{"id":87894,"date":"2026-07-31T07:16:24","date_gmt":"2026-07-30T23:16:24","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/87894.html"},"modified":"2026-07-31T07:16:24","modified_gmt":"2026-07-30T23:16:24","slug":"%e8%b7%a8%e5%b0%ba%e5%ba%a6%e6%8b%93%e6%89%91%e5%85%a8%e5%9f%9f%e7%bb%9f%e4%b8%80%e5%9c%ba%e7%90%86%e8%ae%ba%ef%bc%9a%e5%9f%ba%e4%ba%8e%e5%b1%82%e7%ba%a7%e6%8b%93%e6%89%91%e6%bc%94%e5%8c%96%e7%9a%84","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/87894.html","title":{"rendered":"\u8de8\u5c3a\u5ea6\u62d3\u6251\u5168\u57df\u7edf\u4e00\u573a\u7406\u8bba\uff1a\u57fa\u4e8e\u5c42\u7ea7\u62d3\u6251\u6f14\u5316\u7684\u56db\u5927\u529b\u7edf\u4e00\u4e0e\u5de5\u7a0b\u63a7\u5236\u95ed\u73af\u4f53\u7cfb"},"content":{"rendered":"<p>\u8de8\u5c3a\u5ea6\u62d3\u6251\u5168\u57df\u7edf\u4e00\u573a\u7406\u8bba&#xff1a;\u57fa\u4e8e\u5c42\u7ea7\u62d3\u6251\u6f14\u5316\u7684\u56db\u5927\u529b\u7edf\u4e00\u4e0e\u5de5\u7a0b\u63a7\u5236\u95ed\u73af\u4f53\u7cfb<\/p>\n<h3>\u6458\u8981<\/h3>\n<p>\u73b0\u4ee3\u7269\u7406\u5b66\u4f53\u7cfb\u5b58\u5728\u767e\u5e74\u7ed3\u6784\u6027\u5272\u88c2&#xff1a;\u5e7f\u4e49\u76f8\u5bf9\u8bba\u63cf\u8ff0\u5b8f\u89c2\u5f15\u529b\u3001\u91cf\u5b50\u573a\u8bba\u63cf\u8ff0\u5fae\u89c2\u4e09\u5927\u529b&#xff0c;\u4e24\u5957\u6570\u5b66\u6846\u67b6\u4e0d\u53ef\u4e92\u901a\u3001\u4e0d\u53ef\u91cd\u6574\u5316\u517c\u5bb9&#xff0c;\u7269\u7406\u7ec8\u6781\u7edf\u4e00\u957f\u671f\u65e0\u6cd5\u5b8c\u6210\u3002\u4f20\u7edf\u7edf\u4e00\u573a\u7406\u8bba&#xff08;\u5f26\u8bba\u3001\u5708\u91cf\u5b50\u5f15\u529b&#xff09;\u4ec5\u505c\u7559\u5728\u7eaf\u6570\u7406\u63a8\u6f14&#xff0c;\u65e0\u6cd5\u843d\u5730\u5de5\u7a0b\u4f53\u7cfb\u3002 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\u5173\u952e\u8bcd&#xff1a;\u7edf\u4e00\u573a\u8bba&#xff1b;\u91cf\u5b50\u5f15\u529b&#xff1b;\u8de8\u5c3a\u5ea6\u62d3\u6251&#xff1b;\u56db\u5927\u57fa\u672c\u529b&#xff1b;\u5de5\u7a0b\u63a7\u5236\u8bba&#xff1b;\u901a\u611f\u4e00\u4f53\u5316<\/p>\n<h3>\u9644\u5f55\u524d\u7f6e&#xff1a;\u6838\u5fc3\u539f\u521b\u6982\u5ff5 \u2014 \u5b66\u754c\u6807\u51c6\u672f\u8bed\u5bf9\u7167\u8868<\/h3>\n<table>\n<tbody>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u672c\u6587\u539f\u521b\u547d\u540d\u6982\u5ff5<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u7269\u7406\u5b66\u901a\u7528\u6807\u51c6\u672f\u8bed<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u6982\u5ff5\u7b80\u8981\u91ca\u4e49<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5168\u57df\u672c\u6e90\u62d3\u6251\u6d41\u5f62 $$\\\\Omega(\\\\tau$$<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5168\u57df\u6f14\u5316\u56db\u7ef4\u62d3\u6251\u6d41\u5f62<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u627f\u8f7d\u5168\u90e8\u7269\u8d28\u3001\u573a\u3001\u65f6\u7a7a\u7684\u57fa\u7840\u51e0\u4f55\u7a7a\u95f4&#xff0c;$$\\\\ta$$\u4e3a\u5168\u57df\u7edf\u4e00\u65f6\u5e8f<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5341\u4e09\u9636\u5c3a\u5ea6\u5206\u5c42\u7a7a\u95f4 $$L_1\\\\sim L_{13$$<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u591a\u5c3a\u5ea6\u5d4c\u5957\u62d3\u6251\u5b50\u7a7a\u95f4\u5206\u5c42\u4f53\u7cfb<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u6309\u89c2\u6d4b\u5c3a\u5ea6\u5212\u5206\u7684 13 \u5c42\u8fde\u7eed\u5d4c\u5957\u51e0\u4f55\u533a\u57df&#xff0c;\u5212\u5206\u5fae\u89c2\u3001\u4ecb\u89c2\u3001\u5b8f\u89c2\u4e09\u5927\u57df<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u8de8\u5c3a\u5ea6\u62d3\u6251\u6295\u5f71\u7b97\u5b50 $$\\\\mathcal{T}(\\\\cdot$$<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5c3a\u5ea6\u53d8\u6362\u5fae\u5206\u62d3\u6251\u6620\u5c04\u7b97\u5b50<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5b9e\u73b0\u5fae\u89c2\u91cf\u5b50\u573a\u4e0e\u5b8f\u89c2\u65f6\u7a7a\u573a\u4e92\u76f8\u8f6c\u5316\u7684\u53ef\u9006\u5fae\u5206\u51e0\u4f55\u8fd0\u7b97\u5de5\u5177<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5168\u57df\u7edf\u4e00\u573a\u603b\u65b9\u7a0b<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u591a\u5c3a\u5ea6\u8026\u5408\u7edf\u4e00\u573a\u5f20\u91cf\u65b9\u7a0b<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5355\u6761\u5c01\u95ed\u5f20\u91cf\u65b9\u7a0b&#xff0c;\u7edf\u4e00\u56db\u5927\u57fa\u672c\u76f8\u4e92\u4f5c\u7528\u5168\u90e8\u52a8\u529b\u5b66\u89c4\u5f8b<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5c42\u7ea7\u9000\u5316\u517c\u5bb9\u516c\u7406<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u591a\u5c3a\u5ea6\u6781\u9650\u7406\u8bba\u81ea\u6d3d\u516c\u7406<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u7edf\u4e00\u573a\u65b9\u7a0b\u5728\u5c3a\u5ea6\u7ea6\u675f\u4e0b\u53ef\u9000\u5316\u5f97\u5230\u7ecf\u5178\u7269\u7406\u65b9\u7a0b&#xff0c;\u4fdd\u8bc1\u4e0e\u5b9e\u9a8c\u517c\u5bb9<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>1 \u5f15\u8a00<\/h3>\n<h4>\u7ae0\u8282\u901a\u4fd7\u6982\u8ff0<\/h4>\n<p>\u672c\u7ae0\u4e3b\u8981\u89e3\u51b3\u4e24\u5927\u95ee\u9898&#xff1a;\u4e00\u662f\u68b3\u7406\u73b0\u4ee3\u7269\u7406\u5b66\u4e24\u5927\u6838\u5fc3\u652f\u67f1&#xff08;\u91cf\u5b50\u573a\u8bba\u3001\u5e7f\u4e49\u76f8\u5bf9\u8bba&#xff09;\u957f\u671f\u65e0\u6cd5\u517c\u5bb9\u7684\u5e95\u5c42\u77db\u76fe&#xff0c;\u70b9\u660e\u5f53\u524d\u7269\u7406\u4f53\u7cfb\u7684\u6838\u5fc3\u7f3a\u9677&#xff1b;\u4e8c\u662f\u5206\u6790\u5f26\u8bba\u3001\u5708\u91cf\u5b50\u5f15\u529b\u7b49\u73b0\u6709\u7edf\u4e00\u7406\u8bba\u7684\u5171\u540c\u77ed\u677f \u2014\u2014 \u4ec5\u505a\u7eaf\u6570\u5b66\u63a8\u6f14&#xff0c;\u65e0\u6cd5\u5bf9\u63a5\u5de5\u7a0b\u5e94\u7528&#xff1b;\u6700\u540e\u63d0\u51fa\u672c\u6587\u5b8c\u6574\u521b\u65b0\u8def\u7ebf&#xff0c;\u660e\u786e\u5168\u6587\u7814\u7a76\u76ee\u6807\u3002<\/p>\n<h4>1.1 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\u4e24\u5957\u4f53\u7cfb\u7684\u5272\u88c2&#xff0c;\u662f\u8fd1\u767e\u5e74\u6765\u7406\u8bba\u7269\u7406\u96be\u4ee5\u7a81\u7834\u7684\u6838\u5fc3\u74f6\u9888\u3002<\/p>\n<\/li>\n<h4>1.2 \u73b0\u6709\u7edf\u4e00\u573a\u7406\u8bba\u56fa\u6709\u7f3a\u9677<\/h4>\n<p>\u5b66\u754c\u5df2\u63d0\u51fa\u591a\u79cd\u7edf\u4e00\u56db\u5927\u57fa\u672c\u529b\u7684\u7406\u8bba\u6846\u67b6&#xff0c;\u4f46\u5747\u5b58\u5728\u4e0d\u53ef\u5f25\u8865\u7684\u77ed\u677f&#xff1a;<\/p>\n<li>\n<p>\u5f26\u8bba \/ M \u7406\u8bba&#xff1a;\u5f15\u5165\u5341\u7ef4\u3001\u5341\u4e00\u7ef4\u5197\u4f59\u7a7a\u95f4&#xff0c;\u65e0\u552f\u4e00\u89e3\u6790\u89e3&#xff0c;\u65e0\u6cd5\u8bbe\u8ba1\u53ef\u843d\u5730\u5b9e\u9a8c&#xff0c;\u5b8c\u5168\u8131\u79bb\u5de5\u7a0b\u5e94\u7528&#xff1b;<\/p>\n<\/li>\n<li>\n<p>\u5708\u91cf\u5b50\u5f15\u529b&#xff1a;\u4ec5\u91cf\u5316\u79bb\u6563\u65f6\u7a7a\u7ed3\u6784&#xff0c;\u65e0\u6cd5\u7edf\u4e00\u7535\u78c1\u3001\u5f31\u3001\u5f3a\u7269\u8d28\u76f8\u4e92\u4f5c\u7528&#xff0c;\u4ec5\u80fd\u5355\u4e00\u63cf\u8ff0\u5f15\u529b&#xff1b;<\/p>\n<\/li>\n<li>\n<p>\u6807\u51c6\u6a21\u578b&#xff1a;\u4ec5\u5b8c\u6210\u5fae\u89c2\u4e09\u5927\u529b\u7edf\u4e00&#xff0c;\u5b8c\u5168\u4e0d\u5305\u542b\u5f15\u529b\u573a&#xff0c;\u5c5e\u4e8e\u5c40\u90e8\u7edf\u4e00\u7406\u8bba\u3002 \u4e0a\u8ff0\u6240\u6709\u7406\u8bba\u5747\u5b58\u5728\u540c\u4e00\u7f3a\u9677&#xff1a;\u4ec5\u805a\u7126\u7eaf\u57fa\u7840\u7269\u7406\u63a8\u6f14&#xff0c;\u6ca1\u6709\u642d\u5efa\u4e0e\u5de5\u7a0b\u79d1\u5b66\u7684\u8fde\u63a5\u901a\u9053&#xff0c;\u7406\u8bba\u65e0\u6cd5\u843d\u5730\u4ea7\u4e1a\u6280\u672f\u3002<\/p>\n<\/li>\n<h4>1.3 \u672c\u6587\u6838\u5fc3\u521b\u65b0\u4e0e\u7814\u7a76\u76ee\u6807<\/h4>\n<li>\n<p>\u6784\u5efa\u5341\u4e09\u9636\u5d4c\u5957\u62d3\u6251\u7a7a\u95f4\u6846\u67b6&#xff0c;\u4ece\u51e0\u4f55\u5e95\u5c42\u8bc1\u660e\u91cf\u5b50\u573a\u4e0e\u5f15\u529b\u573a\u4ec5\u4e3a\u5c3a\u5ea6\u6295\u5f71\u5dee\u5f02&#xff0c;\u6d88\u9664\u4e24\u5927\u7269\u7406\u4f53\u7cfb\u5e95\u5c42\u77db\u76fe&#xff1b;<\/p>\n<\/li>\n<li>\n<p>\u63a8\u5bfc\u5355\u4e00\u5c01\u95ed\u7edf\u4e00\u573a\u5f20\u91cf\u4e3b\u65b9\u7a0b&#xff0c;\u53ef\u901a\u8fc7\u5c3a\u5ea6\u7cfb\u6570\u7ea6\u675f\u9000\u5316\u5f97\u5230\u5168\u90e8\u7ecf\u5178\u7269\u7406\u65b9\u7a0b&#xff0c;\u4e0e\u73b0\u6709\u5b9e\u9a8c\u6570\u636e\u5b8c\u5168\u517c\u5bb9&#xff1b;<\/p>\n<\/li>\n<li>\n<p>\u5efa\u7acb\u7edf\u4e00\u573a\u7406\u8bba\u4e0e\u94b1\u5b66\u68ee\u300a\u5de5\u7a0b\u63a7\u5236\u8bba\u300b\u7684\u6570\u5b66\u6620\u5c04\u5173\u7cfb&#xff0c;\u6253\u901a\u57fa\u7840\u7269\u7406\u3001\u6750\u6599\u79d1\u5b66\u3001\u901a\u4fe1\u3001\u822a\u5929\u3001\u667a\u80fd\u63a7\u5236\u5168\u5b66\u79d1\u94fe\u8def&#xff0c;\u5b9e\u73b0\u7406\u8bba\u53ef\u4eff\u771f\u3001\u53ef\u5de5\u7a0b\u843d\u5730\u3002<\/p>\n<\/li>\n<h3>2 \u57fa\u7840\u6570\u5b66\u5b9a\u4e49\u4e0e\u7b26\u53f7\u7cfb\u7edf<\/h3>\n<h4>\u7ae0\u8282\u901a\u4fd7\u6982\u8ff0<\/h4>\n<p>\u672c\u7ae0\u4e3b\u8981\u89e3\u51b3\u300c\u5168\u6587\u6570\u5b66\u7b26\u53f7\u3001\u51e0\u4f55\u7a7a\u95f4\u3001\u7b97\u5b50\u5de5\u5177\u5b9a\u4e49\u4e0d\u7edf\u4e00\u3001\u8bfb\u8005\u65e0\u6cd5\u5bf9\u5e94\u73b0\u6709\u7269\u7406\u77e5\u8bc6\u300d\u7684\u95ee\u9898\u3002\u672c\u7ae0\u9010\u4e00\u89c4\u8303\u6240\u6709\u5f20\u91cf\u3001\u6d41\u5f62\u3001\u7b97\u5b50\u7b26\u53f7&#xff0c;\u6bcf\u4e00\u4e2a\u539f\u521b\u6982\u5ff5\u5747\u5bf9\u5e94\u5b66\u754c\u901a\u7528\u5b9a\u4e49&#xff0c;\u4e3a\u540e\u6587\u5168\u90e8\u6570\u5b66\u63a8\u5bfc\u5efa\u7acb\u7edf\u4e00\u3001\u6807\u51c6\u5316\u7684\u8ba1\u7b97\u57fa\u7840\u3002<\/p>\n<h4>2.1 \u5168\u57df\u672c\u6e90\u62d3\u6251\u6d41\u5f62<\/h4>\n<p>$$\\\\Omega(\\\\tau$$<\/p>\n<li>\n<p>\u7b26\u53f7\u5b9a\u4e49&#xff1a;$$\\\\Omeg$$\u4e3a\u5168\u57df\u57fa\u7840\u56db\u7ef4\u62d3\u6251\u6d41\u5f62&#xff1b;$$\\\\ta$$\u4e3a\u5168\u57df\u7edf\u4e00\u6f14\u5316\u65f6\u5e8f\u53c2\u6570&#xff1b;<\/p>\n<\/li>\n<li>\n<p>\u7269\u7406\u610f\u4e49&#xff1a;\u5b87\u5b99\u5168\u90e8\u573a\u3001\u7c92\u5b50\u3001\u65f6\u7a7a\u66f2\u7387\u7684\u552f\u4e00\u627f\u8f7d\u51e0\u4f55\u7a7a\u95f4&#xff0c;\u65f6\u5e8f\u53c2\u6570\u540c\u65f6\u517c\u5bb9\u91cf\u5b50\u6f14\u5316\u65f6\u95f4\u3001\u76f8\u5bf9\u8bba\u56fa\u6709\u65f6\u3002<\/p>\n<\/li>\n<h4>2.2 \u5341\u4e09\u9636\u5c3a\u5ea6\u5206\u5c42\u7a7a\u95f4<\/h4>\n<p>$$L_1 \\\\sim L_{13$$<\/p>\n<li>\n<p>\u5206\u5c42\u5212\u5206\u89c4\u5219&#xff1a;<\/p>\n<\/li>\n<ul>\n<li>\n<p>$$L_1-L_$$&#xff1a;\u91cf\u5b50\u5fae\u89c2\u57df&#xff0c;\u9002\u7528\u666e\u6717\u514b\u5c3a\u5ea6\u81f3\u539f\u5b50\u6838\u5c3a\u5ea6&#xff0c;\u5bf9\u5e94\u6807\u51c6\u6a21\u578b\u7c92\u5b50\u76f8\u4e92\u4f5c\u7528&#xff1b;<\/p>\n<\/li>\n<li>\n<p>$$L_6-L_$$&#xff1a;\u4ecb\u89c2\u7269\u8d28\u57df&#xff0c;\u9002\u7528\u5206\u5b50\u3001\u56fa\u4f53\u3001\u7535\u78c1\u6ce2\u5c3a\u5ea6&#xff0c;\u5bf9\u5e94\u51dd\u805a\u6001\u3001\u901a\u4fe1\u7535\u78c1\u5b66&#xff1b;<\/p>\n<\/li>\n<li>\n<p>$$L_{10}-L_{13$$&#xff1a;\u5b8f\u89c2\u65f6\u7a7a\u57df&#xff0c;\u9002\u7528\u5929\u4f53\u3001\u5b87\u5b99\u5c3a\u5ea6&#xff0c;\u5bf9\u5e94\u5e7f\u4e49\u76f8\u5bf9\u8bba\u5f15\u529b\u573a&#xff1b;<\/p>\n<\/li>\n<\/ul>\n<li>\n<p>\u7269\u7406\u610f\u4e49&#xff1a;\u5c06\u8fde\u7eed\u5b87\u5b99\u5c3a\u5ea6\u62c6\u5206\u4e3a 13 \u5c42\u5d4c\u5957\u62d3\u6251\u5b50\u7a7a\u95f4&#xff0c;\u5929\u7136\u5b9e\u73b0\u5c3a\u5ea6\u622a\u65ad&#xff0c;\u6d88\u9664\u91cf\u5b50\u573a\u53d1\u6563\u96be\u9898\u3002<\/p>\n<\/li>\n<h4>2.3 \u56db\u5927\u57fa\u672c\u529b\u4e8c\u9636\u8026\u5408\u5f20\u91cf<\/h4>\n<li>\n<p>$$E_{\\\\mu\\\\nu$$&#xff1a;\u7535\u78c1\u4e8c\u9636\u573a\u5f20\u91cf&#xff0c;\u5bf9\u5e94\u7535\u78c1\u573a\u5168\u90e8\u52a8\u529b\u5b66\u884c\u4e3a&#xff1b;<\/p>\n<\/li>\n<li>\n<p>$$W_{\\\\mu\\\\nu$$&#xff1a;\u5f31\u76f8\u4e92\u4f5c\u7528\u8026\u5408\u5f20\u91cf&#xff0c;\u63cf\u8ff0\u8f7b\u5b50\u8870\u53d8\u3001W\/Z 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\u8de8\u5c3a\u5ea6\u62d3\u6251\u6295\u5f71\u7b97\u5b50<\/h4>\n<p>$$\\\\mathcal{T}(\\\\cdot$$<\/p>\n<li>\n<p>\u6570\u5b66\u6027\u8d28&#xff1a;\u5149\u6ed1\u3001\u53ef\u9006\u3001\u8fde\u7eed\u53ef\u5fae\u5fae\u5206\u51e0\u4f55\u6620\u5c04\u7b97\u5b50&#xff1b;<\/p>\n<\/li>\n<li>\n<p>\u7269\u7406\u529f\u80fd&#xff1a;\u5b8c\u6210\u5fae\u89c2\u91cf\u5b50\u573a\u5347\u7ef4\u751f\u6210\u5b8f\u89c2\u5f15\u529b\u573a&#xff0c;\u4e5f\u53ef\u5b9e\u73b0\u5b8f\u89c2\u5f15\u529b\u573a\u964d\u7ef4\u62c6\u89e3\u4e3a\u5fae\u89c2\u76f8\u4e92\u4f5c\u7528\u573a&#xff0c;\u642d\u5efa\u5fae\u89c2\u4e0e\u5b8f\u89c2\u7684\u6570\u5b66\u6865\u6881\u3002<\/p>\n<\/li>\n<h3>3 \u4e09\u5927\u6838\u5fc3\u7edf\u4e00\u516c\u7406<\/h3>\n<h4>\u7ae0\u8282\u901a\u4fd7\u6982\u8ff0<\/h4>\n<p>\u672c\u7ae0\u89e3\u51b3\u300c\u7406\u8bba\u5e95\u5c42\u903b\u8f91\u65e0\u4f9d\u636e\u3001\u65e0\u6cd5\u4e0e\u73b0\u4ee3\u7269\u7406\u516c\u8bbe\u517c\u5bb9\u300d\u7684\u95ee\u9898\u3002\u63d0\u51fa\u4e09\u6761\u81ea\u6d3d\u3001\u65e0\u77db\u76fe\u7684\u57fa\u7840\u516c\u7406&#xff0c;\u5168\u90e8\u517c\u5bb9\u91cf\u5b50\u529b\u5b66\u3001\u5e7f\u4e49\u76f8\u5bf9\u8bba\u57fa\u7840\u516c\u8bbe&#xff0c;\u4e3a\u540e\u6587\u7edf\u4e00\u573a\u65b9\u7a0b\u63a8\u5bfc\u63d0\u4f9b\u5b8c\u6574\u903b\u8f91\u6839\u57fa\u3002<\/p>\n<h4>\u516c\u7406 1 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\u8de8\u5c3a\u5ea6\u8fde\u7eed\u8026\u5408\u516c\u7406<\/h4>\n<p>\u5341\u4e09\u9636\u62d3\u6251\u5b50\u7a7a\u95f4\u8fde\u7eed\u5149\u6ed1\u5d4c\u5957&#xff0c;\u4e0d\u5b58\u5728\u5c3a\u5ea6\u65ad\u5c42&#xff1b;\u501f\u52a9\u8de8\u5c3a\u5ea6\u6295\u5f71\u7b97\u5b50$$\\\\mathcal{T}(\\\\cdot$$&#xff0c;\u5fae\u89c2\u91cf\u5b50\u573a\u53ef\u5347\u7ef4\u8f6c\u5316\u4e3a\u5b8f\u89c2\u5f15\u529b\u573a&#xff0c;\u5b8f\u89c2\u65f6\u7a7a\u573a\u4e5f\u53ef\u901a\u8fc7\u9006\u7b97\u5b50$$\\\\mathcal{T}^{-1}(\\\\cdot$$\u62c6\u89e3\u4e3a\u5fae\u89c2\u76f8\u4e92\u4f5c\u7528\u573a&#xff0c;\u573a\u91cf\u8de8\u5c3a\u5ea6\u6620\u5c04\u5168\u7a0b\u8fde\u7eed\u53ef\u5fae\u3002 \u7269\u7406\u610f\u4e49&#xff1a;\u5efa\u7acb\u5fae\u89c2\u4e0e\u5b8f\u89c2\u4e4b\u95f4\u53ef\u9006\u7684\u6570\u5b66\u8f6c\u5316\u89c4\u5219&#xff0c;\u4ece\u5e95\u5c42\u89e3\u51b3\u91cf\u5b50\u5f15\u529b\u517c\u5bb9\u96be\u9898\u3002<\/p>\n<h4>\u516c\u7406 3 \u5c42\u7ea7\u9000\u5316\u517c\u5bb9\u516c\u7406<\/h4>\n<p>\u672c\u6587\u63a8\u5bfc\u7684\u5168\u57df\u7edf\u4e00\u573a\u65b9\u7a0b&#xff0c;\u5728\u7ed9\u5b9a\u5c3a\u5ea6\u6781\u9650\u7ea6\u675f\u3001\u8c03\u6574\u65e0\u91cf\u7eb2\u5c3a\u5ea6\u6295\u5f71\u7cfb\u6570$$\\\\alpha_1,\\\\alpha_2,\\\\alpha_3,\\\\alpha_$$\u540e&#xff0c;\u53ef\u4e25\u683c\u9000\u5316\u5f97\u5230\u7ecf\u5178\u7269\u7406\u3001\u73b0\u4ee3\u7269\u7406\u5168\u90e8\u57fa\u7840\u573a\u65b9\u7a0b&#xff0c;\u7406\u8bba\u63a8\u5bfc\u7ed3\u679c\u4e0e\u4eba\u7c7b\u767e\u5e74\u6765\u7c92\u5b50\u5bf9\u649e\u3001\u5929\u6587\u89c2\u6d4b\u3001\u5b9e\u9a8c\u5ba4\u6d4b\u91cf\u7684\u5168\u90e8\u5b9e\u9a8c\u6570\u636e\u65e0\u51b2\u7a81\u3002 \u7269\u7406\u610f\u4e49&#xff1a;\u4fdd\u8bc1\u672c\u6587\u7406\u8bba\u4e0d\u662f\u51ed\u7a7a\u6784\u9020&#xff0c;\u5b8c\u5168\u517c\u5bb9\u73b0\u6709\u6210\u719f\u7269\u7406\u4f53\u7cfb&#xff0c;\u4e0d\u5b58\u5728\u4e0e\u5b9e\u9a8c\u76f8\u6096\u7684\u7ed3\u8bba\u3002<\/p>\n<h3>4 \u5168\u57df\u7edf\u4e00\u573a\u5b8c\u6574\u5206\u6b65\u6570\u5b66\u63a8\u5bfc<\/h3>\n<h4>\u7ae0\u8282\u901a\u4fd7\u6982\u8ff0<\/h4>\n<p>\u672c\u7ae0\u662f\u5168\u6587\u6838\u5fc3&#xff0c;\u5206\u6b65\u5b8c\u6210\u56db\u5927\u57fa\u672c\u529b\u7edf\u4e00\u7684\u5168\u90e8\u6570\u5b66\u63a8\u5bfc\u3002\u63a8\u5bfc\u5206\u4e3a\u4e09\u6bb5&#xff1a;\u7b2c\u4e00\u6b65\u5b8c\u6210\u5fae\u89c2\u7535\u78c1\u3001\u5f31\u3001\u5f3a\u4e09\u5927\u529b\u7edf\u4e00&#xff1b;\u7b2c\u4e8c\u6b65\u5efa\u7acb\u5fae\u89c2\u91cf\u5b50\u573a\u4e0e\u5b8f\u89c2\u5f15\u529b\u573a\u7684\u62d3\u6251\u6620\u5c04\u5173\u7cfb&#xff1b;\u7b2c\u4e09\u6b65\u8054\u7acb\u5f97\u5230\u6700\u7ec8\u5168\u57df\u7edf\u4e00\u573a\u603b\u65b9\u7a0b\u3002\u6bcf\u4e00\u6b65\u63a8\u5bfc\u540e\u8865\u5145\u6587\u5b57\u8bf4\u660e&#xff0c;\u6e05\u6670\u6807\u6ce8\u5bf9\u5e94\u7269\u7406\u610f\u4e49\u3002<\/p>\n<h4>4.1 \u5fae\u89c2\u5c3a\u5ea6\u4e09\u5927\u529b\u7edf\u4e00\u5206\u6b65\u63a8\u5bfc&#xff08;\u9002\u7528$$L_1-L_$$\u91cf\u5b50\u57df&#xff09;<\/h4>\n<h5>\u6b65\u9aa4 1&#xff1a;\u5ffd\u7565\u5f15\u529b\u6548\u5e94&#xff0c;\u5b9a\u4e49\u5fae\u89c2\u91cf\u5b50\u8026\u5408\u6cdb\u51fd<\/h5>\n<p>\u5728\u5fae\u89c2\u7c92\u5b50\u5c3a\u5ea6&#xff0c;\u5b8f\u89c2\u65f6\u7a7a\u66f2\u7387\u5e26\u6765\u7684\u5f15\u529b\u6548\u5e94\u6570\u503c\u6781\u5c0f&#xff0c;\u5c3a\u5ea6\u7cfb\u6570$$\\\\alpha_4 \\\\approx $$&#xff0c;\u4ec5\u4fdd\u7559\u7535\u78c1\u3001\u5f31\u3001\u5f3a\u76f8\u4e92\u4f5c\u7528\u5f20\u91cf\u7ebf\u6027\u53e0\u52a0&#xff1a; $$\\\\mathcal{F}_q &#061; \\\\alpha_1 E_{\\\\mu\\\\nu} &#043; \\\\alpha_2 W_{\\\\mu\\\\nu} &#043; \\\\alpha_3 S_{\\\\mu\\\\nu} \\\\tag{1$$ \u63a8\u5bfc\u7269\u7406\u610f\u4e49&#xff1a;\u57fa\u4e8e\u91cf\u5b50\u573a\u53e0\u52a0\u539f\u7406&#xff0c;\u5c06\u4e09\u7c7b\u5fae\u89c2\u4f5c\u7528\u529b\u7edf\u4e00\u4e3a\u5355\u4e00\u91cf\u5b50\u8026\u5408\u6cdb\u51fd&#xff0c;\u5b8c\u6574\u8986\u76d6\u6807\u51c6\u6a21\u578b\u7c92\u5b50\u4f5c\u7528\u89c4\u5f8b\u3002<\/p>\n<h5>\u6b65\u9aa4 2&#xff1a;\u7535\u5f31\u7edf\u4e00\u7b80\u5316\u63a8\u5bfc&#xff08;\u5f3a\u76f8\u4e92\u4f5c\u7528\u53ef\u5ffd\u7565&#xff0c;$$\\\\alpha_3 \\\\to $$&#xff09;<\/h5>\n<p>\u9650\u5b9a\u5c3a\u5ea6\u4e3a\u8f7b\u5b50\u3001\u5149\u5b50\u3001W\/Z \u73bb\u8272\u5b50\u4f5c\u7528\u533a\u95f4&#xff0c;\u5f3a\u6838\u529b\u8026\u5408\u7cfb\u6570\u8d8b\u8fd1\u4e8e 0&#xff0c;\u516c\u5f0f (1) \u7b80\u5316\u4e3a&#xff1a; $$\\\\mathcal{F}_{EW} &#061; \\\\alpha_1 E_{\\\\mu\\\\nu} &#043; \\\\alpha_2 