Interplay of topology and quantization: topological energy quantization in a cavity

The interplay between quantization and topology is investigated in the frame of a topological model of electromagnetism proposed by the author. In that model, the energy of monochromatic electromagnetic radiation in a cubic cavity is $E=(d/4)\hbar \omega$ where $d$ is a topological index equal to the degree of a map between two orbifolds.Comment: 17 pages, no figures, to be published in Physics Letters

The Tremblay-Turbiner-Winternitz system on spherical and hyperbolic spaces : Superintegrability, curvature-dependent formalism and complex factorization

The higher-order superintegrability of the Tremblay-Turbiner-Winternitz system (related to the harmonic oscillator) is studied on the two-dimensional spherical and hiperbolic spaces, S_\k^2 (\k>0), and H_{\k}^2 (\k<0). The curvature $\kappa$ is considered as a parameter and all the results are formulated in explicit dependence of $\kappa$. The idea is that the additional constant of motion can be factorized as the product of powers of two particular rather simple complex functions (here denoted by $M_r$ and $N_\phi$). This technique leads to a proof of the superintegrability of the Tremblay-Turbiner-Winternitz system on S_\k^2 (\k>0) and H_{\k}^2 (\k<0), and to the explicit expression of the constants of motion.Comment: one figur

A topological mechanism of discretization for the electric charge

We present a topological mechanism of discretization, which gives for the fundamental electric charge a value equal to the square root of the Planck constant times the velocity of light, which is about 3.3 times the electron charge. Its basis is the following recently proved property of the standard linear classical Maxwell equations: they can be obtained by change of variables from an underlying topological theory, using two complex scalar fields, the level curves of which coincide with the magnetic and the electric lines, respectively.Comment: 10 pages, LaTeX fil