E. Cartan’s and A. Connnes’ Supersymmetry and Differences of Understanding Physical Phenomena

Abstract

Einstein claimed that one cannot define global time, and proposed defining local time additionally. Such approach was adopted also by E. Cartan, in which fermions are described by spinors with 16 bases and interact with vectors with 8 bases, that consists of a couple of 4 dimensional vectors x i (i = 1, ···, 4) and x i (i = 1, ···, 4). In Cartan's theory, spinors and vectors transform by super symmetric transformations G 23 , G 12 , G 13 , G 123 and G 132 and bases of fermion spinors consist of ξ 0 ,ξ i (i = 1, ···, 4), ξ 1234 , ξ 234 , ξ 134 , ξ 124 , ξ 123 and ξ i,j (i /= j ∈{1,2,3,4}). Except G 23 , the transformations mix spinors and vectors, and operations of G 23 on spinors contain G 23 ξ 4 = ξ 0 and G 23 ξ 123 = ξ 1234 , and operations of G 23 on vectors contain G 23 x 4 = −x 4' and G 23 x 4' = −x 4 . Therefore, there are 14 independent spinor bases and 7 independent vector bases, which corresponds to the number of bases of the G 2 symmetry.From the bases of non-commutative geometry, Connes took two fibers from a point of S 3 basis, and on top of fibers allowed two times propagate following von Neumann algebra, but evolution of the system was assumed to be defined by one-parameter group of transformation. Steenrod stated that the S 7 symmetry can be regarded as S 3 symmetry covered over S 4 symmetry, which allows decomposition of S