Ngtjyty

I'd like to typeset equations like:

I have tried this with the tikz-feynman library, but the diagrams generated by it are just way too large, even with the small option (and also just look awkward). Optimally, I want to type simple diagrams even inline with the text, so that I can avoid awkwardly describing the diagram or using a lot of space and breaking the flow of the document to display the diagram.

AFAIK you do not get bent arrows with tikz-feynman. And since you seem not to need the graph drawing algorithms (and since they cannot be uploaded to the arXv), you may just work with plain TikZ.

documentclass{article}

usepackage{amsmath}

usepackage{mathrsfs}

usepackage{tikz}

usetikzlibrary{arrows.meta,bending,decorations.markings}

% from https://tex.stackexchange.com/a/430239/121799

tikzset{% inspired by https://tex.stackexchange.com/a/316050/121799

    arc arrow/.style args={%

    to pos #1 with length #2}{

    decoration={

        markings,

         mark=at position 0 with {pgfextra{%

         pgfmathsetmacro{tmpArrowTime}{#2/(pgfdecoratedpathlength)}

         xdeftmpArrowTime{tmpArrowTime}}},

        mark=at position {#1-tmpArrowTime} with {coordinate(@1);},

        mark=at position {#1-2*tmpArrowTime/3} with {coordinate(@2);},

        mark=at position {#1-tmpArrowTime/3} with {coordinate(@3);},

        mark=at position {#1} with {coordinate(@4);

        draw[-{Triangle[length=#2,bend]}]       

        (@1) .. controls (@2) and (@3) .. (@4);},

        },

     postaction=decorate,

     },

fermion arc arrow/.style={arc arrow=to pos #1 with length 2.5mm},

Vertex/.style={fill,circle,inner sep=1.5pt},

insert vertex/.style={decoration={

        markings,

         mark=at position #1 with {node[Vertex]{};},

        },

     postaction=decorate}     

}

DeclareMathOperator{tr}{tr}

begin{document}



[mathscr{P}(varphi)=-sumlimits_{n=1}^inftytrleft(Delta L_12right)^2

=vcenter{hbox{begin{tikzpicture} 

 draw[thick,insert vertex=0,fermion arc arrow={0.55}] (0,0) arc(270:-90:0.6);

end{tikzpicture}}}+frac{1}{2}

vcenter{hbox{begin{tikzpicture} 

 draw[thick,insert vertex/.list={0,0.5}](0,0) arc(270:-90:0.6);

 draw[fermion arc arrow/.list={0.3,0.8}] (0,0) arc(270:-90:0.6);

end{tikzpicture}}}

+frac{1}{3}

vcenter{hbox{begin{tikzpicture} 

 draw[thick,insert vertex/.list={0,1/3,2/3}](0,0) arc(270:-90:0.6);

 draw[fermion arc arrow/.list={0.21,0.55,0.88}] (0,0) arc(270:-90:0.6);

end{tikzpicture}}}+dots

]



[

 G(x_1,dots x_n)=sumlimits_{m=0}^inftyfrac{1}{m!}!!

begin{tikzpicture}[baseline={(X.base)}]

 node[circle,draw,thick,inner sep=2pt] (X) at (0,0) {$n+m$};

 foreach X in {60,90,120}

  {draw[thick] (X:0.6) -- (X:0.9) node[Vertex]{};}

 foreach X in {-60,-80,-100,-120}

  {draw[thick] (X:0.6) -- (X:0.9);} 

 node[rotate=-30] at (-120:1.1){$x_1$};

 node[rotate=30] at (-60:1.1){$x_n$};

 node at (-90:1.1){$cdots$};

end{tikzpicture}

]

end{document}