Spontaneous symmetry breaking in the colored Hubbard model

The Hubbard model is reformulated in terms of different "colored" fermion s pecies for the electrons or holes at different lattice sites. Antiferromagn etic ordering or d-wave superconductivity can thm be described in terms of translationally invariant expectation values for colored composite scaler f ields. A suitable mean field approximation for the two-dimensional colored Hubbard model shows indeed phases with antiferromagnetic ordering or d-wave superconductivity at low temperature. At low enough temperature the transi tion to the antiferromagnetic phase is of first order. The present formulat ion also allows an easy extension to more complicated microscopic interacti ons.