{"id":6194,"date":"2024-03-10T15:21:48","date_gmt":"2024-03-10T15:21:48","guid":{"rendered":"https:\/\/science-hub.click\/%E9%9B%BB%E7%A3%81%E3%83%86%E3%83%B3%E3%82%BD%E3%83%AB%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC\/"},"modified":"2024-03-10T15:21:48","modified_gmt":"2024-03-10T15:21:48","slug":"%E9%9B%BB%E7%A3%81%E3%83%86%E3%83%B3%E3%82%BD%E3%83%AB%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=6194","title":{"rendered":"\u96fb\u78c1\u30c6\u30f3\u30bd\u30eb\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"

\u5c0e\u5165<\/h2>
\u79d1\u5b66\u8ad6\u6587<\/b>\u30c6\u30f3\u30bd\u30eb\u306b\u3064\u3044\u3066<\/b><\/div>
\u4e00\u822c\u7684\u306a<\/div>

\u30c6\u30f3\u30bd\u30eb<\/p>

\u6570\u5b66<\/div>

\u30c6\u30f3\u30bd\u30eb (\u6570\u5b66)\u30c6\u30f3\u30bd\u30eb\u7a4d…2 \u3064\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u3046\u3061…2 \u3064\u306e\u7dda\u5f62\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u306e\u30c6\u30f3\u30bd\u30eb\u4ee3\u6570\u30c6\u30f3\u30bd\u30eb\u5834\u30c6\u30f3\u30bd\u30eb\u7a7a\u9593<\/p>

\u7269\u7406\u7684\u306a<\/a><\/span><\/div>

\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u5927\u4f1a\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u30a8\u30cd\u30eb\u30ae\u30fc\u904b\u52d5\u91cf\u30c6\u30f3\u30bd\u30eb\u30ea\u30fc\u30de\u30f3\u30c6\u30f3\u30bd\u30eb… by \u30ea\u30c3\u30c1…\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u8457…\u30ef\u30a4\u30eb\u3088\u308a… \u30ec\u30f4\u30a3\u30fb\u30c1\u30f4\u30a3\u30bf\u3088\u308a…\u6bba\u5bb3\u306b\u3088\u308a…by Killing-Yano …\u30d9\u30eb\u30fb\u30ed\u30d3\u30f3\u30bd\u30f3\u3088\u308a…\u30b3\u30c3\u30c8\u30f3\u30e8\u30fc\u30af\u3088\u308a\u96fb\u78c1\u30c6\u30f3\u30bd\u30eb<\/a><\/span><\/strong>\u5fdc\u529b\u30c6\u30f3\u30bd\u30eb\u3072\u305a\u307f\u30c6\u30f3\u30bd\u30eb<\/p>

\u95a2\u9023\u8a18\u4e8b<\/div>

\u30e2\u30b8\u30e5\u30fc\u30eb\u5c4b\u5916\u4ee3\u6570<\/p>

\u6570\u5b66\u30dd\u30fc\u30bf\u30eb<\/b><\/div>
\u7269\u7406\u30dd\u30fc\u30bf\u30eb<\/b><\/div><\/div>

\u96fb\u78c1\u30c6\u30f3\u30bd\u30eb<\/b>\u3001\u307e\u305f\u306f\u30de\u30af\u30b9\u30a6\u30a7\u30eb \u30c6\u30f3\u30bd\u30eb\u306f\u3001<\/b>\u7279\u5b9a\u306e\u70b9<\/a><\/span>\u306b\u304a\u3051\u308b\u96fb\u78c1\u5834<\/a><\/span>\u306e\u69cb\u9020\u3092\u8a18\u8ff0\u3059\u308b\u6570\u5b66\u7684<\/a><\/span>\u30aa\u30d6\u30b8\u30a7\u30af\u30c8<\/span>(\u30c6\u30f3\u30bd\u30eb) \u306e\u540d\u524d\u3067\u3059\u3002<\/p>

\n\"\u96fb\u78c1\u30c6\u30f3\u30bd\u30eb\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

