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Using the two-loop analysis and the background field method we demonstratethat the local pure scaling operators without derivatives in the Finkel'steinnonlinear sigma model can be constructed by straightforward generalization ofthe corresponding operators for the noninteracting case. These pure scalingoperators demonstrate multifractal behavior and describe mesoscopicfluctuations of the single-particle Green's function. We determine anomalousdimensions of all such pure scaling operators in the interacting theory withinthe two-loop approximation.

Mesoscopic fluctuations of the single-particle Green's function at Anderson transitions with Coulomb interaction