{"id":23311,"date":"2016-01-06T00:49:33","date_gmt":"2016-01-05T16:49:33","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=23311"},"modified":"2018-08-01T16:52:53","modified_gmt":"2018-08-01T08:52:53","slug":"%e3%80%90%e6%8e%a2%e7%b4%a214-8%e3%80%91%e5%bb%a3%e7%be%a9%e7%9b%b8%e5%b0%8d%e8%ab%96%e8%88%87%e6%95%b8%e5%ad%b8","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=23311","title":{"rendered":"\u3010\u63a2\u7d2214-8\u3011\u5ee3\u7fa9\u76f8\u5c0d\u8ad6\u8207\u6578\u5b78"},"content":{"rendered":"
\"photo:www.arageek.com\"
photo:www.arageek.com<\/figcaption><\/figure>\n

\u8b1b\u5e2b\uff5c<\/strong>\u54c8\u4f5b\u5927\u5b78\u6578\u5b78\u7cfb \u4e18\u6210\u6850\u6559\u6388
\n\u64b0\u6587\uff5c<\/strong>\u856d\u7dad\u7ff0<\/p>\n

\u611b\u56e0\u65af\u5766\u66fe\u63d0\u53ca\u79d1\u5b78\u662f\u4ee5\u4e0d\u81ea\u7136\u7684\u65b9\u5f0f\u7406\u89e3\u81ea\u7136\uff0c\u5728\u7b46\u8005\u7684\u7406\u89e3\u4e2d\uff0c\u6b64\u89c0\u9ede\u8207\u6578\u5b78\u5728\u63cf\u8ff0\u81ea\u7136\u73fe\u8c61\u8207\u63d0\u4f9b\u5b9a\u91cf\u7d50\u679c\u7684\u7570\u5e38\u6709\u6548\u662f\u76f8\u4e92\u547c\u61c9\u7684\u3002\u7136\u800c\uff0c\u6578\u5b78\u8ab2\u672c\u4e2d\u4ee4\u4eba\u76ee\u4e0d\u6687\u7d66\u7684\u5b9a\u7406\u4e26\u975e\u7686\u6a6b\u7a7a\u51fa\u4e16\u3001\u5929\u5916\u98db\u4f86\uff0c\u82e5\u6211\u5011\u66f4\u6df1\u5165\u5730\u8a8d\u8b58\u7406\u8ad6\u80cc\u5f8c\u7684\u6b77\u53f2\u8108\u7d61\uff0c\u6703\u767c\u73fe\u6578\u5b78\u9ad4\u7cfb\u7684\u5efa\u69cb\u5e38\u7de3\u8d77\u65bc\u81ea\u7136\u554f\u984c\uff08\u5e38\u5e38\u662f\u7269\u7406\u5b78\uff09\u7684\u89e3\u7b54\u3002<\/p>\n

