Giardino, S.
2014.
``Axisymmmetric empty space: light propagation, orbits and dark matter''. J. Mod. Phys.. 5(15):1402-1411.
AbstractThis study presents an axisymmetric solution of the Einstein equations for empty space. The geometry is studied by determining its Petrov classification and killing vectors. Light propagation, orbital motion and asymptotic and Newtonian limits are also studied. Additionally, cosmological applications of the geometry are also outlined as an alternative model for the inflationary universe and as a substitute for dark matter and quintessence.
Giardino, S, DeLeo S.
2014.
``Dirac solutions for quaternionic potentials''. J. Math. Phys.. 55(2):022301-10.
AbstractThe Dirac equation is solved for quaternionic potentials, i V0 + j W0 (V0∈ℝ,W0∈ℂ). The study shows two different solutions. The first one contains particle and anti-particle solutions and leads to the diffusion, tunneling, and Klein energy zones. The standard solution is recovered taking the complex limit of this solution. The second solution, which does not have a complex counterpart, can be seen as a V0-antiparticle or |W0|-particle solution.
Giardino, S.
2014.
``The Static String''. Mod. Phys. Lett.. A29(03):1450018.
AbstractIn this paper, the quantum fluctuation of a rigid and static string is reported to be identical to a free quantum particle. Solutions similar to this static string have already been found in the semiclassical quantization of pulsating strings, and our results show that the semiclassical quantization of pulsating strings is, in some cases, a perturbation of static strings. We also interpret the energy of the static string as a lower bound for the pulsating string and speculate about a description of quantum mechanics in terms of semiclassical string theory.