{"id":409,"date":"2023-01-01T13:05:02","date_gmt":"2023-01-01T04:05:02","guid":{"rendered":"https:\/\/daba-no-heya.com\/?p=409"},"modified":"2025-08-18T21:02:14","modified_gmt":"2025-08-18T12:02:14","slug":"post-409","status":"publish","type":"post","link":"https:\/\/daba-no-heya.com\/?p=409","title":{"rendered":"\u30c6\u30f3\u30bd\u30eb"},"content":{"rendered":"\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/daba-no-heya.com\/?p=409\/#%E3%83%86%E3%83%B3%E3%82%BD%E3%83%AB%E3%81%AE%E5%AE%9A%E7%BE%A9\" >\u30c6\u30f3\u30bd\u30eb\u306e\u5b9a\u7fa9<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/daba-no-heya.com\/?p=409\/#%E5%85%B1%E5%A4%89%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E3%81%A8%E5%8F%8D%E5%A4%89%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E3%81%AE%E5%A4%89%E6%8F%9B%E5%89%87\" >\u5171\u5909\u30d9\u30af\u30c8\u30eb\u3068\u53cd\u5909\u30d9\u30af\u30c8\u30eb\u306e\u5909\u63db\u5247<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%83%86%E3%83%B3%E3%82%BD%E3%83%AB%E3%81%AE%E5%AE%9A%E7%BE%A9\"><\/span>\u30c6\u30f3\u30bd\u30eb\u306e\u5b9a\u7fa9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u30d9\u30af\u30c8\u30eb\u3092\u4e00\u822c\u5316\u3057\u305f\u3082\u306e\u3068\u3057\u3066\u3001\u5ea7\u6a19\u5909\u63db\u306b\u5bfe\u3057\u3066\u6b21\u306e\u3088\u3046\u306b\u632f\u308b\u821e\u3046\u91cf\u3092\u8003\u3048\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$\nT&#8217;^{\\mu_1\\cdots\\mu_p}_{\\qquad\\nu_1\\cdots\\nu_q}(x&#8217;)=\\frac{\\partial x&#8217;^{\\mu_1}}{\\partial x^{\\rho_1}}\\cdots\\frac{\\partial x&#8217;^{\\mu_p}}{\\partial x^{\\rho_p}}\\frac{\\partial x^{\\sigma_1}}{\\partial x&#8217;^{\\nu_1}}\\cdots\\frac{\\partial x^{\\sigma_q}}{\\partial x&#8217;^{\\nu_q}}T^{\\rho_1\\cdots\\rho_p}_{\\qquad\\sigma_1\\cdots\\sigma_q}(x)\n$$<\/p>\n\n\n\n<p>\u3053\u306e\u3088\u3046\u306b\u5909\u63db\u3059\u308b\u91cf$T^{\\rho_1\\cdots\\rho_p}_{\\qquad\\sigma_1\\cdots\\sigma_q}$\u306e\u3053\u3068\u3092$(p,q)$-<strong>\u30c6\u30f3\u30bd\u30eb<\/strong>(tensor)\u3068\u547c\u3073\u307e\u3059\u3002<br>\u6210\u5206\u306e\u6dfb\u5b57\u306e\u3046\u3061\u4e8c\u3064\u3092\u5165\u308c\u66ff\u3048\u3066\u3082\u5024\u304c\u5909\u308f\u3089\u306a\u3044\u3082\u306e\u3092\u5bfe\u79f0\u30c6\u30f3\u30bd\u30eb\u3001\u6dfb\u5b57\u306e\u3046\u3061\u306e\u4e8c\u3064\u3092\u5165\u308c\u66ff\u3048\u308b\u3068\u7b26\u53f7\u304c\u5909\u308f\u308b\u3082\u306e\u3092\u53cd\u5bfe\u79f0\u30c6\u30f3\u30bd\u30eb\u3068\u8a00\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%85%B1%E5%A4%89%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E3%81%A8%E5%8F%8D%E5%A4%89%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E3%81%AE%E5%A4%89%E6%8F%9B%E5%89%87\"><\/span>\u5171\u5909\u30d9\u30af\u30c8\u30eb\u3068\u53cd\u5909\u30d9\u30af\u30c8\u30eb\u306e\u5909\u63db\u5247<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u57fa\u5e95$\\frac{\\partial}{\\partial x^{\\mu}}$\u306e\u5185\u7a4d\u5024\u3092<\/p>\n\n\n\n<p>$$\n\\frac{\\partial}{\\partial x^{\\mu}}\\cdot\\frac{\\partial}{\\partial x^{\\nu}} \\equiv f(\\frac{\\partial}{\\partial x^{\\mu}},\\frac{\\partial}{\\partial x^{\\nu}})=f_{\\mu\\nu}\n$$<\/p>\n\n\n\n<p>\u3068\u8868\u3059\u3053\u3068\u306b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u66f8\u304d\u65b9\u3092\u4f7f\u3046\u3068\u3001\u53cc\u5bfe\u57fa\u5e95\u306e\u5b9a\u7fa9\u5f0f$dx^{\\mu}\\cdot\\frac{\\partial}{\\partial