\u662f\u4ee5\uff0c\u8207\u5176\u6bd4\u8f03\u6578\u5b78\u8207\u7269\u7406\u4e43\u81f3\u65bc\u5176\u4ed6\u79d1\u5b78\u5b78\u9580\u5728\u6b77\u53f2\u9032\u5c55\u4e0a\u7684\u5148\u5f8c\u512a\u52a3\uff0c\u8a8d\u8b58\u5b83\u5011\u5982\u4f55\u81ea\u5f7c\u6b64\u6c72\u53d6\u990a\u5206\u5f9e\u800c\u4f7f\u4eba\u985e\u79d1\u5b78\u7684\u7586\u57df\u66f4\u52a0\u907c\u95ca\uff0c\u6216\u8a31\u6703\u662f\u4e00\u500b\u8f03\u5065\u5eb7\u7684\u89c0\u9ede\u3002\u7ffb\u95b1\u6b77\u53f2\uff0c\u5341\u4e03\u81f3\u5341\u4e5d\u4e16\u7d00\u7684\u79d1\u5b78\u5de8\u64d8\u5982\u725b\u9813\u3001\u6b50\u62c9\u3001\u62c9\u683c\u6717\u65e5\u3001\u54c8\u5f4c\u723e\u9813\u3001\u5085\u7acb\u8449\u7b49\uff0c\u7121\u4e0d\u540c\u6642\u8eab\u517c\u4e00\u65b9\u6578\u5b78\u8207\u7269\u7406\u5b78\u6cf0\u6597\u7684\u89d2\u8272\uff0c\u6642\u81f3\u4eca\u65e5\uff0c\u5b78\u9580\u7684\u7cbe\u7d30\u5206\u5de5\u4e0b\uff0c\u5982\u6b64\u591a\u68f2\u7684\u5168\u624d\u5df2\u4e0d\u5fa9\u898b\uff0c\u4f46\u7269\u7406\u5b78\u81ea\u6578\u5b78\u7406\u8ad6\u5c0b\u627e\u65b0\u8a9e\u8a00\uff0c\u6578\u5b78\u81ea\u524d\u6cbf\u7269\u7406\u554f\u984c\u523a\u6fc0\u9748\u611f\u8207\u65b9\u5411\uff0c\u5169\u5b78\u9580\u9593\u7684\u4ea4\u6d41\u8207\u4e92\u52d5\uff0c\u8207\u5f80\u65e5\u76f8\u8f03\u5176\u5be6\u6709\u904e\u4e4b\u800c\u7121\u4e0d\u53ca\uff0c\u672c\u7cfb\u5217\u8b1b\u5ea7\u7684\u4e3b\u984c\uff0c\u5ee3\u7fa9\u76f8\u5c0d\u8ad6\uff0c\u5373\u662f\u9019\u7a2e\u4e92\u52d5\u7684\u6975\u4f73\u7bc4\u4f8b\u3002<\/p>\n

