Abstract
The Friedel sum rule is generalized to relativistic systems of spin-$\frac{1}{2}$ particles in two dimensions. The change in energy due to the presence of an impurity is studied. The relation of the sum rule with the relativistic Levinson theorem is presented. Density oscillations in such systems are discussed. Since the Friedel theorem has been of major importance in understanding the impurity scattering in materials, the present results would be helpful to explain some phenomena in two-dimensional fermionic many body systems.
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