After the continuum field theory,
one can write the Hamiltonian as [1]}, [2]}, [3]}, [4]}, [5]},
\(\begin{split}H = \frac{v}{2} \int \left[ \frac{1}{K} {({\partial _x \phi (x) })}^2 +K {({\partial _x \theta (x) })}^2 \right] dx+ \frac{B}{\pi } \int cos(\sqrt{4 \pi } \phi (x)) dx - \frac{\Delta }{\pi } \int cos(\sqrt{4 \pi }\theta (x)) dx\\+ \frac{g_u}{2 {\pi }^2 } \int cos(4 \sqrt{\pi } \phi (x)) dx- \frac{\mu }{\sqrt{\pi }} \int \partial _x \phi (x) dx, \end{split}\) 

После теории поля в континууме, можно записать гамильтониан как [1], [2], [3], [4], [5]:

\(\begin{split}H = \frac{v}{2} \int \left[ \frac{1}{K} {({\partial _x \phi (x) })}^2 +K {({\partial _x \theta (x) })}^2 \right] dx+ \frac{B}{\pi } \int cos(\sqrt{4 \pi } \phi (x)) dx - \frac{\Delta }{\pi } \int cos(\sqrt{4 \pi }\theta (x)) dx\\+ \frac{g_u}{2 {\pi }^2 } \int cos(4 \sqrt{\pi } \phi (x)) dx- \frac{\mu }{\sqrt{\pi }} \int \partial _x \phi (x) dx. \end{split}\)