\u4e00\u500b\u4e16\u7d00\u591a\u524d\uff0c\u4eca\u65e5\u7406\u5de5\u5b78\u9662\u6a19\u6e96\u7684\u6578\u5b78\u8ab2\u7a0b\u5927\u62b5\u5df2\u7d93\u5875\u57c3\u843d\u5b9a\uff0c\u5085\u7acb\u8449\u5206\u6790\u7684\u6280\u8853\u5c07\u51fd\u6578\u90fd\u5beb\u6210\u4e86\u6ce2\uff0c\u5c07\u7dda\u6027\u65b9\u7a0b\u5f0f\u7684\u89e3\u6790\u5316\u70ba\u4e00\u9801\u9801\u983b\u8b5c\u3002\u9ece\u66fc\u5e2b\u627f\u9ad8\u65af\u5c0d\u5fae\u5206\u5e7e\u4f55\u7684\u7814\u7a76\uff0c\u5c07\u5f8c\u8005\u5728\u4e09\u7dad\u7a7a\u9593\u5167\u66f2\u7dda\u8207\u66f2\u9762\u7684\u7406\u89e3\u63a8\u5c55\u81f3\u66f4\u9ad8\u7684\u7dad\u5ea6\uff0c\u5728\u9ad8\u65af\u7684\u6846\u67b6\u4e0b\uff0c\u900f\u904e\u300c\u66f2\u7387\u300d\uff08curvature\uff09\u4ed6\u6709\u7cfb\u7d71\u5730\u7814\u7a76\u4e86\u5982\u4f55\u53bb\u5b9a\u91cf\u8aaa\u660e\u4e09\u7dad\u7a7a\u9593\u5167\u7684\u66f2\u7dda\u6216\u66f2\u9762\u6709\u591a\u300c\u5f4e\u66f2\u300d\uff0c\u4e26\u4e14\u4ed6\u66f4\u8b49\u660e\u66f2\u9762\u7684\u5f4e\u66f2\u662f\u53ef\u4ee5\u7531\u6e2c\u91cf\u66f2\u9762\u672c\u8eab\u7684\u4e00\u4e9b\u5e7e\u4f55\u6027\u8cea\u5f97\u77e5\uff0c\u767d\u8a71\u4e00\u9ede\u8aaa\uff0c\u539f\u5247\u4e0a\u4eba\u985e\u4e26\u4e0d\u9700\u8981\u4e0a\u592a\u7a7a\uff0c\u800c\u53ef\u4ee5\u900f\u904e\u6e2c\u91cf\u5730\u9762\u4e0a\u4e09\u89d2\u5f62\u7684\u5167\u89d2\u548c\u5f97\u77e5\u5730\u7403\u662f\u5713\u7684\uff0c\u9ece\u66fc\u5c07\u9019\u6a23\u7684\u6982\u5ff5\u63a8\u5ee3\u5230\u4e86\u66f4\u9ad8\u7684\u7dad\u5ea6\uff0c\u4e26\u4e14\u900f\u904e\u300c\u5ea6\u898f\u5f35\u91cf\u300d\uff08metric tensor\uff09\u5b9a\u7fa9\u300c\u9577\u5ea6\u300d\uff0c\u5728\u9069\u7576\u7684\u689d\u4ef6\u4e0b\uff0c\u9ad8\u7dad\u5ea6\u7a7a\u9593\u7684\u5f4e\u66f2\u6027\u8cea\u4e5f\u53ef\u4ee5\u900f\u904e\u5ea6\u898f\u5f35\u4eae\u7684\u884d\u751f\u7269\uff0c\u300c\u66f2\u7387\u5f35\u91cf\u300d\uff08curvature tensor\uff09\u6a19\u5b9a\u3002[1]<\/sup><\/sup>\u6b64\u5916\u4eba\u985e\u81ea\u6709\u6587\u660e\u8d77\u5373\u9189\u5fc3\u7684\u5c0d\u7a31\u6027\uff0c\u4e5f\u900f\u904e\u7fa4\u8ad6\u7372\u5f97\u62bd\u8c61\u4e14\u7cfb\u7d71\u6027\u7684\u7406\u89e3\u3002\u5728\u9019\u500b\u610f\u7fa9\u4e0a\u7684\u5c0d\u7a31\uff0c\u53ef\u4ee5\u7406\u89e3\u6210\u6211\u5011\u5c0d\u611f\u8208\u8da3\u7684\u7cfb\u7d71\u9032\u884c\u4e00\u500b\u64cd\u4f5c\uff0c\u800c\u4f7f\u9019\u500b\u7cfb\u7d71\u4e0d\u8b8a ; \u4f8b\u5982\uff0c\u6240\u8b02\u7403\u6709\u8c50\u5bcc\u7684\u65cb\u8f49\u5c0d\u7a31\uff0c\u610f\u6307\u9019\u500b\u7403\u5728\u4efb\u610f\u65cb\u8f49\u5f8c\uff0c\u770b\u8d77\u4f86\u90fd\u4e00\u6a23\u3002\u5c0d\u7a31\u8207\u7269\u7406\u7406\u8ad6\u7d50\u69cb\u66f4\u7d93\u7531\u5fb7\u570b\u6578\u5b78\u5bb6\u8afe\u7279\u7684\u63a8\u5c55\u6df1\u523b\u7684\u5951\u5408\uff0c\u7d04\u7565\u800c\u8a00\uff0c\u5979\u6307\u51fa\u7269\u7406\u7406\u8ad6\u7684\u5c0d\u7a31\u6027[2]<\/sup><\/sup>\u5c0d\u61c9\u5230\u5b88\u6046\u7684\u7269\u7406\u91cf\uff0c\u8b6c\u5982\u65cb\u8f49\u5c0d\u7a31\u6027\u5c0d\u61c9\u5230\u7684\u5373\u662f\u89d2\u52d5\u91cf\u5b88\u6046\uff0c\u8afe\u7279\u5b9a\u7406\u4ee5\u964d\uff0c\u5c0d\u7a31\u6027\u7684\u8003\u91cf\u9010\u6f38\u8b8a\u6210\u7269\u7406\u5b9a\u5f8b\u7684\u6307\u5c0e\u539f\u5247\u3002<\/p>\n

\u5728\u6578\u5b78\u4e16\u754c\u751f\u610f\u76ce\u7136\u7684\u4e8c\u5341\u4e16\u7d00\u521d\uff0c\u5e74\u8f15\u7684\u611b\u56e0\u65af\u5766\u6b63\u8457\u624b\u8981\u99b4\u670d\u91cd\u529b\u81f3\u4ed6\u76f8\u5c0d\u8ad6\u7684\u67b6\u69cb\u5167\u3002<\/p>\n

