The Higgs––physical and number theoretical arguments for the necessity of a triple elementary particle in super symmetric spacetime

Die Elementarteilchen können mit den regulären Körpern in Platos “Timaios” verglichen werden. Sie sind die Urbilder, die Ideen der Materie. (Werner Heisenberg)A careful counting routine of all experimentally confirmed elementary particles plus the theoretically conjectured ones needed for a sound formulation of a mathematically consistent field theory is undertaken within a minimal N=1 super symmetric extension of the standard model of high energy physics. The number arrived at is subsequently linked to certain massless on shell representations connected to the quantized gravity interaction. Finally with the help of number theoretical arguments arising from a rigorous application of the formalism of transfinite Heterotic super string and E-infinity theory, we show that the proposed scheme would lack mathematical consistency and elegant simplicity unless we retain a postulated triplet which is logically identified as the H+, H− and H0 Higgs particles. Connections to the 11 dimensional M theory and Harariʹs extended “sub-quarks” theory is also discussed.