{"id":474,"date":"2020-11-01T11:38:42","date_gmt":"2020-11-01T02:38:42","guid":{"rendered":"https:\/\/hayashiyus.jp\/?p=474"},"modified":"2022-01-05T01:24:11","modified_gmt":"2022-01-04T16:24:11","slug":"%e3%83%84%e3%82%a4%e3%82%b9%e3%82%bf%e3%83%bc%e7%a9%ba%e9%96%93","status":"publish","type":"post","link":"https:\/\/hayashiyus.jp\/?p=474","title":{"rendered":"\u30c4\u30a4\u30b9\u30bf\u30fc\u7a7a\u9593"},"content":{"rendered":"\r\n

\u5149\u5186\u9310\u4e0a\u306e\u4efb\u610f\u306e\u4e00\u70b9\u3092\u6307\u5b9a\u3059\u308b\u3068\uff0c\u305d\u306e\u4e00\u70b9\uff08\u53b3\u5bc6\u306b\u306f\u5149\u7dda\uff09\u306b\u5bfe\u5fdc\u3059\u308b\u30c4\u30a4\u30b9\u30bf\u30fc\u7a7a\u9593\u4e0a\u306e\u4e00\u70b9\u304c\u6c7a\u307e\u308b\uff0e\u305d\u3046\u3057\u305f\u3053\u3068\u3092\uff0c\u4eca\u5e74\u30ce\u30fc\u30d9\u30eb\u8cde\u3092\u53d7\u8cde\u3057\u305f\u30ed\u30b8\u30e3\u30fc\u30fb\u30da\u30f3\u30ed\u30fc\u30ba\u537f\u304c\u8003\u3048\u305f\uff0e<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n

<\/p>\r\n\r\n\r\n\r\n

\uff11. \u30b9\u30d4\u30ce\u30eb\u3068\u56db\u811a\u5834<\/h4>\r\n\r\n\r\n
\r\n

\uff11\u2212\uff11. \u5ea7\u6a19\u3068\u8a08\u91cf<\/h4>\r\n\r\n\r\n

\u6642\u7a7a\u306e\u7dda\u7d20\u3092\u6b21\u306e\u5f0f\u3067\u5b9a\u7fa9\u3059\u308b\uff0e<\/p>\r\n

(1) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle ds^{2} = g_{\mu\nu}dx^{\mu}dx^{\nu} \end{eqnarray*}\"<\/p><\/p>\r\n

\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306e\u7b49\u4fa1\u539f\u7406\u306b\u3088\u308c\u3070\uff0c\u3053\u306e\u8a08\u91cf \"g_{\mu\nu}(x)\" \u306b\u3088\u3063\u3066\u8a18\u8ff0\u3055\u308c\u308b\u6642\u7a7a\u591a\u69d8\u4f53\u306e\u63a5\u7a7a\u9593\u306f\uff0c\u7279\u6b8a\u76f8\u5bfe\u8ad6\u304c\u6210\u308a\u7acb\u3064\u30df\u30f3\u30b3\u30d5\u30b9\u30ad\u30fc\u6642\u7a7a\u3067\u3042\u308b\uff0e\u3053\u306e\u5e73\u3089\u306a\u30df\u30f3\u30b3\u30d5\u30b9\u30ad\u30fc\u6642\u7a7a\u306e\u8a08\u91cf\u3092 \"\eta_{\mu\nu}\" \u3068\u66f8\u304d\uff0c\u4e00\u822c\u306eD\u6b21\u5143\u6642\u7a7a\u3092\u5ff5\u982d\u306b<\/p>\r\n

(2) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \eta_{\mu\nu} = \begin{pmatrix}<\/p><\/p>\r\n

\u3068\u66f8\u304f\u3053\u3068\u306b\u3059\u308b\uff0e<\/p>\r\n\r\n<\/div>\r\n

\r\n

\uff11\u2212\uff12. \u63a5\u7d9a\u3068\u6369\u7387<\/h4>\r\n\r\n\r\n

\u6b21\u306b\uff0c\u5171\u5909\u30d9\u30af\u30c8\u30eb \"A_{\nu}(x)\" \u304a\u3088\u3073\u53cd\u5909\u30d9\u30af\u30c8\u30eb \"A^{\nu}(x)\" \u306e\u5e73\u884c\u79fb\u52d5\u3092\u6b21\u306e\u5f0f\u3067\u66f8\u304f\u3053\u3068\u306b\u3059\u308b\uff0e<\/p>\r\n

