149 lines
4.2 KiB
Plaintext
149 lines
4.2 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"using Combinatorics"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"num_diagrams_small_form (generic function with 3 methods)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"function num_diagrams(m::Int, e::Int, u::Int = 0, t::Int = 0)\n",
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" n = e + u + t\n",
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" return Int(factorial(3n-3) / factorial(2n-1)) * binomial(m+3n-3, 3n-3) * factorial(m) * factorial(e) * factorial(u) * factorial(t)\n",
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"end\n",
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"\n",
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"function num_diagrams_small_form(m::Int, e::Int, u::Int = 0, t::Int = 0)\n",
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" n = e + u + t\n",
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" return Int(factorial(m+3n-3) / factorial(2n-1)) * factorial(e) * factorial(u) * factorial(t)\n",
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"end"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"8\n",
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"8\n"
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]
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}
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],
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"source": [
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"# Trident:\n",
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"println(num_diagrams(1, 2))\n",
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"println(num_diagrams_small_form(1, 2))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[2, 6, 24, 120, 720, 5040, 40320]\n",
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"[2, 6, 24, 120, 720, 5040, 40320]\n"
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]
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}
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],
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"source": [
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"# n-Photon Compton:\n",
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"println([num_diagrams(n, 1) for n in 2:8])\n",
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"println([num_diagrams_small_form(n, 1) for n in 2:8])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[2, 36, 1728, 158400, 23587200, 5181926400]\n",
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"[2, 36, 1728, 158400, 23587200, 5181926400]\n"
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]
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}
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],
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"source": [
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"# fermion scattering\n",
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"println([num_diagrams(0, n) for n in 2:7])\n",
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"println([num_diagrams_small_form(0, n) for n in 2:7])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"n=1, e=1, u=0, t=0 || m=0: 1 | m=1: 1 | m=2: 2 | m=3: 6 | m=4: 24 | m=5: 120\n",
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"n=2, e=1, u=1, t=0 || m=0: 1 | m=1: 4 | m=2: 20 | m=3: 120 | m=4: 840 | m=5: 6720\n",
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"n=2, e=2, u=0, t=0 || m=0: 2 | m=1: 8 | m=2: 40 | m=3: 240 | m=4: 1680 | m=5: 13440\n",
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"n=3, e=1, u=1, t=1 || m=0: 6 | m=1: 42 | m=2: 336 | m=3: 3024 | m=4: 30240 | m=5: 332640\n",
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"n=3, e=2, u=1, t=0 || m=0: 12 | m=1: 84 | m=2: 672 | m=3: 6048 | m=4: 60480 | m=5: 665280\n",
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"n=3, e=3, u=0, t=0 || m=0: 36 | m=1: 252 | m=2: 2016 | m=3: 18144 | m=4: 181440 | m=5: 1995840\n",
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"n=4, e=2, u=1, t=1 || m=0: 144 | m=1: 1440 | m=2: 15840 | m=3: 190080 | m=4: 2471040 | m=5: 34594560\n",
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"n=4, e=2, u=2, t=0 || m=0: 288 | m=1: 2880 | m=2: 31680 | m=3: 380160 | m=4: 4942080 | m=5: 69189120\n",
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"n=4, e=3, u=1, t=0 || m=0: 432 | m=1: 4320 | m=2: 47520 | m=3: 570240 | m=4: 7413120 | m=5: 103783680\n",
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"n=4, e=4, u=0, t=0 || m=0: 1728 | m=1: 17280 | m=2: 190080 | m=3: 2280960 | m=4: 29652480 | m=5: 415134720\n"
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]
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}
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],
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"source": [
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"# tables\n",
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"i = 0\n",
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"nums = [[1, 0, 0], [1, 1, 0], [2, 0, 0], [1, 1, 1], [2, 1, 0], [3, 0, 0], [2, 1, 1], [2, 2, 0], [3, 1, 0], [4, 0, 0]]\n",
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"for (e, u, t) in nums\n",
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" i += 1\n",
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" if (u + t + e == 0) continue end\n",
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" println(\"n=$(e + u + t), e=$e, u=$u, t=$t || m=0: $(num_diagrams(0, e, u, t)) | m=1: $(num_diagrams(1, e, u, t)) | m=2: $(num_diagrams(2, e, u, t)) | m=3: $(num_diagrams(3, e, u, t)) | m=4: $(num_diagrams(4, e, u, t)) | m=5: $(num_diagrams(5, e, u, t))\")\n",
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"end"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Julia 1.10.2",
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"language": "julia",
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"name": "julia-1.10"
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},
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"language_info": {
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"file_extension": ".jl",
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"mimetype": "application/julia",
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"name": "julia",
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"version": "1.10.2"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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