Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-12-14
J.Phys.A38:5359-5377,2005
Physics
High Energy Physics
High Energy Physics - Theory
33 pages
Scientific paper
10.1088/0305-4470/38/23/020
The structure of the observable algebra ${\mathfrak O}_{\Lambda}$ of lattice QCD in the Hamiltonian approach is investigated. As was shown earlier, ${\mathfrak O}_{\Lambda}$ is isomorphic to the tensor product of a gluonic $C^{*}$-subalgebra, built from gauge fields and a hadronic subalgebra constructed from gauge invariant combinations of quark fields. The gluonic component is isomorphic to a standard CCR algebra over the group manifold SU(3). The structure of the hadronic part, as presented in terms of a number of generators and relations, is studied in detail. It is shown that its irreducible representations are classified by triality. Using this, it is proved that the hadronic algebra is isomorphic to the commutant of the triality operator in the enveloping algebra of the Lie super algebra ${\rm sl(1/n)}$ (factorized by a certain ideal).
Jarvis Peter D.
Kijowski Jerzy
Rudolph Gerd
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