On 336 kissing spheres in 10 dimensions, 528 P-Brane states in 11 dimensions and the 60 elementary particles of the standard model

The paper gives a short outline of some interesting relations between sphere packing in higher dimensional spaces, the theory of P-Brane and the number of elementary particles in the standard model. In particular we show that the 336 independent components of the Riemann curvature tensor may be represented by the contact points of 336 nine-dimensional spheres with a single central sphere embedded in 10 dimensions. Subsequently we show that the number of states in the 11-dimensional P-Brane super gravity, namely 528 may be found from the number of the contact points by scale transformation involving the seven-dimensional sphere and 11-dimensional M theory. Finally by eliminating shadow particles and using Kappa-like invariance, the theoretical number of elementary particles to be expected at an energy scale close to that of electro weak unification is found to be N-(SM) = [(336)(11/7)]/8 = 66 Considering that there are at present only 60 experimentally confirmed particles, the result implies that there are some 6 particles still missing. (C) 2004 Elsevier Ltd. All rights reserved.