Semi-fermionic representation of SU(N) Hamiltonians

We represent the generators of the SU(N) algebra as bilinear combinations o f Fermi operators with imaginary chemical potential. The distribution funct ion, consisting of a minimal set of discrete imaginary chemical potentials, is introduced to satisfy the local constraints. This representation leads to the conventional temperature diagram technique with standard Feynman cod ex, except that the Matsubara frequencies are determined by neither integer nor half-integer numbers. The real-time Schwinger-Keldysh formalism is for mulated in the framework of complex equilibrium distribution functions for auxiliary semi-fermionic fields. We discuss the continuous large N and SU(2 ) large spin limits. We illustrate the application of this technique for ma gnetic and spin-liquid states of the Heisenberg model.