Loops

Edit and compile if you like:

\documentclass{standalone}

\usepackage{tikz-feynman}

\begin{document}
$\displaystyle\partial_t \frac{\partial^2 V}{\partial^2 \chi}
  = \raisebox{0.5ex}{\feynmandiagram [inline=(a.base)] {
  a [dot] -- [charged boson, quarter left, edge label=$q$] b
  -- [photon, quarter left] c [dot]
  -- [charged boson, quarter left, edge label=$q$] d [crossed dot]
  -- [charged boson, quarter left, edge label=$q$] a,
  f1 -- c,
  i1 -- a,
  };}
  \enskip+\enskip
  \raisebox{0.5ex}{\feynmandiagram [inline=(a.base)] {
  {i1, i2} -- a [dot]
  -- [charged boson, half left, edge label=$q$] b [crossed dot]
  -- [charged boson, half left, edge label=$q$] a,
  };}$
\end{document}