☰

¿Cómo puedo dibujar diagramas de bucle para la teoría de campo libre (física)?

tag-icon • tag-icon diagrams
¿Cómo puedo dibujar diagramas de bucle para la teoría de campo libre (física)?

diagrama de bucle

Tengo que dibujar las figuras que se muestran en la imagen. Estos son diagramas de bucle dentro de una ecuación.

Respuesta1

Aquí hay una colección de diagramas para la teoría de campos libres, proporcionados como phinman.sty(código al final de esta respuesta). Por motivos de espaciado, hay dos versiones de cada comando, una con etiquetas y otra sin ellas.

ingrese la descripción de la imagen aquí

El código para la demostración anterior:

\documentclass{article}
\usepackage{phinman} % pronounce like Feynman
\usepackage{amsmath}
\usepackage{lipsum}
\begin{document}
\begin{center}
\begin{tabular}{lc@{\quad}lc}
\verb"\PM{-}"    & \PM{-}    & \verb"\PMl{-}{x}{y}"          & \PMl{-}{x}{y}          \\
\verb"\PM{x}"    & \PM{x}    & \verb"\PMl{x}{x}"             & \PMl{x}{x}             \\
\verb"\PM{||}"   & \PM{||}   & \verb"\PMl{||}{u}{v}{x}{y}"   & \PMl{||}{u}{v}{x}{y}   \\
\verb"\PM{=}"    & \PM{=}    & \verb"\PMl{=}{u}{v}{x}{y}"    & \PMl{=}{u}{v}{x}{y}    \\
\verb"\PM{X}"    & \PM{X}    & \verb"\PMl{X}{u}{v}{x}{y}"    & \PMl{X}{u}{v}{x}{y}    \\
\verb"\PM{--}"   & \PM{--}   & \verb"\PMl{--}{x}{y}"         & \PMl{--}{x}{y}         \\
\verb"\PM{-o-}"  & \PM{-o-}  & \verb"\PMl{-o-}{x}{y}{z}"     & \PMl{-o-}{x}{y}{z}     \\
\verb"\PM{8}"    & \PM{8}    & \verb"\PMl{8}{x}"             & \PMl{8}{x}             \\
\verb"\PM{88}"   & \PM{88}   & \verb"\PMl{88}{x}{y}"         & \PMl{88}{x}{y}         \\
\verb"\PM{ooo}"  & \PM{ooo}  & \verb"\PMl{ooo}{x}{y}"        & \PMl{ooo}{x}{y}        \\
\verb"\PM{-8-}"  & \PM{-8-}  & \verb"\PMl{-8-}{x}{y}{z}"     & \PMl{-8-}{x}{y}{z}     \\
\verb"\PM{-88-}" & \PM{-88-} & \verb"\PMl{-88-}{x}{u}{v}{y}" & \PMl{-88-}{x}{u}{v}{y} \\
\verb"\PM{-ooo-}"& \PM{-ooo-}& \verb"\PMl{-ooo-}{x}{u}{v}{y}"& \PMl{-ooo-}{x}{u}{v}{y}\\
\verb"\PM{-o8-}" & \PM{-o8-} & \verb"\PMl{-o8-}{x}{u}{v}{y}" & \PMl{-o8-}{x}{u}{v}{y}
\end{tabular}
\end{center}
\clearpage
\lipsum[1]
\begin{align*}
  \PMl{-}{x}{y}         & = i\Delta(x,y)\\
  \PMl{x}{y}            & = -i\lambda\\
  \langle\phi(x_1)\phi(x_2)\phi(x_3)\phi(x_4)\rangle_0
                        &= \PMl{||}{x_1}{x_2}{x_3}{x_4} + \PMl{=}{x_1}{x_2}{x_3}{x_4}
                           + \PMl{X}{x_1}{x_2}{x_3}{x_4}\\
  \PMl{-o-}{x_1}{x_2}{y}&=\frac{-i\lambda}2\int\cdots\\
  \PMl{-8-}{x_1}{y}{x_2}&=\frac{-i\lambda}6i\Delta(x_1,x_2)\int\cdots\\
  \PMl{8}{y}            &=\frac{-i\lambda}6\int\cdots\\
  \text{denominator}    &=1+\PM{8}+\PM{88}+\PM{ooo}+\cdots\\
  \text{numerator}      &=\PM{--}+\PM{-8-}+\PM{-88-}+\PM{-ooo-}+\cdots\\
                        &\quad+\PM{-o-}+\PM{-o8-}+\cdots
\end{align*}
\lipsum[2]
\end{document}