(3) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle A_{\mu}(x+dx \| x) = A_{\mu}(x) - \Gamma^{\lambda\ \ }_{\ \mu\nu}(x)A_{\lambda}(x)dx^{\nu} \\<\/p><\/p>\r\n

\u3053\u3053\u304b\u3089\uff0c\u305d\u306e\u5171\u5909\u5fae\u5206\u304c\u5c0e\u304b\u308c\u308b\uff0e

(4) <\/span>   <\/span>\"\begin{eqnarray*}& \displaystyle \nabla_{\nu}A_{\mu} = \partial_{\nu}A_{\mu}-\Gamma^{\lambda\ \ }_{\ \mu\nu}A_{\lambda} \\& \displaystyle \nabla_{\nu}A^{\mu} = \partial_{\nu}A^{\mu}+\Gamma^{\mu\ \ }_{\ \lambda\nu}A^{\lambda}\end{eqnarray*}\"<\/p><\/p>\r\n

\u3053\u306e\u3068\u304d\uff0c\u8a08\u91cf\u306e\u5171\u5909\u767a\u6563\u306b\u3064\u3044\u3066<\/p>\r\n

(5) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \nabla_{\lambda}g_{\mu\nu} = \partial_{\lambda}g_{\mu\nu}-\Gamma^{\rho\ \ }_{\ \nu\lambda}g_{\rho\mu}-\Gamma^{\rho\ \ }_{\ \mu\lambda}g_{\nu\rho}=0 \end{eqnarray*}\"<\/p><\/p>\r\n

\u3092\u8981\u8acb\u3059\u308b\uff0e\u3053\u308c\u3092\u8a08\u91cf\u6761\u4ef6\u3068\u547c\u3076\uff0e\u6642\u7a7a\u306b\u8a08\u91cf\u6761\u4ef6\u3092\u8ab2\u3059\uff08\uff1d\u30ea\u30fc\u30de\u30f3\u6642\u7a7a\uff09\u3053\u3068\u306b\u3088\u308a\uff0c\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f \"G_{\mu\nu} = \chi^{2} T_{\mu\nu}\" \u306e\u53f3\u8fba\u306b\u3042\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u30fb\u904b\u52d5\u91cf\u30c6\u30f3\u30bd\u30eb \"T_{\mu\nu}\" \u304c\u4fdd\u5b58\u91cf\u306b\u306a\u308b\u3053\u3068\u304c\u5c0e\u304b\u308c\u308b\uff0e\u3055\u3089\u306b\u3053\u3053\u3067\u30a2\u30d5\u30a1\u30a4\u30f3\u63a5\u7d9a \"\Gamma^{\rho\ \ }_{\ \mu\nu}\" \u306b\u95a2\u3059\u308b\u5bfe\u79f0\u5316\uff0c\u53cd\u5bfe\u79f0\u5316\u306e\u8a18\u53f7\u3092<\/p>\r\n

(6) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \Gamma^{\rho\ \ }_{\ (\mu\nu)} \equiv \frac{1}{2}\left(\Gamma^{\rho\ \ }_{\ \mu\nu}+\Gamma^{\rho\ \ }_{\ \nu\mu}\right) \\& \displaystyle \Gamma^{\rho\ \ }_{\ [\mu\nu]} \equiv \frac{1}{2}\left(\Gamma^{\rho\ }_{\ \mu\nu}-\Gamma^{\rho\ \ }_{\ \nu\mu}\right) \end{eqnarray*}\"<\/p><\/p>\r\n

\u3068\u3059\u308b\u3068\uff0c\u3053\u308c\u3092\u4f7f\u3063\u3066\u6369\u7387\u3092\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e<\/p>\r\n

(7) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle C^{\rho\ \ \ }_{\ ,\mu\nu} = -C^{\rho\ \ \ }_{\ ,\nu\mu}=2\Gamma^{\rho\ \ }_{\ [\mu\nu]} \end{eqnarray*}\"<\/p><\/p>\r\n