\u72f9\u7fa9\u76f8\u5c0d\u8ad6\u63a8\u5ee3\u4e86\u725b\u9813\u904b\u52d5\u5b9a\u5f8b\uff0c\u5f9e\u5c0d\u7a31\u7684\u89c0\u9ede\u8457\u624b\uff0c\u725b\u9813\u904b\u52d5\u5b9a\u5f8b\u662f\u5728\u4e09\u7dad\u65cb\u8f49\u7fa4\u4f5c\u7528\u4e0b\u4e0d\u8b8a\u7684\uff0c\u4f8b\u5982\u4e00\u500b\u4eba\u7684\u8eab\u9ad8\uff08\u9577\u5ea6\uff09\u4e26\u4e0d\u56e0\u70ba\u9762\u5c0d\u7684\u65b9\u5411\u800c\u6709\u6240\u4e0d\u540c\u3002\u72f9\u7fa9\u76f8\u5c0d\u8ad6\u4e2d\u6163\u6027\u5750\u6a19\u7cfb\u9593\u5141\u8a31\u52de\u502b\u8332\uff08 Lorentz transformation\uff09\u8b8a\u63db\uff0c\u6709\u9577\u5ea6\u6536\u7e2e\uff08length contraction\uff09\u7684\u73fe\u8c61\uff0c\u56e0\u800c\u7a7a\u9593\u4e0a\u7684\u9577\u5ea6\u4e0d\u518d\u662f\u653e\u8af8\u56db\u6d77\u7686\u6e96\u7684\u6982\u5ff5\u3002\u6240\u5e78\uff0c\u9594\u8003\u65af\u57fa\u6307\u51fa\u52de\u502b\u8332\u8b8a\u63db\u4f9d\u820a\u5f62\u6210\u4e00\u500b\u7fa4\uff0c\u5728\u5b83\u7684\u4f5c\u7528\u5e95\u4e0b\u4e00\u500b\u300c\u6642\u7a7a\u9593\u7684\u9577\u5ea6\u300d<\/p>\n

\"invariant<\/p>\n

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\u611b\u56e0\u65af\u5766\u4e26\u4e0d\u662f\u7e3d\u5728\u53e3\u888b\u5167\u653e\u4e86\u5f88\u591a\u6578\u5b78\u6b66\u5668\u7684\u7269\u7406\u5de5\u4f5c\u8005\uff0c\u4ed6\u7684\u9577\u8655\u662f\u5927\u91cf\u7684\u60f3\u50cf\u5be6\u9a57\u3002\u5176\u4e2d\u5ee3\u70ba\u4eba\u77e5\u7684\u4e00\u500b\u662f\uff1a\u5728\u81ea\u7531\u4e0b\u589c\u7684\u96fb\u68af\u4e2d\uff0c\u4eba\u611f\u53d7\u4e0d\u5230\u91cd\u529b\uff0c\u52a0\u901f\u5ea6\u8ddf\u91cd\u529b\u662f\u7b49\u6548\u7684\u3002\u73fe\u5728\u6211\u5011\u7a31\u6b64\u70ba\u7b49\u6548\u539f\u7406\uff08equivalence principle\uff09\uff0c\u7b49\u6548\u539f\u7406\u5118\u7ba1\u8db3\u4ee5\u8aaa\u660e\u5149\u7dda\u5728\u91cd\u529b\u5834\u4e2d\u7684\u5f4e\u66f2\u4ee5\u53ca\u5149\u8b5c\u7684\u91cd\u529b\u7d05\u79fb\uff0c\u4f46\u8ddd\u96e2\u4e00\u500b\u5b8c\u6574\u7684\u7406\u8ad6\uff0c\u537b\u9084\u9060\u9060\u4e0d\u8db3\u3002\u7136\u800c\uff0c\u7d93\u9594\u8003\u65af\u57fa\u5e7e\u4f55\u5316\u7684\u76f8\u5c0d\u8ad6\u63d0\u4f9b\u4e86\u4e00\u500b\u6697\u793a\uff1a\u7b49\u6548\u539f\u7406\u4ea6\u53ef\u88ab\u6558\u8ff0\u70ba\uff0c\u5728\u5c40\u90e8\u6642\u7a7a\u9593\u5167\uff0c\u91cd\u529b\u5834\u8ddf\u4e00\u500b\u975e\u6163\u6027\u5750\u6a19\u7cfb\u662f\u7b49\u6548\u7684\uff0c\u5f9e\u9594\u8003\u65af\u57fa\u6642\u7a7a\u7684\u89d2\u5ea6\uff0c\u6240\u8b02\u52a0\u901f\u5750\u6a19\u7cfb\u50c5\u662f\u4e00\u500b\u5750\u6a19\u8f49\u63db\uff0c\u56e0\u800c\u611b\u56e0\u65af\u5766\u5f97\u5230\u4e86\u7dda\u7d22\uff0c\u91cd\u529b\u6216\u8a31\u53ef\u4ee5\u6b78\u7d0d\u70ba\u6642\u7a7a\u7684\u5e7e\u4f55\u52d5\u529b\u6027\u8cea\u3002\u800c\u56e0\u70ba\u5f9e\u6163\u6027\u7cfb\u5230\u975e\u6163\u6027\u7cfb\uff0c\u5750\u6a19\u9078\u64c7\u7684\u81ea\u7531\u5ea6\u5df2\u7d93\u8d85\u8d8a\u4e86\u72f9\u7fa9\u76f8\u5c0d\u8ad6\u7684\u52de\u502b\u8332\u7fa4\uff0c\u53d6\u800c\u4ee3\u4e4b\u7684\u662f\u4efb\u610f\u9078\u64c7\u6642\u7a7a\u5750\u6a19\u7684\u5c0d\u7a31\u6027\uff0c\u5728\u72f9\u7fa9\u76f8\u5c0d\u8ad6\u4e2d\u88ab\u7576\u6210\u662f\u5e38\u6578\u7684\u5ea6\u898f\u5f35\u91cf\uff0c\u7d93\u63a8\u5ee3\u5f8c\u4e5f\u5fc5\u9808\u53cd\u6620\u6642\u7a7a\u7684\u52d5\u529b\u6027\u8cea\u3002<\/p>\n