\u610f\u5473<\/h2>

\u3053\u306e\u30c6\u30f3\u30bd\u30eb\u306f\u3001\u7279\u6b8a\u76f8\u5bfe\u6027\u7406\u8ad6<\/a><\/span>\u306e\u6570\u5b66\u7684\u5f62\u5f0f\u4e3b\u7fa9\u306e\u67a0\u7d44\u307f\u5185\u3067\u5b9a\u7fa9\u3055\u308c\u3001\u6642\u9593\u6b21\u5143\u304c<\/a><\/span>3 \u3064\u306e\u7a7a\u9593\u6b21\u5143\u306b\u8ffd\u52a0\u3055\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001Vector \u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306b\u306f 4 \u3064\u306e\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u304c\u3042\u308b\u305f\u3081\u3001 quadrivector<\/span>\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u96fb\u78c1\u30c6\u30f3\u30bd\u30eb\u306f 4×4 \u884c\u5217\u3068\u3057\u3066\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u305d\u306e\u8981\u7d20\u306f\u30d9\u30af\u30c8\u30eb<\/a><\/span>\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u3068\u547c\u3070\u308c\u308b 4 \u3064\u306e\u30d9\u30af\u30c8\u30eb (\u901a\u5e38\u306fA<\/i>\u3067\u8868\u3055\u308c\u307e\u3059) \u306b\u3088\u3063\u3066\u6c7a\u5b9a\u3055\u308c\u307e\u3059\u3002\u30de\u30af\u30b9\u30a6\u30a7\u30eb \u30c6\u30f3\u30bd\u30eb\u306f\u901a\u5e38F<\/i>\u3067\u8868\u3055\u308c\u3001\u6b21\u306e\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002 <\/p>

$$ {F_{ab} = \\partial_a A_b – \\partial_b A_a} $$<\/div> \u3002<\/dd><\/dl>

\u3053\u306e\u30c6\u30f3\u30bd\u30eb\u306f\u53cd\u5bfe\u79f0\u3067\u3042\u308a\u3001\u30c8\u30ec\u30fc\u30b9<\/a><\/span>\u306f\u30bc\u30ed\u3067\u3059\u3002<\/p>

\n\"\u96fb\u78c1\u30c6\u30f3\u30bd\u30eb\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

\u30c7\u30e5\u30a2\u30eb\u30c6\u30f3\u30bd\u30eb<\/h2>

\u96fb\u78c1\u30c6\u30f3\u30bd\u30eb\u306f\u53cd\u5bfe\u79f0\u306a\u306e\u3067\u30d0\u30a4\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u305d\u306e\u4e8c\u91cd\u30d0\u30a4\u30d9\u30af\u30c8\u30ebF<\/i> *<\/sup>\u3092\u6b21\u306e\u5f0f\u3067\u63a8\u5b9a\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>

$$ {F^*_{ab} = \\frac{1}{2} \\epsilon_{abcd} F^{cd}} $$<\/div> \u3001<\/dd><\/dl>

\u3053\u3053\u3067\u3001\u03b5 \u306f Levi-Civita \u30c6\u30f3\u30bd\u30eb\u3067\u3042\u308a\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {F_{ab}^{*\\;(+—)} = \\left(\\begin{array}{rrrr} 0 & c B^x & c B^y & c B^z \\\\ – c B^x & 0 & \\frac{1}{c} E^z & – \\frac{1}{c} E^y \\\\ – c B^y & – \\frac{1}{c} E^z & 0 & \\frac{1}{c} E^x \\\\ – c B^z & \\frac{1}{c} E^y & – \\frac{1}{c} E^x & 0 \\end{array}\\right)} $$<\/div> \u3001<\/dd><\/dl>

\u305d\u3057\u3066<\/p>

$$ {F_{ab}^{*\\;(-+++)} = \\left(\\begin{array}{rrrr} 0 & – c B^x & – c B^y & – c B^z \\\\ c B^x & 0 & – \\frac{1}{c} E^z & \\frac{1}{c} E^y \\\\ c B^y & \\frac{1}{c} E^z & 0 & – \\frac{1}{c} E^x \\\\ c B^z & – \\frac{1}{c} E^y & \\frac{1}{c} E^x & 0 \\end{array}\\right)} $$<\/div> \u3002<\/dd><\/dl>

\u3069\u3061\u3089\u306e\u5834\u5408\u3082\u3001\u53cc\u5bfe\u5316\u64cd\u4f5c\u306b\u3088\u308a\u3001\u96fb\u5834<\/a><\/span>E \u3092<\/b>c<\/i> B<\/b>\u306b\u3001\u78c1\u5834<\/a><\/span>B \u3092<\/b>– E<\/b> \/ c<\/i>\u306b\u5909\u63db\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>

\n\"\u96fb\u78c1\u30c6\u30f3\u30bd\u30eb\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u306e\u8868\u73fe<\/h2>

