Contour Deformation

Propagator branch cuts, i.e. a continuum of singularities, along the real frequency axis extending from $\pm |\vec p|$ out to $\pm \infty$. Pulled from arxiv:1712.09863.

Edit and compile if you like:

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\documentclass[tikz]{standalone}
\usetikzlibrary{intersections,decorations.markings}
\begin{document}
\begin{tikzpicture}
  \node [style={circle,minimum width=4cm,fill=gray!20},draw=black,name path=A,decoration={markings,mark=at position 0.175 with {\arrow[ultra thick]{>}}},postaction={decorate}] at (0,0) (A) {};
  \node [style={circle,minimum width=1.2cm},name path=C] at (A.north east) (B) {};
  \filldraw (A) circle (2pt) node [above right] {0} (B) circle (2pt) node [right]{$w$};
  \node [above] at (A.north) (annotation) {$z$-contour};
  \draw [thick] (annotation.west) edge[out=180,in=120,->] ++(-0.4,-0.6);
  \node [style={circle,minimum width=4cm,fill=gray!20},draw=black,name path=C,decoration={markings,mark=at position 0.175 with {\arrow[ultra thick]{>}}},postaction={decorate}] at (6cm,0) (C) {};
  \node [style={circle,minimum width=1.2cm},name path=D] at (C.north east) (D) {};
  \filldraw (C) circle (2pt) node [above right] {0} (D) circle (2pt) node [right]{$w$};
  \node [above] at (C.north) (annotation) {$z$-contour};
  \draw [thick] (annotation.west) edge[out=180,in=120,->] ++(-0.4,-0.6);
  \node [style={circle,minimum width=4cm,fill=gray!20},name path=E] at (12cm,0) (E) {};
  \node [style={circle,minimum width=1.2cm,fill=gray!20},name path=F,decoration={markings,mark=at position 0.15 with {\arrow[ultra thick]{>}}},postaction={decorate}] at (E.north east) (F) {};
  \filldraw (E) circle (2pt) node [above right] {0} (F) circle (2pt) node [right]{$w$};
  % intersection points between circles E and F
  \path [name intersections={of = E and F}];
  \coordinate (EF1) at (intersection-1);
  \coordinate (EF2) at (intersection-2);
  % calculate angles from center of E/F to intersection points
  \pgfmathanglebetweenpoints{\pgfpointanchor{E}{center}}{\pgfpointanchor{EF1}{center}}
  \let\EEFone\pgfmathresult
  \pgfmathanglebetweenpoints{\pgfpointanchor{E}{center}}{\pgfpointanchor{EF2}{center}}
  \let\EEFtwo\pgfmathresult
  \pgfmathanglebetweenpoints{\pgfpointanchor{F}{center}}{\pgfpointanchor{EF1}{center}}
  \let\FEFone\pgfmathresult
  \pgfmathanglebetweenpoints{\pgfpointanchor{F}{center}}{\pgfpointanchor{EF2}{center}}
  \let\FEFtwo\pgfmathresult
 
 
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