Abstract
We extend the method of L. Schwartz [1] to classify elementary scalar particles in p-adic space time. Schwartz obtained the states of the elementary particles over real spacetime as tempered distributions on spacetime itself. We obtain the analogous description in p-adic spacetime. We introduce a natural notion of temperedness similar to one introduced by Harish-Chandra in the p-adic case and show that the invariant measures corresponding to the elementary particles are tempered.
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Virtanen, J., Weisbart, D. Elementary particles on p-adic spacetime and temperedness of invariant measures. P-Adic Num Ultrametr Anal Appl 6, 318–332 (2014). https://doi.org/10.1134/S2070046614040074
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DOI: https://doi.org/10.1134/S2070046614040074