{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "24660f3b",
   "metadata": {},
   "source": [
    "# feynamp\n",
    "\n",
    "is a experimental package to demonstrate, that feynml + feynmodel can be used to generate amplitudes for Feynman diagrams. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "0bce9db4-fdac-4103-b9c5-8b81b8bbcca6",
   "metadata": {},
   "outputs": [],
   "source": [
    "from feynml import *\n",
    "import feynamp as fp\n",
    "from feynamp.momentum import *\n",
    "from feynmodel.interface.ufo import load_ufo_model\n",
    "from feynamp.form.color import *\n",
    "from feynamp.form.lorentz import *\n",
    "from feynamp.form.momentum import *\n",
    "from feynamp.amplitude import square\n",
    "from sympy.parsing.sympy_parser import parse_expr\n",
    "from sympy import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "cf2b34d9-c3a4-4906-b85e-6bc53ebd828e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: f78c0ce 'PDF' (394x394)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v1 = Vertex()\n",
    "v2 = Vertex()\n",
    "\n",
    "fd = FeynmanDiagram().add(\n",
    "    v1,v2,\n",
    "    Propagator(pdgid=21).connect(v1,v2),\n",
    "    Leg(pdgid=1).with_target(v1).with_incoming().with_momentum(Momentum(name=\"$p_a$\")),\n",
    "    Leg(pdgid=-1).with_target(v1).with_incoming().with_momentum(Momentum(name=\"$p_b$\")),\n",
    "    Leg(pdgid=2).with_target(v2).with_outgoing().with_momentum(Momentum(name=\"$k_a$\")),\n",
    "    Leg(pdgid=-2).with_target(v2).with_outgoing().with_momentum(Momentum(name=\"$k_b$\")),\n",
    ")\n",
    "fd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "74691d5c-08fc-4cf1-98d7-ad777247ba26",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: 073695c 'PDF' (394x394)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fd.with_rule(\" * { momentum-arrow : true ; momentum-arrow-sense : -1}\")\n",
    "#fd.with_style_property(\"momentum-arrow\",\"true\")\n",
    "#fd.with_style_property(\"momentum-arrow-sense\",1)\n",
    "set_missing_momenta(fd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "c7bb1c44-2315-42d9-a111-dd838bd43c98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: e442b7b 'PDF' (394x394)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fd.conjugated()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "4bb8b75c-2807-4f27-b082-1cebfa125b33",
   "metadata": {},
   "outputs": [],
   "source": [
    "fm = load_ufo_model(\"ufo_sm\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1e889a7-bd1e-4d3b-8401-811b6aca1b81",
   "metadata": {},
   "source": [
    "Feynman amplitude is by default represented as a string to allow easy manipulation, but can be converted to sympy and/or used in form. The definitions from UFO are used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "63f972d1-82d7-4b23-a99c-d5c3391109b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'complex(0,1)*G*T(GluOutPropagator79,ColLeg81,ColLeg80)*Gamma(MuOutPropagator79,SpinLeg81,SpinLeg80) * complex(0,1)*G*T(GluInPropagator79,ColLeg82,ColLeg83)*Gamma(MuInPropagator79,SpinLeg82,SpinLeg83) * VC(ColLeg80,Mom_p_a)*u(SpinLeg80,Mom_p_a) * VC(ColLeg81,Mom_p_b)*v(SpinLeg81,Mom_p_b) * VC(ColLeg82,Mom_k_a)*u_bar(SpinLeg82,Mom_k_a) * VC(ColLeg83,Mom_k_b)*v_bar(SpinLeg83,Mom_k_b) * da(GluInPropagator79,GluOutPropagator79)*Metric(MuInPropagator79,MuOutPropagator79)*Denom(+Mom_p_a+Mom_p_b,0)'"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a=fp.feynman_diagram_to_string(fd,fm)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "dcb60060-f937-4267-ac37-7ad84acbc445",
   "metadata": {},
   "outputs": [],
   "source": [
    "s2 = square([fd],fm,tag=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a6efe35-4e3b-450a-ac4c-5b29b2285f16",
   "metadata": {},
   "source": [
    "We are going to construct a single form script to perform all changes. Again as a string for ease."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "c10981c4-ddd3-4ae7-bf44-25d9927bcdf7",
   "metadata": {},
   "outputs": [],
   "source": [
    "fs = \"\"\n",
    "fs += get_gammas()\n",
    "fs += get_color()\n",
    "fs += get_kinematics()\n",
    "fs += get_onshell(fd,fm)\n",
    "fs += get_mandelstamm_2_to_2(fd,fm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "52b3d386-be65-4fe5-ae10-9cf1c5fab281",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'4*Den(Mom_p_a.Mom_p_a+2*Mom_p_a.Mom_p_b+Mom_p_b.Mom_p_b)^2*G^4*Nc*Cf*msu^2+4*Den(Mom_p_a.Mom_p_a+2*Mom_p_a.Mom_p_b+Mom_p_b.Mom_p_b)^2*G^4*Nc*Cf*mst^2'"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rs =apply(s2,fs)\n",
    "rs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3ab85c5-c755-4f74-9e08-774eb1730ce6",
   "metadata": {},
   "source": [
    "Denominators are treated separately for future loop support."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "2fd6f231-2c5e-409c-99e8-825426958f35",
   "metadata": {},
   "outputs": [],
   "source": [
    "result= apply_den(rs,get_onshell(fd,fm) + get_mandelstamm_2_to_2(fd,fm,replace_u=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "84bf1db5-d408-4903-b095-38f0e6451d6b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{4 G^{4} \\left(t^{2} + u^{2}\\right)}{9 s^{2}}$"
      ],
      "text/plain": [
       "4*G**4*(t**2 + u**2)/(9*s**2)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ret =simplify(parse_expr(result.replace(\"Mom_\",\"\").replace(\".\",\"_\").replace(\"^\",\"**\").replace(\"mss\",\"s\").replace(\"msu\",\"u\").replace(\"mst\",\"t\")))\n",
    "ret = simplify(ret.subs(\"Nc\",\"3\").subs(\"Cf\",\"4/3\"))/2/2/3/3 # average spins and colors\n",
    "ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "d8a252e9-6937-452f-b838-8510caa0c989",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{4 G^{4} \\left(t^{2} + u^{2}\\right)}{9 s^{2}}$"
      ],
      "text/plain": [
       "4*G**4*(t**2 + u**2)/(9*s**2)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Ellis stirling and weber QCD and collider physics Tab 7.1\n",
    "# https://feyncalc.github.io/FeynCalcExamplesMD/QCD/Tree/QiQibar-QjQjbar\n",
    "expected = simplify(parse_expr(\"4*G**4*(t**2+u**2)/(9 *s**2)\"))#.subs(\"s\",\"t+u\")\n",
    "expected"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "490f721b-7f3e-4722-a0d9-f05bd2af25a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compare\n",
    "ret.equals(expected)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "46785175-66a9-4a80-a7f8-77726719a6ec",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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