El código del paquete phinman.sty(se pronuncia como Feynman):

\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{phinman}[2017/04/14 Diagrams for the free field theory]
\RequirePackage{tikz}
\newcommand\PMset{\pgfqkeys{/PM}}
\newcommand\PMldef[1]{\expandafter\def\csname PMl:#1\endcsname}
\newcommand\PMl[1]{\csname PMl:#1\endcsname}
\newcommand\PMdef[1]{\expandafter\def\csname PM:#1\endcsname}
\newcommand\PM[1]{\csname PM:#1\endcsname}
\newlength\PMu
\PMu=2ex

\PMset
  {dot/.style={circle,fill,draw,inner sep=0pt,outer sep=0pt,minimum size=2.5pt},
   line/.style={line width=0.6pt},
   ghostline/.style={line width=2pt,color=white}
  }

\newcommand\PMdot{node[/PM/dot]{}}
\newcommand\PMdotx[1]{node[/PM/dot,label={#1}]{}}
\newcommand\PMdota[1]{\PMdotx{[yshift=-0.5ex]above:{$#1$}}}
\newcommand\PMdotb[1]{\PMdotx{[yshift=0.5ex]below:{$#1$}}}
\newcommand\PMdotl[1]{\PMdotx{[xshift=0.5ex]left:{$#1$}}}
\newcommand\PMdotr[1]{\PMdotx{[xshift=-0.5ex]right:{$#1$}}}

\PMdef{-}%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,0) \PMdot -- (2\PMu,0)\PMdot;%
  }

\PMldef{-}#1#2%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,0) \PMdotb{#1} -- (2\PMu,0)\PMdotb{#2};%
  }

\PMdef{--}%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,0) \PMdot -- (4\PMu,0)\PMdot;%
  }

\PMldef{--}#1#2%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,0) \PMdotb{#1} -- (4\PMu,0)\PMdotb{#2};%
  }

\PMdef{x}%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,0) \PMdot
   (\PMu,\PMu) -- (-\PMu,-\PMu)
   (\PMu,-\PMu) -- (-\PMu,\PMu);%
  }

\PMldef{x}#1%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,0) \PMdotx{below:{$#1$}}
   (\PMu,\PMu) -- (-\PMu,-\PMu)
   (\PMu,-\PMu) -- (-\PMu,\PMu);%
  }

\PMdef{||}%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,\PMu) \PMdot -- (0,-\PMu) \PMdot
   (2\PMu,\PMu) \PMdot -- (2\PMu,-\PMu)\PMdot;%
  }

\PMldef{||}#1#2#3#4%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,\PMu) \PMdotl{#3} -- (0,-\PMu) \PMdotl{#4}
   (2\PMu,\PMu) \PMdotr{#1} -- (2\PMu,-\PMu)\PMdotr{#2};%
  }

\PMdef{=}%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,\PMu) \PMdot -- (2\PMu,\PMu) \PMdot
   (0,-\PMu) \PMdot -- (2\PMu,-\PMu)\PMdot;%
  }

\PMldef{=}#1#2#3#4%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,\PMu) \PMdotl{#3} -- (2\PMu,\PMu) \PMdotr{#1}
   (0,-\PMu) \PMdotl{#4} -- (2\PMu,-\PMu)\PMdotr{#2};%
  }

\PMdef{X}%
  {\tikz[baseline={(0,-0.5ex)}]%
    {\draw[/PM/line] (0,\PMu) \PMdot -- (2\PMu,-\PMu)\PMdot;
     \draw[/PM/ghostline] (0,-\PMu)-- (2\PMu,\PMu);
     \draw[/PM/line](0,-\PMu)\PMdot -- (2\PMu,\PMu) \PMdot;
    }%
  }

