Results 1 - 10 of 13026
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[en] It is proved that the zero weight multiplicities and generalized exponents of the su(3)-algebra coincide with those predicted from the hypothesis of the existence of an integrity basis for the su(3)-submodules of the enveloping algebra of su(3).(author)
[en] Three aspects of the SU(3) fusion coefficients are revisited: the generating polynomials of fusion coefficients are written explicitly; some curious identities generalizing the classical Freudenthal–de Vries formula are derived; and the properties of the fusion coefficients under conjugation of one of the factors, previously analyzed in the classical case, are extended to the affine algebra at finite level.
[en] We study a subgroup Fr(162 × 4) of SU(3) of order 648 which is an extension of D(9, 1, 1; 2, 1, 1) and whose generators arise from anyonic systems. We show that this group is isomorphic to a semi-direct product (Z/18Z×Z/6Z)⋊S3 with respect to conjugation and we give a presentation of the group. We show that the group D(18, 1, 1; 2, 1, 1) from the series (D) in the existing classification for finite SU(3)-subgroups is also isomorphic to a semi-direct product (Z/18Z×Z/6Z)⋊S3, with respect to conjugation. We next exhibit the isomorphism between both groups. We prove that Fr(162 × 4) is not isomorphic to the exceptional SU(3) subgroup Σ(216 × 3) of the same order 648. We further prove that the only SU(3) finite subgroups from the 1916 classification by Blichfeldt or its extended version, in which Fr(162 × 4) may be isomorphic, belong to the (D)-series. Finally, we show that Fr(162 × 4) and D(18, 1, 1; 2, 1, 1) are both conjugate under the orthogonal matrix which we provide. (paper)
[en] The enigmatic properties of quarks have been described by introducing for them a new SU(3) degree of freedom, which is an exact symmetry, with the additional constraint that only states scalar under this new group, named SU/sub c/(3), can be observed. This assumption implies that quarks, which transform under SU/sub c/(3) as the fundamental representation, cannot be observed alone but only in pairs q anti q (mesons) or in triplets (baryons). This new degree of freedom accounts for the symmetry in the other quantum numbers of the baryon wave function and successfully explains (π0 → 2 γ) or reduces (R value) previous discrepancies. The purpose of this work is to show that the octonion algebra supplies a natural framework both for the SU(3) character of the new degree of freedom and for the nonobservability of nonsinglet states
[en] We present analytical results for the N_f"4 and N_f"3 terms of the five-loop Beta function, for a general gauge group. While the former term agrees with results available from large-N_f studies, the latter is new and extends the value known for SU(3) from an independent calculation.
[en] The Clebsch-Gordan coefficients of SU(3) are useful in calculations involving baryons and mesons, as well as in calculations involving arbitrary numbers of quarks. For the latter case, one needs the coupling constants between states of nonintegral hypercharges. The existing published tables are insufficient for many such applications, and therefore this collection has been compiled. This report supplies the isoscalar factors required to reconstruct the Clebsch-Gordan coefficients for a large set of products of representations. 15 refs., 5 tabs
[en] A representation of the exceptional Lie algebras reflecting a simple unifying view, based on realizations in terms of Zorn-type matrices, is presented. The role of the underlying Jordan pair and Jordan algebra content is crucial in the development of the structure. Each algebra contains three Jordan pairs sharing the same Lie algebra of automorphisms and the same external su(3) symmetry. The applications in physics are outlined. (paper)
[en] This paper gives an explicit construction of the Feigin--Fuchs representations of the generalized parafermions associated with SU(n) and write down the screening charges for the parafermionic model of SU(3). The authors show that the two representations the authors use are equivalent to each other and to two other representations recently proposed