Mass spectrum and L\'evy-Schr\"odinger relativistic equation

TL;DR

This paper proposes a modified relativistic Hamiltonian that ensures the relativistic Schrödinger equations are grounded in Lévy processes, allows for multiple particle masses, and guarantees convergence of Feynman diagrams with diverse masses.

Contribution

It introduces a novel modification to the relativistic Hamiltonian linking Schrödinger equations to Lévy processes and ensuring diagram convergence for multiple masses.

Findings

Relativistic Schrödinger equations based on Lévy processes

Multiple particle masses can be incorporated

Feynman diagrams are convergent with at least three different masses

Abstract

We introduce a modification in the relativistic hamiltonian in such a way that (1) the relativistic Schr\"odinger equations can always be based on an underlying L\'evy process, (2) several families of particles with different rest masses can be selected, and finally (3) the corresponding Feynman diagrams are convergent when we have at least three different masses.