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arXiv · 0905.1217

Structure, classifcation, and conformal symmetry, of elementary particles over non-archimedean space-time

V. S. Varadarajan·J. Virtanen
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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.

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V. S. Varadarajan, J. Virtanen. 2009-05-08. Structure, classifcation, and conformal symmetry, of elementary particles over non-archimedean space-time. https://doi.org/10.1007/s11005-009-0351-2

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