\u5177\u5099\u9019\u4e9b\u57fa\u672c\u5143\u7d20\u5f8c\uff0c\u611b\u56e0\u65af\u5766\u9700\u8981\u4e00\u500b\u5fae\u5206\u65b9\u7a0b\u5f0f\u4f86\u63cf\u8ff0\u5ea6\u898f\u5f35\u91cf\u7684\u52d5\u529b\u5b78\uff0c\u9019\u500b\u65b9\u7a0b\u5f0f\u9700\u8981\u7b26\u5408\u4e00\u4e9b\u689d\u4ef6\uff0c\u8b6c\u5982\uff0c\u5b83\u5fc5\u9808\u662f\u500b\u4e8c\u968e\u5fae\u5206\u65b9\u7a0b\uff0c\u7136\u5f8c\uff0c\u56e0\u70ba\u65b9\u7a0b\u5f0f\u9700\u8981\u6709\u660e\u78ba\u7684\u7269\u7406\u610f\u7fa9\uff0c\u5b83\u5fc5\u9808\u7531\u5f35\u91cf\u7d44\u6210\u3002\u7576\u6642\u6240\u77e5\u9053\u9019\u6a23\u7684\u91cf\u4e26\u4e0d\u591a\uff0c\u611b\u56e0\u65af\u5766\u8207\u683c\u7f85\u65af\u66fc\u9078\u5b9a\u91cc\u5947\u66f2\u7387\u5f35\u91cf\uff08Ricci curvature tensor\uff09\u63cf\u8ff0\u6642\u7a7a\u7684\u52d5\u529b\uff0c\u800c\u9a45\u52d5\u6642\u7a7a\u8b8a\u5316\u7684\u4f86\u6e90\uff0c\u5247\u63a8\u5ee3\u4e86\u7269\u8cea\u8cea\u91cf\u5206\u4f48\u7684\u6982\u5ff5\u9078\u5b9a\u80fd\u91cf\u52d5\u91cf\u5f35\u91cf\u3002\u4e00\u5207\u770b\u4f3c\u6c34\u5230\u6e20\u6210\uff0c\u4f46\u9019\u500b\u65b9\u7a0b\u5f0f\u78ba\u6709\u8457\u6578\u5b78\u4e0a\u7684\u81f4\u547d\u50b7 ; \u6839\u64da\u8afe\u7279\u5b9a\u7406\uff0c\u82e5\u4e00\u500b\u7406\u8ad6\u5177\u6709\u6642\u7a7a\u9593\u5e73\u79fb\u7684\u5c0d\u7a31\u6027\uff0c\u80fd\u91cf\u52d5\u91cf\u5f35\u91cf\u662f\u7b26\u5408\u5b88\u6046\u5f8b\u7684\uff0c\u7136\u800c\u91cc\u5947\u5f35\u91cf\u4e26\u6c92\u6709\u5b88\u6046\u7684\u6027\u8cea\uff0c\u6b64\u65b9\u7a0b\u5fc5\u5b9a\u9700\u8981\u4fee\u6b63\u3002\u7d42\u65bc\u5728 1915 \u5e74\uff0c\u611b\u56e0\u65af\u5766\u627e\u5230\u4e86\u4eca\u65e5\u88ab\u547d\u540d\u70ba\u611b\u56e0\u65af\u5766\u5f35\u91cf\u7684\u7d44\u5408\uff0c\u5ee3\u7fa9\u76f8\u5c0d\u8ad6\u7684\u52d5\u529b\u5b78\u611b\u56e0\u65af\u5766\u65b9\u7a0b\u5f0f\u65bc\u7109\u6572\u5b9a\u3002[3]<\/sup><\/sup><\/p>\n

