Effective action for strongly correlated fermions from functional integrals

The Hubbard model is investigated using functional integrals and a Hubbard-Stratonovich decomposition of the interaction term. Using a spin-space reference frame that fluctuates in time and space, the effective action both is spin-rotation invariant and exhibits the correct Hartree-Fock saddle point. For strong correlation the effective action for free carriers and spins coupled via a gauge field is obtained as a systematic expansion in t/U. The spiral state existing for small doping is discussed. The formalism allows straightforward generalization to intermediate and weak coupling.