\u6369\u7387\u304c \"0\" \u3067\u306a\u3044\u3068\u304d\u306f\uff0c\u305d\u306e\u6642\u7a7a\u4e0a\u3067\u306f\u30d9\u30af\u30c8\u30eb\u306e\u5e73\u884c\u79fb\u52d5\u306b\u3088\u3063\u3066\u5e73\u884c\u56db\u8fba\u5f62\u304c\u4f5c\u308c\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3059\u308b\uff0e<\/p>\r\n\r\n<\/div>\r\n

\r\n

\uff11\u2212\uff13. \u56db\u811a\u5834\u8868\u793a<\/h4>\r\n\r\n\r\n

\u66f2\u7387\u3068\u6369\u7387\u304c\u5171\u5b58\u3059\u308b\u3068\u304d\uff0c\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u30c6\u30f3\u30bd\u30eb \"G_{\mu\nu} = R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R\" \u306e\u5171\u5909\u767a\u6563\u3092\u3068\u308b\u3068<\/p>\r\n

(8) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \nabla_{\mu}G^{\mu\nu} = -\left(\frac{1}{2}R^{\ \ \ \ \nu}_{\lambda\sigma,\rho}+\delta^{\nu}_{\lambda}R_{\sigma\rho}\right)C^{\rho,\nu\sigma} \end{eqnarray*}\"<\/p><\/p>\r\n

\u3068\u306a\u3063\u3066\u4e00\u822c\u306b\u306f \"0\" \u306b\u306a\u3089\u306a\u3044\uff0e\u3053\u306e\u307e\u307e\u3067\u306f\uff0c\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f \"G_{\mu\nu} = \chi^{2} T_{\mu\nu}\" \u306e\u53f3\u8fba\u306b\u3042\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u30fb\u904b\u52d5\u91cf\u30c6\u30f3\u30bd\u30eb \"T_{\mu\nu}\" \u304c\u975e\u4fdd\u5b58\u91cf\u3068\u306a\u3063\u3066\u3057\u307e\u3044\u5177\u5408\u304c\u60aa\u3044\uff0e\u305d\u3053\u3067\uff0c\u3053\u306e\u3088\u3046\u306a\u6642\u7a7a\uff08\uff1d\u30ea\u30fc\u30de\u30f3\u30fb\u30ab\u30eb\u30bf\u30f3\u6642\u7a7a\uff09\u4e0a\u3067\u306e\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u3092\u8003\u3048\u308b\u305f\u3081\uff0c\u56db\u811a\u5834 \"b^{i\ }_{\ \mu}\" \u3092\u5c0e\u5165\u3059\u308b\uff0e<\/p>\r\n

(9) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \eta_{ij} = b_{i \mu}b^{\ \mu}_{j\ } = g_{\mu\nu}b^{\ \mu}_{i\ }b^{\ \nu}_{j\ } \\<\/p><\/p>\r\n

\u56db\u811a\u5834\u306f\uff0c\u8a08\u91cf\u30c6\u30f3\u30bd\u30eb\u306e\u5e73\u65b9\u6839\u3068\u307f\u306a\u305b\u308b\uff0e<\/p>\r\n

(10) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle g = \mathrm{det}\left(g_{\mu\nu}\right), \ b = \mathrm{det}\left(b^{i\ }_{\ \mu}\right) \\<\/p><\/p>\r\n

