Isorepresentations of the Lie-isotopic \(SU(2)\) algebra with applications to nuclear physics and to local realism (Q1383867)

The author presents three important applications of the Santilli isotheory. First, he constructs the isotopies SU*(2) of the SU(2) Lie algebra and classifies their isoirreps into regular, irregular and standard, depending on certain features of the isotopic image of roots and weights. He then applies these results, apparently for the first time, to construct the regular irregular and standard isopauli matrices (fundamental isoirrep of SU*(2)). In particular, he proves that the standard isopauli matrices preserve the spin 1/2, although admitting at least two unrestricted ``hidden functions'' in their realization, while the regular and irregular isopauli matrices are broader isoirreps of SU*(2) which do not preserve the conventional spin 1/2. Second, the author applies these results to nuclear physics by showing that SU*(2) permits the reconstruction of the exact isospin symmetry under electromagnetic interactions which is believed to be broken for the convectional realization of Lie's theory. In fact, under SU*(2), the two ``hidden functions'' of the standard isopauli matrices permit the achievement of the same mass for the proton and neutron on isospace over isofields while the conventional masses are recovered via isoeigenvalues or isoexpectation values. The paper then shows that the capability of the Lie-Santilli isotheory to reconstruct as exact symmetries those believed to be broken is a rather general property, which also holds for the exact reconstruction of the rotational symmetry for all signature preserving deformations of the sphere, the reconstruction of the exact Lorentz symmetry for all signature deformations of the Minkowski metric, the reconstruction of the exact parity under weak interactions, and other cases. As a third, also far-reaching application, the author introduces the isotopies of local realism. He first shows that his isotopic theory provides perhaps the only known specific and concrete realizations of the theory of ``hidden variables'', which are in effect extended to the ``hidden operator'' \(T\). He then presents a detailed study of the isotopies of Bell's inequalities and achieves the remarkable result that they admit a well defined classical counterpart, a feature that is proved to be impossible for conventional quantum mechanics precisely by Bell's inequalities.