials.