Supersymmetric spin operators

We develop a supersymmetric representation of spin operators which unifies the Schwinger and Abrikosov representations of $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ spin operators, allowing a second-quantized treatment of representations of the $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ group with both symmetric and antisymmetric character. By applying this to the $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ Kondo model, we show that it is possible to develop a controlled treatment of both magnetism and the Kondo effect within a single large-N expansion.