{"id":1096,"date":"2022-01-17T16:34:44","date_gmt":"2022-01-17T07:34:44","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=1096"},"modified":"2024-08-06T17:04:20","modified_gmt":"2024-08-06T08:04:20","slug":"%e8%a3%9c%e8%b6%b3%ef%bc%9a%e5%ae%8c%e5%85%a8%e5%8f%8d%e5%af%be%e7%a7%b0%e3%81%aa-levi-civita-%e3%83%86%e3%83%b3%e3%82%bd%e3%83%ab","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%83%ad%e3%83%bc%e3%83%ac%e3%83%b3%e3%83%84%e5%a4%89%e6%8f%9b%e3%81%ab%e3%82%88%e3%82%89%e3%81%aa%e3%81%84%e7%9b%b8%e5%af%be%e8%ab%96%e3%81%ae%e7%90%86%e8%a7%a3\/%e9%9b%bb%e7%a3%81%e5%a0%b4%e3%81%ae%e5%a4%89%e6%8f%9b\/%e8%a3%9c%e8%b6%b3%ef%bc%9a%e5%ae%8c%e5%85%a8%e5%8f%8d%e5%af%be%e7%a7%b0%e3%81%aa-levi-civita-%e3%83%86%e3%83%b3%e3%82%bd%e3%83%ab\/","title":{"rendered":"\u88dc\u8db3\uff1a\u5b8c\u5168\u53cd\u5bfe\u79f0\u306a Levi-Civita \u30c6\u30f3\u30bd\u30eb"},"content":{"rendered":"<p>Levi-Civita \u30c6\u30f3\u30bd\u30eb\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u304f\u3002<\/p>\n<p>$$ \\varepsilon_{\\lambda \\mu \\nu \\rho}$$<!--more--><\/p>\n<p>\u300c\u5b8c\u5168\u53cd\u5bfe\u79f0\u300d\u3068\u306f\uff0c\u3069\u306e2\u3064\u306e\u6dfb\u5b57\u306e\u9806\u756a\u3092\u53d6\u308a\u66ff\u3048\u3066\u3082\u8ca0\u53f7\u304c\u3064\u304f\uff0c\u3068\u3044\u3046\u3044\u3046\u3053\u3068\u3067\u3042\u308b\u3002\u3053\u306e\u3053\u3068\u304b\u3089\uff0c4\u3064\u306e\u6dfb\u5b57 \\(\\lambda, \\mu, \\nu ,\\rho \\) \u306e\u3069\u308c\u3067\u30822\u3064\u304c\u540c\u3058\u3067\u3042\u308c\u3070\uff0c\u305d\u306e\u6210\u5206\u306f\u30bc\u30ed\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002\u306a\u305c\u306a\u3089\u3070\uff0c<br \/>\n$$\\varepsilon_{\\lambda {\\color{red}{\\mu}} \\nu {\\color{blue}{\\mu}}} = {\\color{red}{-}} \\varepsilon_{\\lambda {\\color{blue}{\\mu}} \\nu {\\color{red}{\\mu}}}, \\ \\therefore\\ \\varepsilon_{\\lambda \\mu \\nu \\mu} = 0$$<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\uff0cLevi-Civita \u30c6\u30f3\u30bd\u30eb\u306e\u6210\u5206\u306e\u3046\u3061\uff0c\u30bc\u30ed\u3067\u306a\u3044\u3082\u306e\u306f\u6dfb\u5b57\u304c\u5168\u3066\u7570\u306a\u3063\u3066\u3044\u308b\u5834\u5408\u306e\u307f\u3067\u3042\u308b\u3002\u305d\u3053\u3067<br \/>\n$$\\varepsilon_{0123} = +1$$ \u3068\u3057\uff0c\u6dfb\u5b57\u304c\u3053\u306e\u5076\u7f6e\u63db\uff08\u5076\u6570\u56de\u306e\u7f6e\u63db\uff09\u3067\u3042\u308b\u6210\u5206\u306f \\(+1\\)\uff0c\u5947\u7f6e\u63db\u3067\u3042\u308b\u3082\u306e\u306f \\(-1\\) \u306e\u5024\u3092\u3068\u308b\u3002\u305f\u3068\u3048\u3070<br \/>\n$$\\varepsilon_{0{\\color{red}{3}}2{\\color{red}{1}}} = {\\color{red}{-}} \\varepsilon_{0{\\color{red}{1}}2{\\color{red}{3}}} = -1$$<br \/>\n$$\\varepsilon_{1032} = {\\color{red}{-}}\\varepsilon_{{\\color{red}{01}}32} = {\\color{blue}{+}} \\varepsilon_{01{\\color{blue}{23}}} = +1$$<br \/>\n$$\\varepsilon_{1230} = {\\color{red}{-}} 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