ISSN:
1572-9575
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We study the topological structure of thesymmetry group of the 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 of thesespheres) we give a canonical gauge i.e., a canonical setof local trivializations. These formulas give explicitlythe matrices of SU(3) without using the Lie algebra (Gell-Mann matrices). Globally, we prove thatthe characteristic function of SU(3) is the suspensionof the Hopf map $$s^3 \underrightarrow hs^2$$ . We also study the case of SU(n) forarbitrary n, in particular the cases of SU(4), a flavor group, and of SU(5),a candidate group for grand unification. We show thatthe 2-sphere is also related to the fundamentalsymmetries of nature due to its relation to SO0(3, 1), the identity component of the Lorentz group, asubgroup of the symmetry group of several gauge theoriesof gravity.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1026649024484