\u307e\u305f\uff0c\u56db\u811a\u5834\u306f\uff0c\u5c40\u6240\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u306b\u5bfe\u3057\u3066\u306f\u53cd\u5909\u30d9\u30af\u30c8\u30eb\u3068\u3057\u3066\u5909\u63db\u3055\u308c\uff0c\u4e00\u822c\u5ea7\u6a19\u5909\u63db\u306b\u5bfe\u3057\u3066\u306f\u5171\u5909\u30d9\u30af\u30c8\u30eb\u3068\u3057\u3066\u5909\u63db\u3055\u308c\u308b\u91cf\u3067\u3042\u308b\uff0e\u3053\u308c\u306f\u7269\u7406\u7684\u306b\u306f\uff0c\u6642\u7a7a\u306e\u5404\u70b9\u306b\u304a\u3051\u308b\u63a5\u7a7a\u9593\uff08\uff1d\u5c40\u6240\u30ed\u30fc\u30ec\u30f3\u30c4\u7cfb\uff09\u306b\u304a\u3044\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u30b9\u30d4\u30ce\u30eb\u5834\u3068\uff0c\u66f2\u304c\u3063\u305f\u6642\u7a7a\uff08\uff1d\u4e00\u822c\u5ea7\u6a19\u7cfb\uff09\u3092\u7d50\u3073\u3064\u3051\u308b\u5f79\u5272\u3092\u679c\u305f\u3059\uff0e\u3053\u306e\u56db\u811a\u5834\u3092\u4f7f\u3063\u3066\uff0c\u7269\u8cea\u5834\u304c\u30b9\u30d4\u30ce\u30eb\u5834\u3092\u542b\u3080\u5834\u5408\u306e\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u3092\u5c0e\u51fa\u3057\u3088\u3046\uff0e\u307e\u305a\uff0c\u7269\u8cea\u5834\u306b\u30b9\u30d4\u30ce\u30eb\u5834\u3092\u542b\u3080\u5834\u5408\u306e\u5168\u30e9\u30b0\u30e9\u30f3\u30b8\u30a2\u30f3 \"\mathcal{L}\" \u3092\u6b21\u5f0f\u3067\u4e0e\u3048\u308b\uff0e<\/p>\r\n

(11) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \mathcal{L} = \mathcal{L}_{G} + \mathcal{L}_{m} = \boxed{b\frac{1}{2}R} + \boxed{bL_{m}} \end{eqnarray*}\"<\/p><\/p>\r\n

\u3053\u306e\u3068\u304d\u5168\u30e9\u30b0\u30e9\u30f3\u30b8\u30a2\u30f3\u306b\u5bfe\u3059\u308b\u56db\u811a\u5834\u306e\u30aa\u30a4\u30e9\u30fc\u5fae\u5206\u306f<\/p>\r\n

(12) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \frac{\delta\mathcal{L}}{\delta b^{\ \mu}_{k\ }} = b\left(G^{k\ }_{\ \mu} - T^{k\ }_{\ \mu}\right) = \boxed{b\left(R^{k\ }_{\ \mu}-\frac{1}{2}b^{k\ }_{\ \mu}R\right)} - \boxed{bT^{k\ }_{\ \mu}} = 0 \end{eqnarray*}\"<\/p><\/p>\r\n

\u3068\u306a\u308b\u306e\u3067\uff0c\u6369\u7387\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u306b\u4e00\u822c\u5316\u3055\u308c\u305f\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308b\uff0e<\/p>\r\n

(13) <\/span>   <\/span>\"\begin{eqnarray*}& \displaystyle G_{\mu\nu} = \chi^{2} T_{\mu\nu} \end{eqnarray*}\"<\/p><\/p>\r\n

\u56db\u811a\u5834 \"b_{k\mu}\" \u306f\uff0c\u5c40\u6240\u30ed\u30fc\u30ec\u30f3\u30c4\u7cfb\u306b\u304a\u3051\u308b\u5e73\u884c\u79fb\u52d5\u306b\u3082\uff0c\u4e00\u822c\u5ea7\u6a19\u7cfb\u306b\u304a\u3051\u308b\u5e73\u884c\u79fb\u52d5\u306b\u3082\uff0c\u305d\u308c\u305e\u308c\u5171\u5909\u30d9\u30af\u30c8\u30eb\u306e\u3088\u3046\u306b\u632f\u308b\u821e\u3046\u3002\u56db\u811a\u5834\u306e\u3053\u306e\u6027\u8cea\u306b\u6ce8\u76ee\u3057\u3066\uff0c\u305d\u308c\u305e\u308c\u306e\u5ea7\u6a19\u5909\u63db\u306b\u304b\u304b\u308b\u56db\u811a\u5834\u306e\u4e0d\u5909\u6027\u3092\u8981\u8acb\u3059\u308b\u65b0\u3057\u3044\u5171\u5909\u5fae\u5206\uff08\uff1d\u5168\u5171\u5909\u5fae\u5206\uff09 \"\mathcal{D}_{\mu}\" \u3092\u4ee5\u4e0b\u3067\u5b9a\u7fa9\u3059\u308b\uff0e<\/p>\r\n

