Spin semi-invariant expansion for the Kondo Hamiltonian: A simple derivation of the scaling laws

The first- and second-order scaling laws for the Kondo Hamiltonian are rederived using a bandwidth cut-off scaling procedure that requires simply the invariance of electronic self-energy near the Fermi surface. To this end the latter quantity is calculated up to fourth-order in perturbation theory using the spin semi-invariant diagrammatic expansion technique that ensures the validity of linked-cluster theorem. The essential details of this technique, which can be applied as well in the study of the corresponding Kondo-lattice model, are presented.