NDLI: Topology of the Symmetry Group of the Standard Model

Content Provider	Springer Nature Link
Author	Aguilar, M. A. Socolovsky, M.
Copyright Year	1999
Abstract	We study the topological structure of thesymmetry group of the standard model, G$_{SM}$ =U(1) × SU(2) × SU(3). Locally,G$_{SM}$ ≃ S$^{1}$ ×(S3)$^{2}$ × S$^{5}$. For SU(3), whichis an S$^{3}$-bundle over S$^{5}$ (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 SO$^{0}$(3, 1), the identity component of the Lorentz group, asubgroup of the symmetry group of several gauge theoriesof gravity.
Starting Page	2485
Ending Page	2509
Page Count	25
File Format	PDF
ISSN	00207748
Journal	International Journal of Theoretical Physics
Volume Number	38
Issue Number	10
e-ISSN	15729575
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	1999-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Physics Quantum Physics Mathematical and Computational Physics Elementary Particles, Quantum Field Theory
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy Mathematics

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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