(14) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \mathcal{D}_{\mu}b_{k\nu} = \partial_{\mu}b_{k\nu} + \omega_{kj,\mu}b^{j\ }_{\ \nu} - \Gamma^{\lambda\ \ }_{\ \nu\mu}b_{k\lambda} \\<\/p><\/p>\r\n

\u3053\u306e\u3068\u304d\uff0c\u8a08\u91cf\u306e\u5171\u5909\u767a\u6563\u304c \"0\" \u3068\u306a\u308b\uff08\u3088\u3046\u306b\uff0c\u30b9\u30d4\u30f3\u63a5\u7d9a \"\omega_{kj,\mu}\" \u3092\u5b9a\u3081\u308b\uff09\uff0e<\/p>\r\n

(15) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \mathcal{D}_{\rho}g_{\mu\nu} = \left(\mathcal{D}_{\rho}b^{\ \ }_{k\mu}\right)b^{k\ }_{\ \nu} + b_{k\mu}\left(\mathcal{D}_{\rho}b^{k\ }_{\ \nu}\right) \\<\/p><\/p>\r\n

\u3053\u306e\u3088\u3046\u306b\u5168\u5171\u5909\u5fae\u5206\u3092\u5b9a\u3081\u308b\u3068\uff0c\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u30c6\u30f3\u30bd\u30eb\u306e\u5171\u5909\u767a\u6563\u306b\u3064\u3044\u3066\u6b21\u304c\u5c0e\u304b\u308c\u308b\uff0e<\/p>\r\n

(16) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle \mathcal{D}_{k}G^{k\ }_{\ \mu} = \mathcal{D}_{k}\left(R^{k\ }_{\ \mu}-\frac{1}{2}b^{k\ }_{\ \mu}R\right) \\<\/p><\/p>\r\n\r\n<\/div>\r\n

\r\n

\uff11\u2212\uff14. \u30c4\u30a4\u30b9\u30bf\u30fc\u7a7a\u9593<\/h4>\r\n

<\/p>\r\n

<\/p>\r\n

\u5c40\u6240\u30df\u30f3\u30b3\u30d5\u30b9\u30ad\u30fc\u6642\u7a7a\u4e0a\u306e\u30ed\u30fc\u30ec\u30f3\u30c4\u5ea7\u6a19\u3092\u5c40\u6240\u30ed\u30fc\u30ec\u30f3\u30c4\u5ea7\u6a19\u3068\u547c\u3076\uff0e\u56db\u811a\u5834\u306b\u306f\uff0c\u6642\u7a7a\u306e\u5ea7\u6a19 \"x^{\mu}\" \u3068\u5c40\u6240\u30ed\u30fc\u30ec\u30f3\u30c4\u5ea7\u6a19 \"X^{i}\" \u3092\u7d50\u3073\u3064\u3051\u308b\u50cd\u304d\u304c\u3042\u308b\uff0e<\/p>\r\n

(17) <\/span>   <\/span>\"\begin{eqnarray*}& \displaystyle b_{\ \mu}^{i\ } = \frac{\partial X^{i}}{\partial x^{\mu}} ,\ b_{i\ }^{\ \mu} = \frac{\partial x^{\mu}}{\partial X^{i}}&<\/p><\/p>\r\n

\u3053\u3053\u3067\u5c40\u6240\u30df\u30f3\u30b3\u30d5\u30b9\u30ad\u30fc\u6642\u7a7a\u4e0a\u306e\u30cc\u30eb\u6e2c\u5730\u7dda\u3068\u30cc\u30eb\u76f4\u7dda\u3092<\/p>\r\n

(18) <\/span>   <\/span>\"\begin{eqnarray*}& \displaystyle \eta_{ij}P^{i}P^{j} = g_{\mu\nu}b^{\ \mu}_{i\ }b^{\ \nu}_{j\ } P^{i}P^{j} = g_{\mu\nu}p^{\mu}p^{\nu} = 0 \\<\/p><\/p>\r\n

\u3068\u5b9a\u3081\u308b\u3068\uff0c\u5c40\u6240\u30ed\u30fc\u30ec\u30f3\u30c4\u5ea7\u6a19\u306b\u5bfe\u5fdc\u3059\u308b\u30b9\u30d4\u30ce\u30eb\u7b49\u4fa1\u7269\u3092<\/p>\r\n