\u904b\u52d5\u65b9\u7a0b\u5f0f\u7684\u6c7a\u5b9a\u4e26\u975e\u6545\u4e8b\u7684\u7d50\u675f\uff0c\u611b\u56e0\u65af\u5766\u65b9\u7a0b\u5f0f\u56fa\u7136\u7c21\u6f54\u512a\u96c5\uff0c\u4f46\u672c\u8cea\u537b\u662f\u8907\u96dc\u7684\u975e\u7dda\u6027\u65b9\u7a0b\u5f0f\uff0c\u7814\u7a76\u8a72\u65b9\u7a0b\u5f0f\u7684\u89e3\u4ee5\u53ca\u89e3\u8207\u65b9\u7a0b\u5f0f\u6240\u9810\u6e2c\u7684\u73fe\u8c61\u6b63\u9762\u5730\u56de\u994b\u5230\u5fae\u5206\u5e7e\u4f55\u672c\u8cea\u7684\u7814\u7a76\uff0c\u4f8b\u5982\u4e18\u6210\u6850\u6559\u6388\u8207 Richard Schoen \u65bc 1979 \u5e74\u8b49\u660e\u7684\u6b63\u80fd\u91cf\u5b9a\u7406\uff0c\u5373\u662f\u78ba\u5b9a\u611b\u56e0\u65af\u5766\u65b9\u7a0b\u8207\u5176\u89e3\u7a69\u5b9a\u6027\u7684\u57fa\u672c\u5de5\u4f5c\u3002\u66f4\u9032\u4e00\u6b65\uff0c\u4e00\u5982\u524d\u5169\u671f\u8ad6\u5176\u9ed1\u6d1e\u91cf\u5b50\u6548\u61c9\u6642\u6240\u8a00\uff0c\u5c07\u91cd\u529b\u91cf\u5b50\u5316\u7684\u9032\u5c55\u81f3\u4eca\u5c1a\u672a\u660e\u6717\u3002<\/p>\n

\u7269\u7406\u5b78\u5bb6\u4e0d\u4e00\u5b9a\u6703\u7279\u5730\u70ba\u4e86\u5de5\u4f5c\u767c\u660e\u5c6c\u65bc\u81ea\u5df1\u7684\u6578\u5b78\uff0c\u56e0\u800c\u4e00\u8def\u770b\u4f86\u6211\u5011\u53ef\u4ee5\u7406\u89e3\u5ee3\u7fa9\u76f8\u5c0d\u8ad6\u7684\u5efa\u7acb\u5c11\u4e0d\u4e86\u7576\u4ee3\u6578\u5b78\u5de8\u64d8\u5982\u9594\u8003\u65af\u57fa\u3001\u683c\u7f85\u65af\u66fc\u3001\u5e0c\u723e\u4f2f\u7279\u7b49\u4eba\u7684\u53c3\u8207\uff0c\u540c\u6642\u7269\u7406\u5b78\u7406\u8ad6\u78ba\u7acb\u5f8c\uff0c\u4e5f\u8ff8\u767c\u8a31\u591a\u660e\u78ba\u4f46\u61f8\u800c\u4e0d\u6c7a\u7684\u554f\u984c\u5438\u5f15\u65b0\u4e00\u4ee3\u6578\u5b78\u5bb6\u5011\u653b\u514b\u3002<\/p>\n

