AbstractWe will show that the Hopf map
$$S^{15} \xrightarrow{{S^7 }}S^8$$
admits a sourceless, topologically non-trivial gauge field. This result will be cast in the form of a solution to eight… Expand

It is shown that, despite the long lifetime of the QCD axion with respect to spontaneous decay into photon pairs, stimulated decay becomes significant above a minimum axion density and leads to extremely bright lasers, suggesting a possible link to the observed fast radio bursts.Expand

The use of non-Abelian discrete groups G as family symmetries is discussed in detail. Out of all such groups up to order g=31, the most appealing candidates are two subgroups of SU(2): the dicyclic… Expand

Standard calculations suggest that the entropy of our universe is dominated by black holes, whose entropy is of order their area in Planck units, although they comprise only a tiny fraction of its… Expand