(19) <\/span>   <\/span>\"\begin{eqnarray*}& \displaystyle \begin{aligned}\left(X^{\alpha \beta}\right) & := \left(X^{i} \gamma_{i}^{\alpha \beta}\right) \\<\/p><\/p>\r\n

\u3068\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u308b\uff08\u305f\u3060\u3057\uff0c\"\gamma_{i}\"\u306f\u30d1\u30a6\u30ea\u884c\u5217\u304b\u3089\u751f\u6210\u3055\u308c\u308b\u30af\u30ea\u30d5\u30a9\u30fc\u30c9\u4ee3\u6570\u306e\u751f\u6210\u5b50\uff1d\u30c7\u30a3\u30e9\u30c3\u30af\u884c\u5217 \"\left\{\gamma_{i}, \gamma_{j}\right\} = 2 \eta_{i j}\" \u304b\u3064 \"\left\{\gamma_{\mu}, \gamma_{\nu}\right\} = 2 g_{\mu \nu}\"\uff09\uff0e\u3053\u308c\u306f\u307e\u305f<\/p>\r\n

(20) <\/span>   <\/span>\"\begin{eqnarray*}& \displaystyle \begin{aligned}\left(x^{\alpha \beta}\right) &:= \left( x^{\mu} \gamma_{\mu}^{\alpha \beta}\right) \\<\/p><\/p>\r\n

\u3092\u6e80\u305f\u3059\uff0e\u3064\u307e\u308a\uff0c\u4e00\u822c\u306e\u66f2\u304c\u3063\u305f\u6642\u7a7a\u3068\u5c40\u6240\u30df\u30f3\u30b3\u30d5\u30b9\u30ad\u30fc\u6642\u7a7a\u306e\u305d\u308c\u305e\u308c\u306b\u304a\u3044\u3066\u30b9\u30d4\u30ce\u30eb\u7b49\u4fa1\u7269\u304c\u5b9a\u7fa9\u3067\u304d\uff0c\u305d\u308c\u3089\u3092\u56db\u811a\u5834\u3092\u4ecb\u3057\u3066\u5bfe\u5fdc\u4ed8\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u3053\u306e\u305f\u3081\uff0c\u30cc\u30eb\u76f4\u7dda\u306e\u30b9\u30d4\u30ce\u30eb\u7b49\u4fa1\u7269\u306f\u4e00\u822c\u5ea7\u6a19\u3092\u7528\u3044\u3066<\/p>\r\n

(21) <\/span>   <\/span>\"\begin{eqnarray*} x^{\alpha \beta} - \lambda \omega^{\alpha}\overline{\omega}^{\beta} + t \pi^{\alpha}\overline{\pi}^{\beta} = 0<\/p><\/p>\r\n

\u3068\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u30cc\u30eb\u76f4\u7dda\u304c\u3042\u3089\u308f\u3059\u5149\u7dda\u4e0a\u306e\u70b9\u306f\u3059\u3079\u3066\u65b9\u7a0b\u5f0f<\/p>\r\n

(22) <\/span>   <\/span>\"\begin{eqnarray*} x^{\alpha \beta}\pi_{\beta} = \lambda \omega^{\alpha} \left( \overline{\omega}^{\beta}\pi_{\beta} \right) \end{eqnarray*}\"<\/p><\/p>\r\n

\u3092\u6e80\u305f\u3059\uff0e\u66f4\u306b\uff0c\u3053\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3068<\/p>\r\n

(23) <\/span>   <\/span>\"\begin{eqnarray*}& \omega^{\alpha} = i x^{\alpha \beta} \pi_{\beta} &<\/p><\/p>\r\n

\u3068\u306a\u308b\u306e\u3067\uff0c\u5149\u7dda\u4e0a\u306e\u4efb\u610f\u306e\u70b9\uff08\u306b\u5bfe\u5fdc\u3059\u308b2-\u30b9\u30d4\u30ce\u30eb\uff09\"x^{\alpha \beta}\"\u3092\u6307\u5b9a\u3059\u308b\u3068\uff0c\u3044\u3064\u3067\u3082\u305d\u308c\u306b\u5bfe\u5fdc\u3059\u308b\u30b9\u30d4\u30ce\u30eb\u5bfe\"\left(\omega^{\alpha}, \pi_{\beta} \right)\"\u3092\u898b\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u3053\u306e\u30b9\u30d4\u30ce\u30eb\u5bfe\u306e\u3053\u3068\u3092\u30c4\u30a4\u30b9\u30bf\u30fc\"Z^{a} = \left(\omega^{\alpha}, \pi_{\beta} \right)\"\u3068\u547c\u3076\uff0e<\/p>\r\n

