Pictures in LaTeX

DiagramToTikZ gives the pictures of DiagramPlot as TikZ code for a paper: a sum of tikzpictures, each with its weight, to be used in math mode. ExpressionToLaTeX gives the formula of the same expression.

The TikZ code

The self-energy of φ⁴ theory at first order:

Needs["FunctionalDiagrams`"]
DeclareSource[J]; DeclareField[phi, J]; DeclareSymmetric[D0]; DeclareCoupling[lambda];
Zb = Exp[1/2 IntegralOver[J[x] D0[x, y] J[y], {x, y}]];
phi4 = lambda/24 IntegralOver[phi[z]^4, {z}];
propagator = PerturbativeCorrelationFunction[Zb, {phi[a], phi[b]}, phi4, {1}];
sigma = AmputateExternalLegs[propagator, {a, b}, {D0}];
DiagramToTikZ[sigma, {a, b}]

\frac{1}{2}\,\begin{tikzpicture}[x=0.700cm, y=0.700cm, line width=0.700pt, baseline={([yshift=-0.6ex]0,0)}]
  \draw (0.000,0.000) arc[start angle=270.000, end angle=630.000, radius=0.280];
  \draw (0.000,0.000) -- (-0.600,0.000);
  \draw (0.000,0.000) -- (0.600,0.000);
  \fill (0.000,0.000) circle (0.064);
  \node[font=\small, inner sep=0pt, anchor=0] at (-0.690,0.000) {$a$};
  \node[font=\small, inner sep=0pt, anchor=180] at (0.690,0.000) {$b$};
\end{tikzpicture}

The code needs, in the preamble,

\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}

(for the wavy and zigzag lines; the pictures compile at any scale). Write the code to a file,

Export["sigma.tex", DiagramToTikZ[sigma, {a, b}], "Text"]

sigma.tex

and input it in math mode, where the pictures sit on the math axis, aligned with the signs and the weights:

The self-energy of $\phi^4$ theory at first order is
\[ \Sigma(a, b) = \input{sigma.tex} \]

DiagramToTikZ ignores the option "Appearance" of DiagramPlot: its code is for white pages. On a page that may be dark (a README, a wiki), put the picture on a white card.

Size and labels

The options of DiagramPlot work here too ("ExternalOrder", "LegDirections", "Couplings", ...); these set the look on the page:

option	value by default	what it sets
"Scale"	0.7	centimetres per unit of the drawing
"LineWidth"	Automatic: 0.7	the width of the lines in pt; arrow heads, dashes, waves and double lines follow it
"LabelFont"	"\\small"	the font command of the labels
"Labels"	{}	rules from labels to LaTeX, {a -> "x_1"}; by default x12 is written x₁₂, lambda λ, etabar η̄

SetOptions[DiagramToTikZ, "Scale" -> 0.5] changes a default for the session. The showcase uses "Scale" -> 0.34, "LineWidth" -> 0.42 and "LabelFont" -> "\\tiny" for its small pictures.

One picture at a time

"Output" -> "List" gives the pairs {weight, picture} as strings, to arrange them yourself (a table, an align environment, a sum broken over several lines):

pieces = DiagramToTikZ[sigma, {a, b}, "Output" -> "List"];
{Length[pieces], First[pieces[[1]]]}

{1, \frac{1}{2}}

The whole sum, as DiagramToTikZ gives it, puts \allowbreak between the terms: in inline math ($...$) a long sum breaks between two terms at the end of a line.

Formulas

ExpressionToLaTeX[sigma, "Names" -> {D0 -> "D_0"}]

-\frac{1}{2}\,\lambda\,D_0(a,a)\,\delta(a,b)

"Names" gives the LaTeX of heads (and of subexpressions), "Labels" that of labels, "Subscripts" the heads whose arguments are written as a subscript, ξ_p for xi[p]. The integrals are written with their variables as a subscript, the Grassmann products in their order. See the manual, sections Pictures and Formulas in LaTeX.