Authors: Jérémy Kerneis
Interactions are produced, at small scale, by Lorentz transformations around extra dimensions. As a simple example, we include simultaneously a "Kaluza-Klein fth dimension" and minimal coupling in Klein-Gordon equation applied to Hydrogen (all equations can be written in dimensionless form). Instead of solving the last separable equation for f(R), we require one more eigeinvalue equation, and require that the eccentricity of the system vanishes, to deduce the energy levels. With 4 spatial dimensions, there are naturally 6 rotations and 2 angular momenta (a classical one with parity+ and a spin with parity-). The SO(4) degeneracy and Schrodinger's energy levels are deduced, but the ne structure requires a modication : we give an example with a linear equation. We observe that the extra degree of freedom naturally disappears at classical scale (objects made of a large number of elementary particles). We then observe that the quantum principle of minimal coupling (here produced by Lorentz transformations) is analogous to a modication of the metric inside the wave function. We use the corresponding metric (no coordinate singularity, the central one being naturally solved by the Lorentz transformation with extra dimensions) to describe gravitation : the deduced equation of motion reduces, in the low eld approximation, to the equation given by general relativity. More generally, extra dimensions may be usefull in particles physics : conservation of lepton numbers could be understood as conservation of momentum along other dimensions, and unconvenient divergences could be solved.
Comments: 31 Pages.
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