The Bethe Ansatz

\[ H_{LL} = \int_0^L dx \left\{ \partial_x \Psi^{\dagger}(x) \partial_x \Psi(x) + c \Psi^{\dagger}(x) \Psi^{\dagger}(x) \Psi(x) \Psi(x) \right \} \]

and the generalization to an arbitrary symmetry of the wavefunction.