1. Introduction Advances in the physics of electronic devices requires the computation of the wave func- tion for confined geometries and strong interactions. A possible way to study such cases is the use of quantum constraints. A particular situation occurs in quantum wires when the short range electron-electron interaction is governed by a large repulsive Hubbard interac- tion. When this interaction obeys U → ∞ , double occupancy is prohibited. This problem, known in the literature as the Hubbard model at U = ∞ [2–8], can be studied using the method of Dirac’s constraints [1]. Interestingly the physics of quantum wire seems to depend on the electron-electron in- teractions [9–13]. The physics of electron-electron interactions in one-dimensional metals is described by a Luttinger liquid which replaces the traditional Fermi liquid description. For large Hubbard interactions, U → ∞ at finite temperatures, one obtains an incoherent Luttinger liquid [19, 20] characterized by magnetic excitations which are negligible in com- parison to the temperature. The physics of the Hubbard model at U → ∞ might be relevant for studies of the 0 . 7 conductance anomaly discovered in quantum wires [14–17]. Experiments suggest that the anomalous conductance is observed at low electronic densities [18] and short in wires [24]. Recent Monte Carlo simulations, performed in the limit of large Hubbard U and finite temperature, show that the one-dimensional conductance is anomalous [21]. In ref.[22], the one-dimensional itinerant electron model with ferromagnetic coupling has also been investigated. Performing a Monte-Carlo study, the authors in ref.[22] have found that the conductance in this case is anomalous as well . From the work of ref. [23], we know that a one dimensional model with nearest neighbor hopping elements and U → ∞ has a ferromagnetic ground state at zero temperature. The strongly interacting Hubbard model U = ∞ and the ferromagnetic interactions are both characterized by the exclusion of double occupancy. Therefore, it seems that the anomalous conductance reported by [21] and [22] might have the same origin. Experimentally, the anomalous conductance was observed in GaAs/AlGaAs at low elec- tronic density where the long range Coulomb interaction plays a significant role [25–27, 29]. In ref. [29], it has been shown that the long range Coulomb interactions in the limit of low electronic density drives the one dimensional wire to the U → ∞ limit. 2