Structure, classifcation, and conformal symmetry, of elementary particles over non-archimedean space-time
Abstract
It is known that no length or time measurements are possible in sub-Planckian regions of spacetime. The Volovich hypothesis postulates that the micro-geometry of spacetime may therefore be assumed to be non-archimedean. In this letter, the consequences of this hypothesis for the structure, classification, and conformal symmetry of elementary particles, when spacetime is a flat space over a non-archimedean field such as the -adic numbers, is explored. Both the Poincar\'e and Galilean groups are treated. The results are based on a new variant of the Mackey machine for projective unitary representations of semidirect product groups which are locally compact and second countable. Conformal spacetime is constructed over -adic fields and the impossibility of conformal symmetry of massive and eventually massive particles is proved.
Keywords
Cite
@article{arxiv.0905.1217,
title = {Structure, classifcation, and conformal symmetry, of elementary particles over non-archimedean space-time},
author = {V. S. Varadarajan and J. Virtanen},
journal= {arXiv preprint arXiv:0905.1217},
year = {2009}
}