{"id":237,"date":"2022-01-05T15:40:37","date_gmt":"2022-01-05T06:40:37","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=237"},"modified":"2022-01-23T12:04:15","modified_gmt":"2022-01-23T03:04:15","slug":"%e3%82%a2%e3%82%a4%e3%83%b3%e3%82%b7%e3%83%a5%e3%82%bf%e3%82%a4%e3%83%b3%e3%81%ae%e8%a6%8f%e7%b4%84%e3%81%a8%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%ae%e5%86%85%e7%a9%8d","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e4%b8%80%e8%88%ac%e7%9b%b8%e5%af%be%e8%ab%96%e7%9a%84%e6%99%82%e7%a9%ba%e3%81%ae%e8%a1%a8%e3%81%97%e6%96%b9\/%e3%82%a2%e3%82%a4%e3%83%b3%e3%82%b7%e3%83%a5%e3%82%bf%e3%82%a4%e3%83%b3%e3%81%ae%e8%a6%8f%e7%b4%84%e3%81%a8%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%ae%e5%86%85%e7%a9%8d\/","title":{"rendered":"\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306e\u898f\u7d04\u3068\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d"},"content":{"rendered":"

\u8868\u793a\u306e\u7c21\u5358\u5316\u306e\u305f\u3081\uff0c
\n\\begin{equation}
\nx^1 \\equiv x,\\quad x^2\\equiv y,\\quad x^3 \\equiv z
\n\\end{equation}
\n\u306e\u3088\u3046\u306b\uff0c\u4e0a\u6dfb\u3048\u5b57\u30671\u756a\u76ee\uff0c2\u756a\u76ee\uff0c3\u756a\u76ee\u306e\u7a7a\u9593\u5ea7\u6a19\u3092\u8868\u3059\u3002\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u3082\u540c\u69d8\u306b\uff0c
\n\\begin{equation}
\n\\vec{e}_1\\equiv\\vec{e}_x,\\quad
\n\\vec{e}_2\\equiv\\vec{e}_y,\\quad
\n\\vec{e}_3 \\equiv \\vec{e}_z
\n\\end{equation}
\n\u3068\u3059\u308b\u3068\uff0c\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb<\/strong><\/span> \\(\\vec{r}\\) \u306f
\n\\begin{equation}
\n\\vec{r} = \\sum_{i=1}^3 x^i \\,\\vec{e}_i \\equiv x^i
\n\\,\\vec{e}_i
\n\\end{equation}
\n\u3068\u66f8\u3051\u308b\u3002\u6700\u5f8c\u306e\u8868\u8a18\u304c\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306e\u898f\u7d04<\/strong><\/span>\u3068\u547c\u3070\u308c\uff0c\u4e0a\u6dfb\u5b57\u3068\u4e0b\u6dfb\u5b57\u306b\u540c\u3058\u6587\u5b57 \\(i\\) \u304c\u3042\u3063\u305f\u3089\uff0c\u305f\u3068\u3048 \\(\\displaystyle\\sum\\) \u304c\u306a\u304f\u3066\u3082 \\(1\\) \u304b\u3089 \\(3\\) \u307e\u3067\u8db3\u3057\u3042\u3052\u308b\u3068\u3044\u3046\u7d04\u675f\u3067\u3042\u308b\u3002<\/p>\n

3\u6b21\u5143\u306e\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306e\u898f\u7d04<\/strong><\/span>\u3092\u8868\u3059\u683c\u8a00
\n\u4eba\u751f\u306b\u306f \\(i\\) \uff08\u30a2\u30a4\uff09\u304c\u5fc5\u8981\u3060\u3002\u305d\u308c\u3082\u30da\u30a2\u3067\u306d\u3002<\/strong><\/span><\/p>\n

\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306e\u898f\u7d04<\/strong><\/span>\u3092\u4f7f\u3063\u3066\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u3092\u66f8\u304f\u3068\u304d\uff0c\u601d\u3044\u3042\u307e\u3063\u3066
\n\\begin{equation}
\nr^2 = \\vec{r}\\cdot\\vec{r}
\n= \\left(x^i\\,\\vec{e}_i \\right)
\n\\cdot\\left(x^i\\,\\vec{e}_i \\right)\\quad \\mbox{\uff08\u4e0d\u9069\u5207\uff09}
\n\\end{equation}
\n\u3068\u66f8\u304d\u305d\u3046\u306b\u306a\u308b\u304c\uff0c\u3053\u308c\u306b\u3082\u683c\u8a00\u3092\u7528\u610f\u3057\u3066\u3042\u308b\u3002<\/p>\n

\u4eba\u751f\u306b \\(i\\) \uff08\u30a2\u30a4\uff09\u306f\u5fc5\u8981\u3060\u3002\u3057\u304b\u3057\u591a\u3059\u304e\u308b \\(i\\) \uff08\u30a2\u30a4\uff09\u306f\u30c8\u30e9\u30d6\u30eb\u306e\u5143\u3002<\/strong><\/span><\/p>\n

\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306e\u898f\u7d04<\/strong><\/span>\u306e\u76f8\u624b\u304c\u308f\u304b\u308b\u3088\u3046\u306b\uff0c\u7247\u65b9\u306e\u30c0\u30df\u30fc\u306e\u6dfb\u5b57\u3092 \\(j\\) \u306b\u5909\u3048\u3066
\n\\begin{eqnarray}
\nr^2 &=& \\left(x^i\\,\\vec{e}_i \\right)
\n\\cdot\\left(x^j\\,\\vec{e}_j \\right) \\\\
\n&=&\\vec{e}_i\\cdot\\vec{e}_j \\,x^i x^j \\\\
\n&\\equiv&
\n\\delta_{ij}\\,x^i x^j
\n\\end{eqnarray}
\n\u3068\u66f8\u304f\u306e\u304c\u9069\u5207\u3067\u3042\u308b\u3002\\(\\delta_{ij}\\) \u306f\u30af\u30ed\u30cd\u30c3\u30ab\u30fc\u306e\u30c7\u30eb\u30bf<\/strong><\/span>\u3067\u3042\u308a\uff0c3\u6b21\u5143\u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19\u7cfb\u3067\u306e\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u306e\u6210\u5206<\/strong><\/span>\u306b\u76f8\u5f53\u3059\u308b\u3002<\/p>\n

\\begin{equation} \\delta_{ij} = \\left \\{ \\begin{array}{cc} 1 & (i=j) \\\\\u00a0 0 & (i \\ne j) \\end{array} \\right.\\end{equation}<\/p>\n

\u6b21\u7bc0\u3067\u6539\u3081\u3066\u8ff0\u3079\u308b\u304c\uff0c\u4e00\u822c\u306b<\/p>\n

\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u306e\u6210\u5206\u3068\u306f\uff0c\u57fa\u672c\u30d9\u30af\u30c8\u30eb\u540c\u58eb\u306e\u5185\u7a4d\u3092\u8868\u3059<\/strong><\/span><\/p>\n

\u3068\u3044\u3046\u3053\u3068\u3060\u3051\u3092\u899a\u3048\u3066\uff0c\u3044\u3088\u3044\u30884\u6b21\u5143\u6642\u7a7a\u3078\u9032\u3082\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":0,"parent":67,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-237","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/237","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=237"}],"version-history":[{"count":11,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/237\/revisions"}],"predecessor-version":[{"id":1409,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/237\/revisions\/1409"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/67"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=237"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}