17 research outputs found
Mass spectrum and Lévy-Scrödinger relativistic equation
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
Mass spectrum from stochastic Levy-Schroedinger relativistic equations: possible qualitative predictions in QCD
Starting from the relation between the kinetic energy of a free Levy-Schroedinger particle and the logarithmic characteristic of the underlying stochastic process, we show that it is possible to get a precise relation between renormalizable field theories and a specific Levy process. This subsequently leads to a particular cut-off in the perturbative diagrams and can produce a phenomenological mass spectrum that allows an interpretation of quarks and leptons distributed in the three families of the standard model
Phenomenology from relativistic Levy-Schroedinger equations: Application to neutrinos
In continuation of a previous paper a close connection between Feynman propagators and a particular L\'evy stochastic process is established. The approach can be easily applied to the Standard Model SU_C(3)xSU_L(2)xU(1) providing qualitative interesting results. Quantitative results, compatible with experimental data, are obtained in the case of neutrinos
Mass spectrum from stochastic Levy-Schroedinger relativistic equations: possible qualitative predictions in QCD
Starting from the relation between the kinetic energy of a free
Levy-Schroedinger particle and the logarithmic characteristic of the underlying
stochastic process, we show that it is possible to get a precise relation
between renormalizable field theories and a specific Levy process. This
subsequently leads to a particular cut-off in the perturbative diagrams and can
produce a phenomenological mass spectrum that allows an interpretation of
quarks and leptons distributed in the three families of the standard model.Comment: 8 pages, no figures. arXiv admin note: substantial text overlap with
arXiv:1008.425
Levy processes and Schroedinger equation
We analyze the extension of the well known relation between Brownian motion
and Schroedinger equation to the family of Levy processes. We consider a
Levy-Schroedinger equation where the usual kinetic energy operator - the
Laplacian - is generalized by means of a selfadjoint, pseudodifferential
operator whose symbol is the logarithmic characteristic of an infinitely
divisible law. The Levy-Khintchin formula shows then how to write down this
operator in an integro--differential form. When the underlying Levy process is
stable we recover as a particular case the fractional Schroedinger equation. A
few examples are finally given and we find that there are physically relevant
models (such as a form of the relativistic Schroedinger equation) that are in
the domain of the non-stable, Levy-Schroedinger equations.Comment: 10 pages; changed the TeX documentclass; added references [21] and
[22] and comments about them; changed definitions (11) and (12); added
acknowledgments; small changes scattered in the tex
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