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We investigate the operator -\Delta-lpha\delta (x-\Gamma) in -\Delta-lpha\delta (x-\Gamma) , where -\Delta-lpha\delta (x-\Gamma) is a smooth surface which is either compact or periodic and satisfies suitable regularity requirements. We find an asymptotic expansion for the lower part of the spectrum as -\Delta-lpha\delta (x-\Gamma) which involves a``two-dimensional''comparison operator determined by the geometry of the surface -\Delta-lpha\delta (x-\Gamma) . In the compact case the asymptotics concerns negative eigenvalues, in the periodic case Floquet eigenvalues. We also give a bandwidth estimate in the case when a periodic -\Delta-lpha\delta (x-\Gamma) decomposes into compact connected components. Finally, we comment on analogous systems of lower dimension and other aspects of the problem.

A construction of conservation laws for -models in two dimensions is generalized in the framework of noncommutative geometry of commutative algebras. This is done by replacing theordinary calculus of differential forms with other differentialcalculi and introducing an analogue of the Hodge operator on thelatter. The general method is illustrated with several examples.

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S-transformation is a unitary transformation accomplishing the main part of the diagonalization of the interaction Hamiltonian in strong coupling theories. For a compact symmetry group the action of the S-transformation on the integrals of motion is derived.