Scale relativity is a new approach to the problem of the origin of fundamental scales and of scaling laws in physics, which consists in generalizing Einstein’s principle of relativity to the case of scale transformations of resolutions. We recall here how it leads one to the concept of fractal space-time, and to introduce a new complex time derivative operator which allows to recover the Schröd...

Elementary demonstrations of the 3-body Efimov effect are provided for several models involving a light particle and two heavy ones, and differing by the nature of the 2-body (local or non-local) potentials which bind at zero energy the light particle to each of the heavy ones. The proofs rely on Born-Oppenheimer approximations, which are actually projections of the Hamiltonian into suitable su...

In present paper we construct classical and quantum models of an extended charged particle. One shows that consecutive modelling might be founded on the hollow charged texture which acquires gravitational mass due to the electromagnetic interaction. We demonstrate that such a model has equilibrium states at the radius equal to the classical radius of a charged particle. Also we consider quantum...

Neutrinos have been playing an important role in the evolution of our understanding of elementary particles and could have some signi cant impact on the evolution of the universe. We have strong motivations to search for non-zero neutrino mass both from theoretical and experimental aspects. Various observational data which are indicating the existence of neutrino mass and avor mixing are piling...

OVERVIEW Alan Guth introduced cosmologists to inflation at the 1980 Texas Symposium. Since, inflation has had almost as much impact on cosmology as the big-bang model itself. However, unlike the big-bang model, it has little observational support. Hopefully, that situation is about to change as a variety and abundance of data begin to test inflation in a significant way. The observations that a...

The method of multidimensional SUSY Quantum Mechanics is applied to the investigation of supersymmetrical N−particle systems on a line for the case of separable center-of-mass motion. New decomposition of the superhamiltonian into block-diagonal form with elementary matrix components is constructed. Matrices of coefficients of these minimal blocks are shown to coincide with matrices of irreduci...

The data indicating existence of different forms of dark matter in the universe as well as the role of this matter in structure formation are briefly reviewed. It is argued that vacuum energy gives a dominant contribution into the total energy density of the universe. The model of structure formation with unstable tau-neutrino with MeV-mass and KeV-majoron is described. 1 It is commonly agreed ...

Large Hadron Collider (LHC) experiments this year have shown the existence of a new boson that resembles the Higgs boson. Although it is known that this particle has couplings to other particles that increase with their masses, the spin of the newly discovered boson is undetermined as of yet. The Higgs boson has been predicted to be a spin 0 particle. The LHC boson is not a spin 1 particle, sug...

We study the slow singular limit for planar anharmonic oscillatory motion of a charged particle under the influence of a perpendicular magnetic field when the mass of the particle goes to zero. This model has been used by the authors as a toy model for exploring variational high order approximations to the slow dynamics in rotating fluids. In this paper, we address the long time validity of the...