By Badiale M.

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Cliff(60 ) ≡ N times N Cliff(60 (n)) (153) n=1 as †-algebras. This case of the squad lemma is the hexad lemma. It shows how a huge squadron of prelocal anticommuting elementary processes can break up into a Maxwell-Boltzmann sequence of commuting hexads of local operations — the seed of classical space-time. Similar results obtain for any squad. 15 The spinors of V form the spinor N space Σ(N60 ) = N 1 80 = 80 . 15 Eight-component spinors have also been used in physics by Penrose [41], Robson and Staudte [44], and Lunsford [35]; though not to unify spin with space-time.

29 SIMPLIFYING EXTERNAL VARIABLES The compound symmetry group for the Dirac equation is the covering group of the Poincar´e group ISO(M). We represent this as the contraction of a simple group SO(3, 3) acting on the spinor pseudo-Hilbert (ket) space of 6N Clifford generators γ ω (n) (ω = 0, . . , 5; n = 1, . . , N) of the orthogonal group SO(3N, 3N). The size of the experiment fixes the parameter N. As in Dirac one-electron theory (where the spin generators are represented by second-degree elements h ¯ h ¯ (66) Sˆµν := [γ µ , γ ν ] ≡ γ µν , µ, ν = 0, .

I0 (1)], 54 (144) by two indices, an internal hexad index ω = 0, 1, 2, . . , 5 and an external hexad index n = 1, 2, . . , N. The generators iω (n) obey the usual Clifford algebraic relations {iω (n), iρ (n′ )} = +2δ(n, n′ )Gωρ (n), (145) with (Gωρ ) = (gµν ) 0 , 0 (δαβ ) +1 0 0 0 0 −1 0 0 , (gµν ) = 0 −1 0 0 0 0 0 −1 (δαβ ) = 1 0 , 0 1 (146) and are symmetric with respect to the metric Gωρ : iω (n)† = +iω (n). (147) Define the top element of each hexad, i↑ (n) := i5 (n) .