Geometric models of matter
Abstract
Inspired by soliton models, we propose a description of static particles in terms of Riemannian 4manifolds with selfdual Weyl tensor. For electrically charged particles, the 4manifolds are noncompact and asymptotically fibred by circles over physical 3space. This is akin to the KaluzaKlein description of electromagnetism, except that we exchange the roles of magnetic and electric fields, and only assume the bundle structure asymptotically, away from the core of the particle in question. We identify the Chern class of the circle bundle at infinity with minus the electric charge and the signature of the 4manifold with the baryon number. Electrically neutral particles are described by compact 4manifolds. We illustrate our approach by studying the TaubNUT manifold as a model for the electron, the AtiyahHitchin manifold as a model for the proton, CP^2 with the FubiniStudy metric as a model for the neutron, and S^4 with its standard metric as a model for the neutrino.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 May 2012
 DOI:
 10.1098/rspa.2011.0616
 arXiv:
 arXiv:1108.5151
 Bibcode:
 2012RSPSA.468.1252A
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 38 pages, 4 figures