Topology of the Symmetry Group of the Standard Model

摘要: We study the topological structure of thesymmetry group standard model, GSM =U(1) × SU(2) SU(3). Locally,GSM ≃ S1 ×(S3)2 S5. For SU(3), whichis an S3-bundle over S5 (and therefore a local product thesespheres) we give canonical gauge i.e., setof trivializations. These formulas explicitlythe matrices SU(3) without using Lie algebra (Gell-Mann matrices). Globally, prove thatthe characteristic function is suspensionof Hopf map \(s^3 \underrightarrow hs^2\). also case SU(n) forarbitrary n, in particular cases SU(4), flavor group, and SU(5),a candidate for grand unification. show 2-sphere related to fundamentalsymmetries nature due its relation SO0(3, 1), identity component Lorentz asubgroup symmetry several theoriesof gravity.