\"\"<\/p>\r\n

<\/p>\r\n<\/div>\r\n

<\/p>\r\n

\uff12. \u30cc\u30eb\u30c4\u30a4\u30b9\u30bf\u30fc\u306e\u5e7e\u4f55<\/h4>\r\n

<\/p>\r\n

\r\n

\uff12\u2212\uff11. \u8cea\u91cf\u306a\u3057\u7c92\u5b50\u306e\u30d8\u30ea\u30b7\u30c6\u30a3\u30fc<\/h4>\r\n

<\/p>\r\n

<\/p>\r\n

\u5404\u30c4\u30a4\u30b9\u30bf\u30fc\"Z^{a}\"\u306b\u306f\u305d\u306e\u8907\u7d20\u5171\u5f79\"\overline{Z}_{a}\"\u304c\u5b58\u5728\u3057<\/p>\r\n

(24) <\/span>   <\/span>\"\begin{eqnarray*} Z^{a} = \left(\omega^{\alpha}, \pi_{\beta} \right) \mapsto \overline{Z}_{a} = \left(\overline{\pi}_{\alpha}, \overline{\omega}^{\beta} \right) \end{eqnarray*}\"<\/p><\/p>\r\n

\u3068\u3059\u308b\u8907\u7d20\u5171\u5f79\u5199\u50cf\u3092\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u3053\u306e\u3068\u304d\"2\"\u3064\u306e\u30c4\u30a4\u30b9\u30bf\u30fc\"Z^{a} = \left(\omega^{\alpha}, \pi_{\beta} \right)\"\u3068\"U^{a} = \left(\lambda^{\alpha}, \mu_{\beta} \right)\"\u306e\u9593\u306e\u30a8\u30eb\u30df\u30fc\u30c8\u5185\u7a4d\"\Phi\left(Z,U\right)\"\u3092<\/p>\r\n

(25) <\/span>   <\/span>\"\begin{eqnarray*} \Phi\left(Z,U\right) = Z^{a} \overline{U}_{a} = \omega^{\alpha}\mu_{\alpha} + \pi_{\beta}\overline{\lambda}^{\beta} \end{eqnarray*}\"<\/p><\/p>\r\n

\u3067\u5b9a\u7fa9\u3067\u304d\u308b\uff0e\u3053\u306e\u5185\u7a4d\u306f\u6b63\u5b9a\u5024\u3067\u306f\u306a\u3044\uff0e \u4f8b\u3048\u3070\uff0c\u30cc\u30eb\u76f4\u7dda\u304c\u3042\u3089\u308f\u3059\u5149\u7dda\u306b\u5bfe\u5fdc\u3059\u308b\u30c4\u30a4\u30b9\u30bf\u30fc\"Z^{a}\"\u3068\u305d\u306e\u8907\u7d20\u5171\u5f79\"\overline{Z}_{a}\"\u306e\u30a8\u30eb\u30df\u30fc\u30c8\u5185\u7a4d\u306f<\/p>\r\n

(26) <\/span>   <\/span>\"\begin{eqnarray*} 0 = Z^{a} \overline{Z}_{a} = \omega^{\alpha}\overline{\pi}_{\alpha} + \pi_{\beta}\overline{\omega}^{\beta} = 2\mathcal{R}\left( \omega^{\alpha}\overline{\pi}_{\alpha} \right) \end{eqnarray*}\"<\/p><\/p>\r\n