\u81fa\u5927\u7fc1\u79c9\u4ec1\u6559\u6388\u66fe\u8ad6\u53ca\u8fd1\u4ee3\u6578\u5b78\u7684\u8da8\u52e2\u662f\u5e7e\u4f55\u5316\u8207\u62d3\u6a38\u5316\uff0c\u5176\u5be6\u7269\u7406\u7406\u8ad6\u81ea\u5ee3\u7fa9\u76f8\u5c0d\u8ad6\u8d77\uff0c\u4e5f\u6709\u8457\u5e7e\u4f55\u5316\u7684\u8da8\u52e2\uff1a\u91cd\u529b\u7684\u7269\u7406\u73fe\u8c61\u88ab\u6b78\u7d0d\u6210\u6642\u7a7a\u7684\u5e7e\u4f55\u6027\u8cea\uff0c\u9ad8\u80fd\u7269\u7406\u4e2d\u7684\u898f\u7bc4\u5834\u8ad6\u4ea6\u53ef\u7406\u89e3\u70ba\u5fae\u5206\u5e7e\u4f55\u300c\u7e96\u7dad\u53e2\u300d\uff08fibre bundle\uff09\u7684\u6982\u5ff5\u3002\u7d42\u6975\u7406\u8ad6\u7684\u5019\u9078\u4eba\u4e4b\u4e00\uff0c\u8d85\u5f26\u7406\u8ad6\uff0c\u9700\u8981\u8db3\u5920\u5927\u7684\u6642\u7a7a\u7dad\u5ea6\u4f86\u652f\u6490\u81ea\u7531\u5ea6\u7684\u6578\u76ee\uff0c\u70ba\u4e86\u89e3\u91cb\u591a\u9918\u7684\u7dad\u5ea6\u7121\u6cd5\u89c0\u6e2c\uff0c\u5176\u57fa\u672c\u60f3\u6cd5\u4e4b\u4e00\u5373\u5728\u56db\u7dad\u6642\u7a7a\u4e2d\u6bcf\u4e00\u9ede\u90fd\u8ce6\u4e88\u4e00\u500b\u6975\u5c0f\u7684\u5361\u62c9\u6bd4-\u4e18\u7a7a\u9593\uff0c\u6b64\u7a7a\u9593\u96d6\u5c0f\u4f46\u5b83\u5e7e\u4f55\u6027\u8cea\u537b\u8db3\u4ee5\u6c7a\u5b9a\u5f26\u7684\u7269\u7406\u7279\u6027\uff0c\u6b64\u5916\uff0c\u8d85\u5f26\u7406\u8ad6\u7684\u64c1\u6709\u9023\u7d50\u8cbb\u7c73\u5b50\uff08fermion\uff09\u8207\u73bb\u8272\u5b50\uff08boson\uff09\u7684\u8d85\u5c0d\u7a31\uff0c\u5176\u8868\u73fe\u6280\u8853\u4e5f\u88ab\u904b\u7528\u5728\u6307\u6a19\u5b9a\u7406\uff08index theorem\uff09\u7b49\u6578\u5b78\u554f\u984c\u4e0a\u3002\u5c0d\u65bc\u91cd\u529b\u5b78\u8005\u800c\u8a00\uff0c\u91cf\u5b50\u91cd\u529b\u7406\u8ad6\u7684\u89e3\u6c7a\u7121\u7591\u662f 21 \u4e16\u7d00\u7684\u73e0\u7a46\u6717\u746a\u5cf0\u3002\u5118\u7ba1\u6211\u8f29\u4e26\u672a\u8eac\u9022\u53e4\u5178\u5ee3\u7fa9\u76f8\u5c0d\u8ad6\u5728\u7269\u7406\u5b78\u8207\u6578\u5b78\u4e92\u76f8\u6fc0\u76ea\u4e2d\u8a95\u751f\u7684\u4e16\u4ee3\uff0c\u4f46\u4e0b\u500b\u767e\u5e74\uff0c\u6211\u5011\u4f9d\u820a\u53ef\u4ee5\u671f\u5f85\u5169\u5b78\u9580\u6089\u5fc3\u690d\u683d\u5f8c\u7e41\u82b1\u7684\u76db\u958b\u3002<\/p>\n

