<p>The original Weber action at a distance theory is valid for slowly varying effects, and it in addition to predicting all of the usual electrodynamical results, leads to crucial effects where the Maxwell theory fails. The Weber’s approach is an alternative to <a title="Maxwell's Equations" href="http://en.wikipedia.org/wiki/Maxwell%27s_Equations">Maxwell electrodynamics</a>, where the <a title="Coulomb's Law" href="http://en.wikipedia.org/wiki/Coulomb%27s_Law">Coulomb's law</a> becomes velocity dependent [1-6]. Here we prove that the Weber’s theory gives the fine structure energy level splitting for the hydrogen atom without the assumption of mass change with velocity.</p>
It is very known that if the operator acts on each term into a convergent Fourier Series (FS), then it may result a divergent series. This situation is remedied applying the symmetric derivative to FS, which implies the existence of the important Fejér-Lanczos Factors. In this paper, we show that the orthogonal derivative also leads to these Factors.
We exhibit that from Cayley-Hamilton's quaternionic expression or via the matrix relation of Olinde Rodrigues-Cartan, it is possible to construct 3-rotations. Besides, we obtained the generators for O(3) and SU(2).
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