\u3068\u6e80\u305f\u3059\uff0e\"\Phi\left(Z,Z\right)=0\"\u3068\u306a\u308b\u30c4\u30a4\u30b9\u30bf\u30fc\"Z^{a}\"\u306e\u3053\u3068\u3092\u30cc\u30eb\u30c4\u30a4\u30b9\u30bf\u30fc\u3068\u547c\u3076\uff0e\u3053\u3046\u3057\u3066\u5c40\u6240\u30df\u30f3\u30b3\u30d5\u30b9\u30ad\u30fc\u6642\u7a7a\u4e0a\u306e\u5149\u7dda\uff08\u30cc\u30eb\u76f4\u7dda\uff09\u3092\u6307\u5b9a\u3059\u308b\u3068\uff0c\u30c4\u30a4\u30b9\u30bf\u30fc\u7a7a\u9593\u4e0a\u306e\u70b9\uff08\u30cc\u30eb\u30c4\u30a4\u30b9\u30bf\u30fc\uff09\u304c\u5b9a\u307e\u308b\u3053\u3068\u3092\u307f\u3066\u304d\u305f\u304c\uff0c\u305d\u306e\u9006\u3082\u6210\u308a\u7acb\u3064\uff0e\u3059\u306a\u308f\u3061\uff0c\u4e0e\u3048\u3089\u308c\u305f\u30cc\u30eb\u30c4\u30a4\u30b9\u30bf\u30fc\"Z^{a}\"\u306b\u5bfe\u3057\u3066<\/p>\r\n

(27) <\/span>   <\/span>\"\begin{eqnarray*} x^{\alpha \beta} - \left( \overline{\omega}^{\alpha^{\prime}}\pi_{\alpha^{\prime}} \right)^{-1} \omega^{\alpha}\overline{\omega}^{\beta} + t \pi^{\alpha}\overline{\pi}^{\beta} = 0 \end{eqnarray*}\"<\/p><\/p>\r\n

\u304c\u6210\u308a\u7acb\u3064\uff0e<\/p>\r\n

\u7c92\u5b50\u306e\u30d8\u30ea\u30b7\u30c6\u30a3\u30fc\"s\"\u306f\uff0c\u30c4\u30a4\u30b9\u30bf\u30fc\u306e\u30ce\u30eb\u30e0\u3068\u3057\u3066\u3042\u3089\u308f\u3059\u3053\u3068\u304c\u3067\u304d\u308b\uff0e<\/p>\r\n

(28) <\/span>   <\/span>\"\begin{eqnarray*} s = \frac{1}{2} \Phi\left(Z,Z\right) = \frac{1}{2} Z^{a} \overline{Z}_{a} \end{eqnarray*}\"<\/p><\/p>\r\n

\"\"<\/p>\r\n

<\/p>\r\n<\/div>","protected":false},"excerpt":{"rendered":"

\u5149\u5186\u9310\u4e0a\u306e\u4efb\u610f\u306e\u4e00\u70b9\u3092\u6307\u5b9a\u3059\u308b\u3068\uff0c\u305d\u306e\u4e00\u70b9\uff08\u53b3\u5bc6\u306b\u306f\u5149\u7dda\uff09\u306b\u5bfe\u5fdc\u3059\u308b\u30c4\u30a4\u30b9\u30bf\u30fc\u7a7a\u9593\u4e0a\u306e\u4e00\u70b9\u304c\u6c7a\u307e\u308b\uff0e\u305d\u3046\u3057\u305f\u3053\u3068\u3092\uff0c\u4eca\u5e74\u30ce\u30fc\u30d9\u30eb\u8cde\u3092\u53d7\u8cde\u3057\u305f\u30ed\u30b8\u30e3\u30fc\u30fb\u30da\u30f3\u30ed\u30fc\u30ba\u537f\u304c\u8003\u3048\u305f\uff0e<\/p>\n","protected":false},"author":135576855,"featured_media":593,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"{title}\n\n{excerpt}\n\n{url}","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[1],"tags":[],"class_list":["post-474","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/hayashiyus.jp\/wp-content\/uploads\/2020\/11\/keiko-kimoto-scan-5.png?fit=2016%2C1742&ssl=1","jetpack_likes_enabled":true,"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/pcnxx5-7E","_links":{"self":[{"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/posts\/474","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/users\/135576855"}],"replies":[{"embeddable":true,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=474"}],"version-history":[{"count":99,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/posts\/474\/revisions"}],"predecessor-version":[{"id":1633,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/posts\/474\/revisions\/1633"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=\/wp\/v2\/media\/593"}],"wp:attachment":[{"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=474"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=474"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hayashiyus.jp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=474"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}