Mass spectrum and Lévy–Schrödinger relativistic equation

In this note we adopt the space-time relativistic approach of Feynman’s propagators (for bosons and fermions) instead of the canonical LagrangianHamiltonian quantized field theory. Indeed the former alternative is preferred to the latter for the developments of our basic ideas that exhibit the connection between the propagator of quantum mechanics and Lévy’s stochasticity. More precisely the relativistic Feynman propagators are here linked with a dynamical theory based on a particular Lévy stochastic process. This point, already mentioned in a previous paper [1], is here analyzed thoroughly with the purpose of deducing its consequences for the case of fundamental fermions and bosons (quarks, leptons, gluons etc. . .) of the Standard Model (SM) characterized by the symmetry SUC(3)×SUL(2)×U(1). To this end we now recall that a Lévy process is a stochastic process X(t), t ≥ 0 on a probability space (Ω,F ,P) such that