Theory of the quasi-one-dimensional electron gas with strong "on-site" interactions

It is shown that a quasi-one-dimensional system with strong attractive or repulsive coupling between electrons on the same site is equivalent to a Bose gas with hard core and longer-range interactions and to a Heisenberg-Ising magnet. Interchain and intrachain hopping and coupling are included and the equivalences are derived by elementary degenerate perturbation theory. Electronic correlation functions are derived from known pseudomagnetic ones and are used to discuss the circumstances in which superconductivity, charge- or spin-density wave transitions occur in the coupled chains.