From a8f2d7f58e68701f11404f12bdb02e65d5c63454 Mon Sep 17 00:00:00 2001
From: Remco de Boer <redeboer@gmx.com>
Date: Fri, 19 Mar 2021 14:15:29 +0100
Subject: [PATCH] docs: add Mandelstam variable illustration

---
 cspell.json                    |  6 ++-
 docs/theory/introduction.ipynb | 97 ++++++++++++++++++++++++++++++++++
 2 files changed, 102 insertions(+), 1 deletion(-)

diff --git a/cspell.json b/cspell.json
index 23aa3376..d5343472 100644
--- a/cspell.json
+++ b/cspell.json
@@ -84,6 +84,9 @@
         "doctests",
         "eval",
         "expertsystem",
+        "figsize",
+        "fontsize",
+        "frameon",
         "genindex",
         "graphviz",
         "htmlcov",
@@ -137,6 +140,7 @@
         "venv",
         "xlabel",
         "xlim",
-        "ylabel"
+        "ylabel",
+        "ylim"
     ]
 }
\ No newline at end of file
diff --git a/docs/theory/introduction.ipynb b/docs/theory/introduction.ipynb
index bdf693cf..07bd8fcb 100644
--- a/docs/theory/introduction.ipynb
+++ b/docs/theory/introduction.ipynb
@@ -192,6 +192,103 @@
    "source": [
     "## Isobar model"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Mandelstam variables"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "jupyter": {
+     "source_hidden": true
+    },
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "from feynman import Diagram\n",
+    "\n",
+    "fig, ax = plt.subplots(1, 3, figsize=(9, 3), frameon=False, tight_layout=True)\n",
+    "fig.patch.set_visible(False)\n",
+    "for a in ax:\n",
+    "    a.axis(\"off\")\n",
+    "    a.set_xlim(0, 1)\n",
+    "    a.set_ylim(0, 0.8)\n",
+    "\n",
+    "s_channel = Diagram(ax[0])\n",
+    "# Vertices\n",
+    "v_p1 = s_channel.vertex(xy=(0.1, 0.7), marker=\"\")\n",
+    "v_p2 = s_channel.vertex(v_p1.xy, dy=-0.6, marker=\"\")\n",
+    "v_p3 = s_channel.vertex(v_p1.xy, dx=0.8, marker=\"\")\n",
+    "v_p4 = s_channel.vertex(v_p3.xy, dy=-0.6, marker=\"\")\n",
+    "v1 = s_channel.vertex(v_p1.xy, dx=0.2, dy=-0.3, marker=\"\")\n",
+    "v2 = s_channel.vertex(v_p3.xy, dx=-0.2, dy=-0.3, marker=\"\")\n",
+    "# Lines\n",
+    "p1 = s_channel.line(v_p1, v1, arrow=False)\n",
+    "p2 = s_channel.line(v1, v_p2, arrow=False)\n",
+    "interaction = s_channel.line(v1, v2, style=\"dotted\", arrow=False)\n",
+    "e4 = s_channel.line(v2, v_p3, arrow=False)\n",
+    "e5 = s_channel.line(v_p4, v2, arrow=False)\n",
+    "# Labels\n",
+    "v_p1.text(\"$p_1$\", x=-0.06, y=0)\n",
+    "v_p2.text(\"$p_2$\", x=-0.06, y=0)\n",
+    "v_p3.text(\"$p_3$\", x=+0.06, y=0)\n",
+    "v_p4.text(\"$p_4$\", x=+0.06, y=0)\n",
+    "s_channel.text(0.5, 0, \"$s$-channel\", fontsize=15)\n",
+    "s_channel.plot();\n",
+    "\n",
+    "t_channel = Diagram(ax[1])\n",
+    "# Vertices\n",
+    "v_p1 = t_channel.vertex(xy=(0.1, 0.7), marker=\"\")\n",
+    "v_p2 = t_channel.vertex(v_p1.xy, dy=-0.6, marker=\"\")\n",
+    "v_p3 = t_channel.vertex(v_p1.xy, dx=0.8, marker=\"\")\n",
+    "v_p4 = t_channel.vertex(v_p3.xy, dy=-0.6, marker=\"\")\n",
+    "v1 = t_channel.vertex(v_p1.xy, dx=0.4, dy=-0.15, marker=\"\")\n",
+    "v2 = t_channel.vertex(v_p2.xy, dx=0.4, dy=+0.15, marker=\"\")\n",
+    "# Lines\n",
+    "p1 = t_channel.line(v_p1, v1, arrow=False)\n",
+    "p2 = t_channel.line(v1, v_p3, arrow=False)\n",
+    "interaction = t_channel.line(v1, v2, style=\"dotted\", arrow=False)\n",
+    "e4 = t_channel.line(v2, v_p2, arrow=False)\n",
+    "e5 = t_channel.line(v_p4, v2, arrow=False)\n",
+    "# Labels\n",
+    "v_p1.text(\"$p_1$\", x=-0.06, y=0)\n",
+    "v_p2.text(\"$p_2$\", x=-0.06, y=0)\n",
+    "v_p3.text(\"$p_3$\", x=+0.06, y=0)\n",
+    "v_p4.text(\"$p_4$\", x=+0.06, y=0)\n",
+    "t_channel.text(0.5, 0, \"$t$-channel\", fontsize=15)\n",
+    "t_channel.plot();\n",
+    "\n",
+    "u_channel = Diagram(ax[2])\n",
+    "# Vertices\n",
+    "v_p1 = u_channel.vertex(xy=(0.1, 0.7), marker=\"\")\n",
+    "v_p2 = u_channel.vertex(v_p1.xy, dy=-0.6, marker=\"\")\n",
+    "v_p3 = u_channel.vertex(v_p1.xy, dx=0.8, marker=\"\")\n",
+    "v_p4 = u_channel.vertex(v_p3.xy, dy=-0.6, marker=\"\")\n",
+    "v1 = u_channel.vertex(v_p1.xy, dx=0.4, dy=-0.15, marker=\"\")\n",
+    "v2 = u_channel.vertex(v_p2.xy, dx=0.4, dy=+0.15, marker=\"\")\n",
+    "# Lines\n",
+    "p1 = u_channel.line(v_p1, v1, arrow=False)\n",
+    "p2 = u_channel.line(v1, v_p4, arrow=False)\n",
+    "interaction = u_channel.line(v1, v2, style=\"dotted\", arrow=False)\n",
+    "e4 = u_channel.line(v2, v_p2, arrow=False)\n",
+    "e5 = u_channel.line(v_p3, v2, arrow=False)\n",
+    "# Labels\n",
+    "v_p1.text(\"$p_1$\", x=-0.06, y=0)\n",
+    "v_p2.text(\"$p_2$\", x=-0.06, y=0)\n",
+    "v_p3.text(\"$p_3$\", x=+0.06, y=0)\n",
+    "v_p4.text(\"$p_4$\", x=+0.06, y=0)\n",
+    "u_channel.text(0.5, 0, \"$u$-channel\", fontsize=15)\n",
+    "u_channel.plot();"
+   ]
   }
  ],
  "metadata": {