\u96fb\u78c1\u30c6\u30f3\u30bd\u30eb\u306b\u3088\u308a\u3001\u8377\u96fb\u7c92\u5b50\u306b\u4f5c\u7528\u3059\u308b\u30ed\u30fc\u30ec\u30f3\u30c4\u529b<\/a><\/span>\u3092\u518d\u8003\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u529b<\/a><\/span>f \u306f<\/b>\u6b21\u306e\u5f0f\u3092\u6301\u3061\u307e\u3059\u3002 <\/p>

$$ {{\\mathbf{f}} = q {\\mathbf{E}} + q {\\mathbf{v}} \\wedge {\\mathbf{B}}} $$<\/div> \u3002<\/dd><\/dl>

\u7279\u6b8a\u76f8\u5bfe\u6027\u7406\u8ad6\u3067\u306f\u3001\u305d\u306e\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>

f<\/i> a<\/i><\/sup> = q<\/i> F<\/i> a<\/i><\/sup> b<\/i><\/sub> u<\/i> b<\/i><\/sup><\/span> \u3001<\/dd><\/dl>

\u3053\u3053\u3067\u3001 u \u306f<\/i>\u8003\u616e\u3055\u308c\u3066\u3044\u308b\u7c92\u5b50\u306e\u56db\u4e57\u901f\u5ea6<\/span>\u3067\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19\u7cfb<\/a><\/span>\u3067\u30de\u30af\u30b9\u30a6\u30a7\u30eb \u30c6\u30f3\u30bd\u30eb\u306e\u6210\u5206\u3092\u518d\u69cb\u7bc9\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {F^a{}_b = \\left(\\begin{array}{rrrr} 0 & \\frac{1}{c^2} E^x & \\frac{1}{c^2} E^y & \\frac{1}{c^2} E^z \\\\ E^x & 0 & B^z & – B^y \\\\ E^y & – B^z & 0 & B^x \\\\ E^z & B^y & – B^x & 0 \\end{array}\\right)} $$<\/div> \u3002<\/dd><\/dl>

F<\/i>\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u306e\u5f0f\u306f\u3001\u4f7f\u7528\u3055\u308c\u308b\u30e1\u30c8\u30ea\u30c3\u30af\u306e\u7f72\u540d\u898f\u5247<\/span>\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002\u3053\u308c\u304c (+—) \u30bf\u30a4\u30d7\u3067\u3042\u308b\u4eee\u8aac\u3067\u306f\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {F_{ab}^{(+—)} = \\left(\\begin{array}{rrrr} 0 & E^x & E^y & E^z \\\\ – E^x & 0 & – B^z & B^y \\\\ – E^y & B^z & 0 & – B^x \\\\ – E^z & – B^y & B^x & 0 \\end{array}\\right)} $$<\/div> \u3002<\/dd><\/dl>

\u9006\u306e<\/a><\/span>\u5834\u5408\u3001\u898f\u5247 (-+++) \u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {F_{ab}^{(-+++)} = \\left(\\begin{array}{rrrr} 0 & – E^x & – E^y & – E^z \\\\ E^x & 0 & B^z & – B^y \\\\ E^y & – B^z & 0 & B^x \\\\ E^z & B^y & – B^x & 0 \\end{array}\\right)} $$<\/div> \u3002<\/dd><\/dl>

\u96fb\u5834E<\/i>\u3068\u78c1\u5834B \u3092<\/i>\u30d9\u30af\u30c8\u30eb\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u306e\u95a2\u6570\u3068\u3057\u3066\u8868\u73fe\u3059\u308b\u3068\u3001\u3053\u308c\u3089 2 \u3064\u306e\u8868\u8a18\u6cd5\u306e\u9055\u3044\u306f\u306a\u304f\u306a\u308a\u307e\u3059\u3002 F<\/i>\u306e\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {F_{xy} = \\partial_x A_y – \\partial_y A_x} $$<\/div> \u3002<\/dd><\/dl>

\u898f\u7d04 (-+++) \u3067\u306f\u3001\u3053\u308c\u306f\u6b21\u306b\u3082\u5bfe\u5fdc\u3057\u307e\u3059\u3002 <\/p>

$$ {F^{(-+++)}_{xy} = \\partial_x A^y – \\partial_y A^x} $$<\/div> \u3002<\/dd><\/dl>

