1997
DOI: 10.2172/534536
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The geometry of SU(3)

Abstract: The group SU(3) is parameterized in terms of generalized "Euler angles". The differential operators of SU(3) corresponding to the Lie Algebra elements are obtained, the invariant forms are found, the group invariant volume element is found, and some relevant comments about the geometry of the group manifold are made.

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Cited by 16 publications
(57 citation statements)
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“…and by observation of the corresponding structure constants f ijk one can see the relationship in the algebra that can help generate the Cartan decomposition of SU (N ) (shown for SU (3) in [9] and for SU (4) in [1]). Knowledge of the structure constants allows us to define two subspaces of the SU (N ) group manifold hereafter known as K and P .…”
Section: Deriving the Euler Angle Parametrization For Su (N )mentioning
confidence: 99%
See 3 more Smart Citations
“…and by observation of the corresponding structure constants f ijk one can see the relationship in the algebra that can help generate the Cartan decomposition of SU (N ) (shown for SU (3) in [9] and for SU (4) in [1]). Knowledge of the structure constants allows us to define two subspaces of the SU (N ) group manifold hereafter known as K and P .…”
Section: Deriving the Euler Angle Parametrization For Su (N )mentioning
confidence: 99%
“…. , λ (N −1) 2 −1 }, combined with λ N 2 −1 and thus can be written as (see [1,9] 2 − 1 term Euler angle representation of the SU (N − 1) subgroup. Now, as for P , of the 2(N − 1) elements in L(P ) we chose the λ 2 analogue, λ X SU (N ) , for SU (N ) and write any element of P as…”
Section: Deriving the Euler Angle Parametrization For Su (N )mentioning
confidence: 99%
See 2 more Smart Citations
“…In example if in SU(3) we want to gauge the U (1) 2 abelian subgroup generated by λ 3 , λ 8 (Gell-Mann matrices), we can choose the following parametrization for g ∈ SU(3) [Byr97]: The deep reason that lies behind this property (differentiating symmetric and asymmetric deformations) is the fact that not only the currents used for the deformation are preserved (as it happens in both cases), but here their very expression is just modified by a constant factor. In fact, if we write the deformed metric as in Eq.…”
Section: A No-renormalization Theoremmentioning
confidence: 99%