A new discrete view to the quantum world
  Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These graphs only consist of few space-like edges, e.g. the ground state of atoms is described by two nodes and one edge, and interactions only take place at the nodes.   The fundament is an extremal principle for a relativistic invariant "Lagrangian sum", from which "field-equations" and "equations of motion" are derived, so the states (including the graph nodes) are completely determined.   As important validations of the model, the corresponding graphs for the stationary Dirac-equation for the atom are drawn and the correct spectra are computed (Sommerfeld-levels).   Also a discrete Schroedinger approximation and an associated "Hamiltonian sum" are derived and the correct equation of a classical moving particle under Lorentz-force is presented.   I hope, that this new approach will help, to overcome some problems of current quantum mechanics by making the wave function superfluous. 
Wolfgang Koehler