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- Title
Structure, Classification, and Conformal Symmetry, of Elementary Particles over Non-Archimedean Space–Time.
- Authors
VARADARAJAN, V. S.; VIRTANEN, JUKKA
- 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 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.
- Subjects
PARTICLES (Nuclear physics); HYPOTHESIS; P-adic numbers; GALILEAN group; P-adic fields
- Publication
Letters in Mathematical Physics, 2009, Vol 89, Issue 3, p171
- ISSN
0377-9017
- Publication type
Article
- DOI
10.1007/s11005-009-0351-2