A complete discussion of the anomalous conductance must include the ferromagnetic interaction proposed by [22]. According to [22], the emergence of the 0 . 7 conductance anomaly is due to ferromagnetic interactions. Since the effect of constraints takes into consideration the exclusion of double occupancy, which also holds for the ferromagnetic case, we believe that our results include, in a qualitative way, the results obtained in ref. [22]. The results reported by [22] show that in the presence of Zeeman magnetic field the 0 . 7 plateau evolves into a robust 0 . 5 plateau. In our case, the value of the conductance varies from 0 . 5 to 0 . 7 (in the absence of the Zeeman interaction). These values are determined by the function h ( x, d ) the temperature and length of the wire. In order to consider the effect of a Zeeman interaction, we observe that the Fermi velocity v is replaced by: v ↑ = v + Δ $_{2}$, v ↓ = v − Δ 2 where Δ = ( ¯ h $_{m$_{e}$}$) K$_{F}$ [ √ 1 + g$_{|}$$_{|}$µ$_{B}$B$_{|}$$_{|}$ E$_{F}$ − √ 1 − g$_{|}$$_{|}$µ$_{B}$B$_{|}$$_{|}$ E$_{F}$ ] represents the Zeeman interaction, K$_{F}$ = K ↑ $_{F}$+ K ↓ F 2 is the Fermi momentum, $^{B}$| | is the magnetic field and m$_{e}$ is the electronic mass. As a result, the Hamiltonian for the wire takes the form: This Hamiltonian must be accompanied by the constraint operator of exclusion of double occupancy. where Q Zeeman 1 ( x ) is the Bosonic constraint in the presence of the Zeeman interaction: The Hamiltonian and the constraint operator show that neither the spin current nor the charge current are conserved. For a finite repulsive interaction and next nearest neighbor, this problem has been studied in the past [37]. One finds two different Luttinger liquids for spin up and spin down, which give rise to two different conductances as functions of the spin polarization [37] (see equations (26 − 27) and figures (1 − 2) in reference [37]). 18 Q Zeeman 1 ( x ) = cos [2 K$_{F}$ x + √$_{2}$$_{πϑ}$$_{e}$$_{(}$$_{x}$$_{)] +}$$_{cos}$$_{[(}$ m$_{e}$ ¯ h )Δ x + √$_{2}$$_{πϑ}$$_{s}$$_{(}$$_{x}$$_{)];}$ Q Zeeman 1 ( x ) | F > = 0 (43) $^{Ψ}$↑( x $^{)Ψ}$↓( x ) | F > = 2 e − $_{i}$√$_{4}$$_{πϕ}$$_{e}$$_{(}$$_{x}$$_{)}$$_{Q}$$_{Zeeman}$ 1 ( x ) | F > = 0; − d 2 ≤ x ≤ d 2 (42) H$_{wire}$ = ∫ d 2 − d 2 dx ([ ¯ h ( v + Δ $_{2}$) 2 ( ∂$_{x}$$^{ϕ}$↑ ( x )) 2 + ( ∂$_{x}$$^{ϑ}$↑ ( x )) $^{2}$] + [ ¯ h ( v − Δ $_{2}$) 2 ( ∂$_{x}$$^{ϕ}$↓ ( x )) 2 + ( ∂$_{x}$$^{ϑ}$↓ ( x )) $^{2}$]) (41) 7. The effect of the Zeeman magnetic field