The Lie algebra of area-preserving diffeomorphisms on closed membranes of arbitrary topology is investigated. On the basis of a harmonic decomposition we define the structure constants as well as two other tensors which appear in the supermembrane Lorentz generators. We derive certain identities between these tensors and analyze their validity when the areapreserving diffeomorphisms are approximated by SU(N). One of the additional tensors can then be identified with the invariant symmetric three-index tensor of SU(N), while the second has no obvious analog. We prove that the Lorentz generators are classically conserved in the light-cone gauge for arbitrary membrane topology, as a consequence of these tensor identities. This formulation allows a systematic study of the violations of Lorentz invariance in the SU(N) approximation.

In a model in which the gluon condensate is simulated by a stochastic background field we can evaluate the shift of the energy levels of heavy quarkonia due to the gluon condensate as a function of the correlation time of the background field. By introducing a correlation time for the quark system it is possible to decide whether the description by Shifman-Vainshtein-Zakharov sum rules or potential models is more appropriate.

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