Introduction of a quantum of Time ("chronon"), and its consequences for the Electron in Quantum and Classical Physics

In this paper we discuss the consequences of the introduction of a "chronon" of time tau_0 in the formalism of non-relativistic QM. The obtained "finite difference" theory forwards -at the classical level- a solution e.g. for the motion of an electron in an external electromagnetic field, when its charge is NON-negligible; and -at the quantum level- yields a remarkable mass spectrum for leptons. Our first aim is compare to one another the new representations of QM resulting from it, in the Schroedinger, Heisenberg and density-operator pictures, respectively. For each picture, three (retarded, symmetric and advanced) formulations are possible: the "retarded" one does describe QM with friction, i.e., dissipative quantum systems. In this sense, discretized QM is much richer than the ordinary one. We obtain the retarded Schroedinger equation also within the Feynman path integral approach, as well as the time-evolution operators of this discrete theory, and use them to get the finite-difference Heisenberg equations. Some typical applications and examples are afterward studied. At last, the density matrix formalism is applied to the solution of the measurement problem in QM.