According to Anderson ([1], p. 54) "the equivalent of BCS theory for a full
y spin-charge separated Luttinger liquid has not been formally worked out".
We consider a model for two one-dimensional spinning Luttinger liquids cou
pled via a Cooper tunnelling Hamiltonian. We show that the partition functi
on is the four-dimensional integral of an exponential whose exponent has an
extremal point obtained solving an anomalous non-BCS self-consistence equa
tion. If the extremal point is a global minimum the model is completely sol
ved by the saddle point theorem and the anomalous gap generation is proved.
We find that the Luttinger interaction enhances strongly T-c if the intrac
hain Luttinger interaction is much bigger than the interchain interaction.