Embedding Standard Model particles inside Cl(0,8) - Video 11/12 скачать в хорошем качестве

Embedding Standard Model particles inside Cl(0,8) - Video 11/12

We describe how Standard Model particles may be embedded inside Cl(0,8), and how they transform under our proposed action. We find that 229/252 (~91%) of the degrees of freedom transform in accordance with what we would expect from the Standard Model. Could it be possible to obtain this last 9%? Maybe. It might be possible to describe the missing right-handed leptons if we are able to break the electroweak block in a particular way. This would involve introducing a second octonionic imaginary unit, orthogonal to the first. Another way to say it: we introduce a quaternionic subalgebra. The introduction of such an additional imaginary unit might be expected upon the construction of a gauge theory, in the context of what's known as an "almost complex manifold". In the end, we would then have 8 real degrees of freedom left over in Cl(0,8). It would be ideal to be able to associate these with two Higgs fields: one transforming under SU(2)_L and the other under SU(2)_R. However, it is too early at this point to make this identification. NB: I misspoke at the end of this video when I said "left-handed Higgs" and "right-handed Higgs". I meant "active under SU(2)_L" and "active under SU(2)_R".