Skip to main content
Open Access Publications from the University of California

Structure, Classification, and Conformal Symmetry, of Elementary Particles over Non-Archimedean Space–Time

  • Author(s): Varadarajan, V. S.
  • Virtanen, Jukka
  • et al.

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 p-adic numbers, is explored. Both the Poincaré 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 p-adic fields and the impossibility of conformal symmetry of massive and eventually massive particles is proved.

Many UC-authored scholarly publications are freely available on this site because of the UC Academic Senate's Open Access Policy. Let us know how this access is important for you.

Main Content
Current View