Inspired by the Monte-Carlo results [21, 22], we will compute the conductance for a one dimensional wire in the limit U = ∞ at finite temperature using the method of Dirac’s constraints. The limit U = ∞ gives rise to exclusion of double occupancy (this means that in the ground state the fermion occupation number takes only two values , zero or one ). Therefore, the statistics is similar to the statistics of spinless electrons. The exclusion of double occupancy is taken into consideration, by demanding that the ground state wave function | F > $^{must be annihilated by the pair operator Ψ}$↓( x $^{)Ψ}$↑( x ) | F > = 0 ( Ψ$_{σ}$( x ) is the single electron operator). Following Dirac [1, 8, 30], we learn that the constraints must be satisfied at any time. As a result, one generates a set of constraints which satisfy the equation Q$_{i}$ ( ⃗x ) | F > = 0 , i = 1 , 2 , 3 .. 

In the language of quantum mechanics this means that one has to find the wave function | F > which is annihilated by the set of constraints Q$_{i}$ ( ⃗x ) | F > = 0, i = 1 , 2 , 3 .. and is an eigenstate of the Hamiltonian H | F > = E | F > . When the commutator of the constraints [ Q$_{i}$ ( ⃗x ) , Q$_{j}$ ( ⃗ x ′ )] with i ̸ = j can be inverted, the commutation relations are modified to the Dirac commutators [8, 30]. As a result, the Heisenberg equation of motion for an observable A is modified from i ¯ h dA dt = [ A, H ] to i ¯ h dA dt = [ A, H ]$_{D}$ where [ A, H ]$_{D}$ is the Dirac commutator given by [ A, H ]$_{D}$ ≡ [ A, H ] − [ A, Q$_{1}$ ]([ Q$_{1}$, Q$_{2}$ ]) − $^{1}$[ Q$_{2}$, H ] − [ A, Q$_{2}$ ]([ Q$_{2}$, Q$_{1}$ ]) − $^{1}$[ Q$_{1}$, H ]. The presence of the constraints [ Q$_{1}$, Q$_{2}$ ] (in the Dirac commutator) modifies the Pauli statistics to the spinless electrons statistics. 

For U = ∞ , the Luttinger liquid at finite temperature is replaced by the incoherent Lut- tinger liquid characterized by the pinned spin excitations and propagating spinless electron. Therefore, only the electron current is conserved. As a result, when an electron with spin up or spin down is injected at one end of the wire, we find that the electron which reaches the other end of the wire has an arbitrary spin. The interactions are restricted to the wire and are absent in the leads. Therefore, the density in the wire corresponds to the spinless electron density which is half the density of the non-interacting electrons in the leads. This change of the density will modify the commutation equation for the Bosonic densities by a factor of two. The effect of this modification is observed at a finite temperature when a voltage difference is applied between the two reservoirs which are connected to the wire- leads system. The injected current from the reservoirs will be twice the transmitted current into the wire. The interface between the leads and wire randomizes the spin and causes the electrons to behave as spinless particles at finite temperatures in the wire. Therefore, the 