x^{\\nu}}=\\delta^{\\mu}_{\\;\\nu}$\u306f\u3001<\/p>\n\n\n\n<p>$$\ndx^{\\mu}\\cdot\\frac{\\partial}{\\partial x^{\\nu}}=f(dx^{\\mu},\\frac{\\partial}{\\partial x^{\\nu}})=\\delta^{\\mu}_{\\;\\nu}\n$$<\/p>\n\n\n\n<p>\u3068\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30c6\u30f3\u30bd\u30eb$f$\u306b\u95a2\u3059\u308b\u4e0a\u306e\u95a2\u4fc2\u5f0f\u3092\u7528\u3044\u308b\u3068\u3001\u5171\u5909\u30d9\u30af\u30c8\u30eb\u3068\u53cd\u5909\u30d9\u30af\u30c8\u30eb\u306e\u9593\u306e\u5909\u63db\u5247\u3092\u6c42\u3081\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>$V^{\\mu}(x)\\frac{\\partial}{\\partial x^{\\mu}}=V_{\\mu}(x)dx^{\\mu}$\u306e\u4e21\u8fba\u3068\u5225\u306e\u30d9\u30af\u30c8\u30eb$W=W^{\\nu}\\frac{\\partial}{\\partial x^{\\nu}}$\u3068\u306e\u5185\u7a4d\u3092\u3068\u308b\u3068\u3001<\/p>\n\n\n\n<p>$$\n\\begin{align*}\n    &amp;f(V^{\\mu}\\frac{\\partial}{\\partial x^{\\mu}},W^{\\nu}\\frac{\\partial}{\\partial x^{\\nu}})=f(V_{\\mu}dx^{\\mu},W^{\\nu}\\frac{\\partial}{\\partial x^{\\nu}}) \\\\\n    &amp;\\Leftrightarrow V^{\\mu}W^{\\nu}f(\\frac{\\partial}{\\partial x^{\\mu}},\\frac{\\partial}{\\partial x^{\\nu}})=V_{\\mu}W^{\\nu}f(dx^{\\mu},\\frac{\\partial}{\\partial x^{\\nu}}) \\\\\n    &amp;\\Leftrightarrow V^{\\mu}W^{\\nu}f_{\\mu\\nu}=V_{\\mu}W^{\\mu}\n\\end{align*}\n$$<\/p>\n\n\n\n<p>\u3053\u306e\u5f0f\u304c\u4efb\u610f\u306e$W^{\\mu}$\u306b\u5bfe\u3057\u3066\u6210\u7acb\u3059\u308b\u306e\u3067\u3001$V^{\\mu}f_{\\mu\\nu}=V_{\\nu}$\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u3001$f_{\\mu\\nu}$\u306e\u9006\u884c\u5217$f^{\\mu\\nu}$\u3092$f^{\\mu\\nu}f_{\\nu\\rho}=\\delta^{\\mu}_{\\;\\rho}$<em>\u3067\u5c0e\u5165\u3059\u308b\u3068\u3001<\/em>$V^{\\mu}=V_{\\nu}f^{\\nu\\mu}$\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u307e\u3068\u3081\u308b\u3068\u3001\u5171\u5909\u30d9\u30af\u30c8\u30eb\u3068\u53cd\u5909\u30d9\u30af\u30c8\u30eb\u306e\u5909\u63db\u5247\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ \\left\\{ \\begin{aligned} V_{\\nu}&amp;=V^{\\mu}f_{\\mu\\nu} \\\\ V^{\\mu}&amp;=V_{\\nu}f^{\\nu\\mu} \\end{aligned} \\right. $$<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u30c6\u30f3\u30bd\u30eb\u306e\u5b9a\u7fa9 \u30d9\u30af\u30c8\u30eb\u3092\u4e00\u822c\u5316\u3057\u305f\u3082\u306e\u3068\u3057\u3066\u3001\u5ea7\u6a19\u5909\u63db\u306b\u5bfe\u3057\u3066\u6b21\u306e\u3088\u3046\u306b\u632f\u308b\u821e\u3046\u91cf\u3092\u8003\u3048\u307e\u3059\u3002 $$ T&#8217;^{\\mu_1\\cdots\\mu_p}_{\\qquad\\nu_1\\cdots\\nu_q}(x&#038;#82 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,10],"tags":[],"class_list":["post-409","post","type-post","status-publish","format-standard","hentry","category-9","category-10"],"_links":{"self":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/409","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=409"}],"version-history":[{"count":8,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/409\/revisions"}],"predecessor-version":[{"id":1604,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/409\/revisions\/1604"}],"wp:attachment":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=409"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=409"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=409"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}