Freudental magic square and its dimensional implication for α¯0≃137 and high energy physics

Modern theories of high energy physics are based in one way or another on Lie symmetry group's considerations. In particular the exceptional family plays a pivotal role in superstring and E-infinity theory. For a long time the very existence of the famous 5 exceptional Lie groups G2, F4, E6, E7 and E8 with dimensions 14; 52, 78, 133 and 248 was bizarre. Freudental magic square gives some reasons to believe that the exceptional groups are not that exceptional. In the present work we elaborate this point further still and show that the sum of the dimension of E8, E7 and E6 when adding the dimensions of the two grand unification groups SO(10) and SU(4) to them amounts to the number of states in Witten's p = 5 Brane model, namely 528. Furthermore when taking the standard model SU(3) SU(2) U(1) and an eight degrees of freedom Higgs field into account, the number rises to 4 multiplied with 137 of the inverse electromagnetic fine structure constant 528+12+8=4α¯0=(4)(137)=548. The general implications of these results for high energy physics are briefly discussed.