Bott Periodic factorization - Video 6/12 скачать в хорошем качестве

Bott Periodic factorization - Video 6/12

The Standard Model's unconstrained states amount to roughly 250 real degrees of freedom. However, this RCHO algebra we are interested in is only 64 real dimensional. One way out of this dilemma is to take a hint from Nature. That is, just as Nature builds up the human genome via sequences of only 4 bases (A,C,T,G), we will consider sequences of RCHO elements multiplying RCHO elements. This space forms a new algebra known as RCHO's 'multiplication algebra'. This multiplication algebra can be thought of as the complex Clifford algebra Cl(10). However, it is Cl(10) with extra division algebraic substructure. Incidentally, this additional division algebraic substructure allows for an interesting factorization. Cl(10) can be factorized as Cl(0,8), familiar from the Bott periodicity of real Clifford algebras, and complex Cl(2), familiar from the Bott periodicity of complex Clifford algebras. If we're lucky, this might relate to what John Baez and others call the Tenfold Way. The proposal here is to identify Cl(0,8) with the Standard Model's unconstrained degrees of freedom, and Cl(2) = Cl(3,0) with a spatial base manifold.