scispace - formally typeset
Journal ArticleDOI: 10.1007/BF02846949

A q deformation of Gell-Mann-Okubo mass formula

01 Mar 1996-Pramana (Springer Science and Business Media LLC)-Vol. 46, Iss: 3, pp 223-227
Abstract: We explore the possibility of deforming Gell-Mann-Okubo (GMO) mass formula within the framework of a quantized enveloping algebra. A small value of the deformation parameter is found to provide a good fit to the observed mass spectra of theπ, K andη mesons.

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References
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Journal ArticleDOI: 10.1007/BF01217730
Edward Witten1Institutions (1)
Abstract: It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms. In this version, the Jones polynomial can be generalized fromS 3 to arbitrary three manifolds, giving invariants of three manifolds that are computable from a surgery presentation. These results shed a surprising new light on conformal field theory in 1+1 dimensions.

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Topics: Bracket polynomial (71%), HOMFLY polynomial (68%), Jones polynomial (67%) ...read more

4,727 Citations


Journal ArticleDOI: 10.1007/BF00704588
Michio Jimbo1Institutions (1)
Abstract: Aq-difference analogue of the universal enveloping algebra U(g) of a simple Lie algebra g is introduced. Its structure and representations are studied in the simplest case g=sl(2). It is then applied to determine the eigenvalues of the trigonometric solution of the Yang-Baxter equation related to sl(2) in an arbitrary finite-dimensional irreducible representation.

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Topics: Universal enveloping algebra (64%), (g,K)-module (64%), Filtered algebra (61%) ...read more

2,730 Citations


Open accessJournal ArticleDOI: 10.1007/BF01219077
Stanisław Lech Woronowicz1Institutions (1)
Abstract: The compact matrix pseudogroup is a non-commutative compact space endowed with a group structure. The precise definition is given and a number of examples is presented. Among them we have compact group of matrices, duals of discrete groups and twisted (deformed)SU(N) groups. The representation theory is developed. It turns out that the tensor product of representations depends essentially on their order. The existence and the uniqueness of the Haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived. The form of these relations differs from that in the group case. This is due to the fact that the Haar measure on pseudogroups is not central in general. The corresponding modular properties are discussed. The Haar measures on the twistedSU(2) group and on the finite matrix pseudogroup are found.

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Topics: Locally compact group (66%), Compact group (64%), Group algebra (63%) ...read more

1,844 Citations


Open accessJournal ArticleDOI: 10.1103/PHYSREV.175.2195
Murray Gell-Mann1, R. J. Oakes2, B. Renner1Institutions (2)
25 Nov 1968-Physical Review
Abstract: We investigate the behavior under SU3×SU3 of the hadron energy density and the closely related question of how the divergences of the axial-vector currents and the strangeness-changing vector currents transform under SU3×SU3. We assume that two terms in the energy density break SU3×SU3 symmetry; under SU3 one transforms as a singlet, the other as the member of an octet. The simplest possible behavior of these terms under chiral transformations is proposed: They are assigned to a single (3,3*)+(3*,3) representation of SU3×SU3 and parity together with the current divergences. The commutators of charges and current divergences are derived in terms of a single constant c that describes the strength of the SU3-breaking term relative to the chiral symmetry-breaking term. The constant c is found not to be small, as suggested earlier, but instead close to the value (-sqrt[2]) corresponding to an SU2×SU2 symmetry, realized mainly by massless pions rather than parity doubling. Some applications of the proposed commutation relations are given, mainly to the pseudoscalar mesons, and other applications are indicated.

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Topics: Pseudoscalar (53%), Parity (physics) (51%), Pion (51%) ...read more

1,414 Citations


Journal ArticleDOI: 10.1016/0370-2693(90)90845-W
Thomas Curtright1, Cosmas K. Zachos2Institutions (2)
28 Jun 1990-Physics Letters B
Abstract: We find explicit functionals that map SU(2) algebra generators to those of several quantum deformations of that algebra, as well as their SU(1, 1) analogs. We explain how any such quantized algebra can be mapped to any other, and how representations of any such algebra can be expressed as simple functions of SU(2) representations. We also discuss comultiplication rules, and explore quantum deformations of the Virasoro algebra.

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Topics: Algebra representation (70%), Current algebra (69%), Cellular algebra (68%) ...read more

314 Citations