\documentclass{standalone}

\usepackage{tikz-feynman}

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