\u8a3b\u89e3\uff1a<\/p>\n

[1]<\/sup><\/sup>\u6240\u8b02\u300c\u5f35\u91cf\u300d\u662f\u4e00\u4e9b\u6709\u660e\u78ba\u610f\u7fa9\u7684\u91cf\uff0c\u56e0\u70ba\u5b83\u672c\u8eab\u7684\u610f\u7fa9\u662f\u660e\u78ba\u7684\uff0c\u56e0\u800c\u5728\u5750\u6a19\u8f49\u63db\u6642\uff0c\u5f35\u91cf\u7684\u5206\u91cf\u9700\u8981\u9032\u884c\u7279\u5b9a\u7684\u7d44\u5408\u3002\u8209\u4f8b\u800c\u8a00\uff0c\u6b50\u6c0f\u7a7a\u9593\u7684\u5411\u91cf\u662f\u4e00\u7a2e\u5f35\u91cf\uff0c\u5047\u5b9a\u5728\u67d0\u4e00\u500b\u5750\u6a19\u7cfb\u4e2d\u6709\u4e00\u500b\u5411\u91cf v = (1, 0, 0)\uff0c\u5b83\u7684\u9577\u5ea6\u662f\u6709\u660e\u78ba\u610f\u7fa9\u7684\uff0c\u4ea6\u5373\u5728\u65cb\u8f49\u4f5c\u7528\u4e0b\u5b83\u7684\u9577\u5ea6 1 \u4e0d\u8b8a\uff0c\u82e5\u6709\u53e6\u5916\u4e00\u500b\u4eba\u9078\u64c7\u7528\u53e6\u4e00\u500b\u65cb\u8f49 90 \u5ea6\u7684\u5750\u6a19\u53bb\u63cf\u8ff0 v \uff0c\u90a3\u9ebc v \u7684\u5206\u91cf\u5728\u5750\u6a19\u8f49\u63db\u4e0b\u8981\u91cd\u65b0\u7d44\u5408\u6210 v\u2019 = (0, -1, 0)\uff0c\u4f7f\u5f97\u5b83\u7684\u610f\u7fa9\u4e0d\u8b8a\uff0c\u53e6\u4e00\u65b9\u9762\uff0c\u540c\u6a23\u4e00\u500b\u62ec\u865f (\u8461\u8404, \u860b\u679c, \u9999\u8549) \u5c31\u4e0d\u6703\u662f\u5411\u91cf\uff0c\u56e0\u70ba\u5728\u5750\u6a19\u66f4\u63db\u4e4b\u4e0b\uff0c\u6c34\u679c\u4e4b\u9593\u4e26\u6c92\u6709\u9053\u7406\u53bb\u7d44\u5408\u5728\u4e00\u8d77\u3002<\/p>\n

[2]<\/sup><\/sup>\u66f4\u7cbe\u78ba\u800c\u8a00\u662f\u4f5c\u7528\u91cf\uff08action\uff09\u7684\u5c0d\u7a31\u6027\u3002<\/p>\n

[3]<\/sup><\/sup>\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u8207\u611b\u56e0\u65af\u5766\u5728\u91cd\u529b\u554f\u984c\u4e0a\u6709\u66f8\u4fe1\u5f80\u4f86\u53ca\u6df1\u5165\u8a0e\u8ad6\u7684\u6578\u5b78\u5bb6\u5e0c\u723e\u4f2f\u7279\uff0c\u7368\u7acb\u4e14\u5e7e\u4e4e\u540c\u6642\uff08\u6216\u8aaa\u66f4\u65e9\uff09\u5f9e\u6700\u5c0f\u4f5c\u7528\u91cf\u539f\u7406\u7684\u89d2\u5ea6\u767c\u73fe\u611b\u56e0\u65af\u5766\u65b9\u7a0b\u5f0f\u3002<\/p>\n

 <\/p>\n

--
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 <\/p>\n

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