\u3053\u306e\u5f0f\u306f\u3001 A<\/i>\u306e 3 \u6b21\u5143\u56de\u8ee2<\/a><\/span>\u306ez<\/i>\u306b\u6cbf\u3063\u305f\u6210\u5206\u306b\u5bfe\u5fdc\u3057\u3001\u30de\u30af\u30b9\u30a6\u30a7\u30eb\u306e\u65b9\u7a0b\u5f0f<\/span>\u306b\u3088\u308c\u3070\u3001\u898f\u7d04 (-+++) \u306eF<\/i>\u306e\u5f0f\u306b\u5f93\u3063\u3066B z<\/sup><\/i>\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u540c\u69d8\u306b\u3001\u898f\u7d04 (+—) \u3067\u306f\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {F^{(+—)}_{xy} = \\partial_y A^x – \\partial_x A^y} $$<\/div> \u3001<\/dd><\/dl>

\u3053\u308c\u306f\u3001\u4e0a\u8a18\u306e-B z<\/sup><\/i>\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u540c\u69d8\u306b\u3001\u79c1\u305f\u3061\u3082<\/p>

$$ {F_{xt} = \\partial_x A_t – \\partial_t A_x} $$<\/div> \u3002<\/dd><\/dl>

\u6163\u4f8b (-+++) \u3067\u306f\u3001\u3053\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u66f8\u304b\u308c\u307e\u3059\u3002 <\/p>

$$ {F^{(-+++)}_{xt} = – c^2 \\partial_x A^t – \\partial_t A^x} $$<\/div> \u3001<\/dd><\/dl>

\u3057\u305f\u304c\u3063\u3066\u3001\u96fb\u4f4d<\/a><\/span>V \u3092<\/i>c<\/i> 2<\/sup> A t<\/sup><\/i>\u306b\u7b49\u3057\u3044\u3068\u3059\u308b\u3068\u3001 x<\/i>\u306b\u5fdc\u3058\u305fE<\/i>\u306e\u6210\u5206\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u304c\u3001\u6163\u4f8b (+—) \u3067\u306f\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {F^{(+—)}_{xt} = c^2 \\partial_x A^t + \\partial_t A^x} $$<\/div> \u3001<\/dd><\/dl>

\u3053\u308c\u306f-E x<\/sup><\/i>\u306b\u3088\u304f\u5bfe\u5fdc\u3057\u307e\u3059\u3002<\/p>

\u53cd\u5909\u6210\u5206\u306f\u540c\u3058\u65b9\u6cd5\u3067\u8868\u73fe\u3055\u308c\u307e\u3059\u3002 <\/p>

$$ {F^{ab}{}^{(+—)} = \\left(\\begin{array}{rrrr} 0 & -\\frac{1}{c^2} E^x & -\\frac{1}{c^2} E^y & -\\frac{1}{c^2} E^z \\\\ \\frac{1}{c^2} E^x & 0 & – B^z & B^y \\\\ \\frac{1}{c^2} E^y & B^z & 0 & – B^x \\\\ \\frac{1}{c^2} E^z & – B^y & B^x & 0 \\end{array}\\right)} $$<\/div> \u3001<\/dd><\/dl>

\u305d\u3057\u3066<\/p>

$$ {F^{ab}{}^{(-+++)} = \\left(\\begin{array}{rrrr} 0 & \\frac{1}{c^2} E^x & \\frac{1}{c^2} E^y & \\frac{1}{c^2} E^z \\\\ -\\frac{1}{c^2} E^x & 0 & B^z & – B^y \\\\ -\\frac{1}{c^2} E^y & – B^z & 0 & B^x \\\\ -\\frac{1}{c^2} E^z & B^y & – B^x & 0 \\end{array}\\right)} $$<\/div> \u3002<\/dd><\/dl><\/div>
\n\"\u96fb\u78c1\u30c6\u30f3\u30bd\u30eb\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

\u53c2\u8003\u8cc7\u6599<\/h2>
  1. Tensor electromagn\u00e8tic \u2013 catalan<\/a><\/li>
  2. Tenzor intenzity elektromagnetick\u00e9ho pole \u2013 tch\u00e8que<\/a><\/li>
  3. Elektromagnetischer Feldst\u00e4rketensor \u2013 allemand<\/a><\/li>
  4. Electromagnetic tensor \u2013 anglais<\/a><\/li>
  5. Tensor de campo electromagn\u00e9tico \u2013 espagnol<\/a><\/li>
  6. Elektromagnetv\u00e4lja tensor \u2013 estonien<\/a><\/li><\/ol><\/div>\n
    \n

    \n \u96fb\u78c1\u30c6\u30f3\u30bd\u30eb\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n
    \n \n
    \n
    \n