\PMldef{X}#1#2#3#4%
  {\tikz[baseline={(0,-0.5ex)}]%
    {\draw[/PM/line] (0,\PMu) \PMdotl{#3} -- (2\PMu,-\PMu)\PMdotr{#2};
     \draw[/PM/ghostline] (0,-\PMu)-- (2\PMu,\PMu);
     \draw[/PM/line](0,-\PMu)\PMdotl{#4}-- (2\PMu,\PMu) \PMdotr{#1};
    }%
  }

\PMdef{-o-}%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,0) \PMdot -- ++(2\PMu,0)\PMdot
   arc(-90:270:0.6\PMu) -- ++(2\PMu,0)\PMdot;%
  }

\PMldef{-o-}#1#2#3%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,0) \PMdotb{#1} -- ++(2\PMu,0)\PMdotb{#2}
   arc(-90:270:0.6\PMu) -- ++(2\PMu,0)\PMdotb{#3};%
  }

\PMdef{-8-}%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,0) \PMdot -- ++(4\PMu,0)\PMdot
   (2\PMu,0.8\PMu)\PMdot arc (0:360:0.6\PMu)
   arc (180:540:0.6\PMu);%
  }

\PMldef{-8-}#1#2#3%
  {\tikz[baseline={(0,0.5ex)}]\draw[/PM/line]
   (0,0) \PMdotb{#1} -- ++(4\PMu,0)\PMdotb{#3}
   (2\PMu,0.8\PMu)\PMdotx{above:{$#2$}} arc (0:360:0.6\PMu)
   arc (180:540:0.6\PMu);%
  }


\PMdef{-ooo-}%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,0) \PMdot -- ++(4\PMu,0)\PMdot
   (1.3\PMu,0.8\PMu)\PMdot arc (0:360:0.6\PMu)
   arc (180:360:0.6\PMu) \PMdot
   arc (180:540:0.6\PMu) arc (0:180:0.6\PMu);%
  }

\PMldef{-ooo-}#1#2#3#4%
  {\tikz[baseline={(0,0.5ex)}]\draw[/PM/line]
   (0,0) \PMdotb{#1} -- ++(4\PMu,0)\PMdotb{#4}
   (1.3\PMu,0.8\PMu)\PMdotx{above:{$#2$}} arc (0:360:0.6\PMu)
   arc (180:360:0.6\PMu) \PMdotx{above:{$#3$}}
   arc (180:540:0.6\PMu) arc (0:180:0.6\PMu);%
  }

\PMdef{8}%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,0) \PMdot arc (0:360:0.6\PMu)
   arc (180:540:0.6\PMu);%
  }

\PMldef{8}#1%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,0) \PMdotx{below:{$#1$}} arc (0:360:0.6\PMu)
   arc (180:540:0.6\PMu);%
  }

\PMdef{88}%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,-0.7\PMu) \PMdot arc (0:360:0.6\PMu) arc (180:540:0.6\PMu)
   (0,0.7\PMu) \PMdot arc (0:360:0.6\PMu) arc (180:540:0.6\PMu);%
  }

\PMldef{88}#1#2%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,-0.7\PMu) \PMdotx{below:{$#2$}} arc (0:360:0.6\PMu) arc (180:540:0.6\PMu)
   (0,0.7\PMu) \PMdotx{above:{$#1$}} arc (0:360:0.6\PMu) arc (180:540:0.6\PMu);%
  }

\PMdef{ooo}%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,0) \PMdot arc (0:360:0.6\PMu)
   arc (180:360:0.6\PMu) \PMdot
   arc (180:540:0.6\PMu) arc (0:180:0.6\PMu);%
  }

\PMldef{ooo}#1#2%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,0) \PMdotx{below:{$#1$}} arc (0:360:0.6\PMu)
   arc (180:360:0.6\PMu) \PMdotx{below:{$#2$}}
   arc (180:540:0.6\PMu) arc (0:180:0.6\PMu);%
  }

