="section level3">
<h3>The Hamiltonian</h3>
<p>The joint density <span class="math inline">\(p(\rho, \theta)\)</span> defines a Hamiltonian</p>
<p><span class="math display">\[
\begin{array}{rcl}
H(\rho, \theta) &amp; = &amp; - \log p(\rho, \theta)
\\[3pt]
&amp; = &amp; - \log p(\rho | \theta) - \log p(\theta).
\\[3pt]
&amp; = &amp; T(\rho | \theta) + V(\theta),
\end{array}
\]</span></p>
<p>where the term</p>
<p><span class="math display">\[
T(\rho | \theta) = - \log p(\rho | \theta)
\]</span></p>
<p>is cal