\PMdef{-88-}%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,-0.8\PMu) \PMdot arc (0:360:0.6\PMu) arc (180:540:0.6\PMu)
   (-2\PMu,0) \PMdot -- (2\PMu,0)\PMdot
   (0,0.8\PMu) \PMdot arc (0:360:0.6\PMu) arc (180:540:0.6\PMu);%
  }

\PMldef{-88-}#1#2#3#4%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,-0.8\PMu) \PMdotx{below:{$#3$}} arc (0:360:0.6\PMu) arc (180:540:0.6\PMu)
   (-2\PMu,0) \PMdotb{#1} -- (2\PMu,0)\PMdotb{#4}
   (0,0.8\PMu) \PMdotx{above:{$#2$}} arc (0:360:0.6\PMu) arc (180:540:0.6\PMu);%
  }


\PMdef{-o8-}%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,-0.8\PMu) \PMdot arc (0:360:0.6\PMu) arc (180:540:0.6\PMu)
   (-2\PMu,0) \PMdot -- (0,0) \PMdot
   arc (-90:270:0.6\PMu) -- (2\PMu,0)\PMdot;%
  }

\PMldef{-o8-}#1#2#3#4%
  {\tikz[baseline={(0,-0.5ex)}]\draw[/PM/line]
   (0,-1.5\PMu) \PMdotx{below:{$#3$}} arc (0:360:0.6\PMu) arc (180:540:0.6\PMu)
   (-2\PMu,0) \PMdotb{#1} -- (0,0) \PMdotb{#2}
   arc (-90:270:0.6\PMu) -- (2\PMu,0)\PMdotb{#4};%
  }


\endinput

Respuesta2

Puedes dibujarlo con Tikz. A continuación he creado un par de comandos para los símbolos en tu dibujo (probablemente puedas encontrar mejores nombres para ellos). Tuve que ajustar la altura 2ptmanualmente para alinear las líneas con los +carteles. Las lipsums son sólo para ver el espaciado vertical. Puedes ajustar la longitud de las líneas y el tamaño de los círculos.

\documentclass{article}
\usepackage{amsmath}
\usepackage{lipsum}
\usepackage{tikz}
\usetikzlibrary{calc,arrows}
\newcommand\SajadLineLength{15mm}
\newcommand\SajadCircleRadii{3mm}
\newcommand\SajadLine[2]{\tikz[baseline=-2pt]{%
    \draw[*-*](0,0) -- (\SajadLineLength,0)node[pos=0,below]{$#1$}node[pos=1,below]{$#2$};
  }}
\newcommand\SajadLineCircleMid[2]{\tikz[baseline=-2pt]{%
    \draw[*-*](0,0) -- (\SajadLineLength,0)node[pos=0,below]{$#1$}node[pos=1,below]{$#2$};
    \draw (0.5*\SajadLineLength,0) circle (\SajadCircleRadii);
  }}
\newcommand\SajadLineCircle[2]{\tikz[baseline=-2pt]{%
    \draw[*-*](0,0) -- (\SajadLineLength,0)node[pos=0,below]{$#1$}node[pos=1,below]{$#2$};
    \draw (0.5*\SajadLineLength,\SajadCircleRadii) circle (\SajadCircleRadii);
  }}
\newcommand\SajadLineDoubleCircle[2]{\tikz[baseline=-2pt]{%
    \draw[*-*](0,0) -- (\SajadLineLength,0)node[pos=0,below]{$#1$}node[pos=1,below]{$#2$};
    \draw (0.5*\SajadLineLength,\SajadCircleRadii) circle (\SajadCircleRadii);
    \draw (0.5*\SajadLineLength,3*\SajadCircleRadii) circle (\SajadCircleRadii);
  }}

\begin{document}
\lipsum[1]
\begin{displaymath}
  A=
  \SajadLine{x_1}{x_2} 
  +\SajadLineCircle{x_1}{x_2}
  +\SajadLineCircleMid{x_1}{x_2}
  +\SajadLineDoubleCircle{x_1}{x_2}
\end{displaymath}
\lipsum[2]
\end{document}

ingrese la descripción de la imagen aquí

información relacionada