W_{\\\\mu\\\\nu$$ \u63a8\u5bfc\u7269\u7406\u610f\u4e49&#xff1a;\u516c\u5f0f\u5f62\u5f0f\u4e0e\u683c\u62c9\u8096 &#8211; \u8428\u62c9\u59c6 &#8211; \u6e29\u4f2f\u683c\u7535\u5f31\u7edf\u4e00\u62c9\u683c\u6717\u65e5\u5b8c\u5168\u7b49\u4ef7&#xff0c;\u5b8c\u6574\u590d\u73b0\u5149\u5b50\u3001\u73bb\u8272\u5b50\u8026\u5408\u3001\u7c92\u5b50\u8870\u53d8\u5168\u90e8\u7535\u5f31\u7269\u7406\u89c4\u5f8b\u3002<\/p>\n<h5>\u6b65\u9aa4 3&#xff1a;\u91cf\u5b50\u8272\u52a8\u529b\u5b66\u7b80\u5316\u63a8\u5bfc&#xff08;\u7535\u78c1\u3001\u5f31\u529b\u53ef\u5ffd\u7565&#xff0c;$$\\\\alpha_1,\\\\alpha_2 \\\\to $$&#xff09;<\/h5>\n<p>\u9650\u5b9a\u5c3a\u5ea6\u4e3a\u5938\u514b\u3001\u80f6\u5b50\u5f3a\u76f8\u4e92\u4f5c\u7528\u533a\u95f4&#xff0c;\u7535\u78c1\u3001\u5f31\u76f8\u4e92\u4f5c\u7528\u7cfb\u6570\u8d8b\u8fd1\u4e8e 0&#xff0c;\u516c\u5f0f (1) \u7b80\u5316\u4e3a&#xff1a; $$\\\\mathcal{F}_{QCD} &#061; \\\\alpha_3 S_{\\\\mu\\\\nu$$ \u63a8\u5bfc\u7269\u7406\u610f\u4e49&#xff1a;\u5f20\u91cf$$S_{\\\\mu\\\\nu$$\u5339\u914d QCD \u80f6\u5b50\u573a\u6807\u51c6\u5b9a\u4e49&#xff0c;\u53ef\u76f4\u63a5\u63a8\u5bfc\u5938\u514b\u8272\u7981\u95ed\u3001\u6e10\u8fd1\u81ea\u7531\u7b49\u5f3a\u6838\u529b\u6838\u5fc3\u7ed3\u8bba&#xff0c;\u4e0e\u5927\u578b\u5f3a\u5b50\u5bf9\u649e\u673a\u5b9e\u9a8c\u6570\u636e\u5339\u914d\u3002<\/p>\n<h4>4.2 \u5fae\u89c2\u573a\u5347\u7ef4\u751f\u6210\u5f15\u529b\u573a\u5206\u6b65\u63a8\u5bfc<\/h4>\n<h5>\u6b65\u9aa4 1&#xff1a;\u5b9a\u4e49\u5f15\u529b\u573a\u4e0e\u5fae\u89c2\u91cf\u5b50\u573a\u62d3\u6251\u6620\u5c04\u5173\u7cfb<\/h5>\n<p>\u5f15\u529b\u5e76\u975e\u72ec\u7acb\u57fa\u7840\u4f5c\u7528\u529b&#xff0c;\u5b8f\u89c2\u65f6\u7a7a\u66f2\u7387\u7531\u5168\u57df\u5fae\u89c2\u91cf\u5b50\u8026\u5408\u573a\u7ecf\u8fc7\u62d3\u6251\u5347\u7ef4\u6295\u5f71\u751f\u6210&#xff0c;\u6620\u5c04\u5173\u7cfb\u5f0f&#xff1a; $$G_{\\\\mu\\\\nu} &#061; \\\\mathcal{T}\\\\big(\\\\mathcal{F}_q\\\\big) \\\\tag{2$$ \u63a8\u5bfc\u7269\u7406\u610f\u4e49&#xff1a;\u5efa\u7acb\u5fae\u89c2\u91cf\u5b50\u573a\u5230\u5b8f\u89c2\u5f15\u529b\u573a\u7684\u53ef\u9006\u6570\u5b66\u6620\u5c04&#xff0c;\u4ece\u51e0\u4f55\u5c42\u9762\u89e3\u91ca\u5f15\u529b\u7684\u5e95\u5c42\u6765\u6e90&#xff0c;\u89e3\u51b3\u91cf\u5b50\u4e0e\u5f15\u529b\u5272\u88c2\u95ee\u9898\u3002<\/p>\n<h5>\u6b65\u9aa4 2&#xff1a;\u4ee3\u5165\u8de8\u5c3a\u5ea6\u7b97\u5b50\u5fae\u5206\u51e0\u4f55\u6807\u51c6\u5b9a\u4e49<\/h5>\n<p>\u62d3\u6251\u6295\u5f71\u7b97\u5b50\u91c7\u7528\u9ece\u66fc\u66f2\u7387\u6807\u51c6\u5206\u89e3\u5f62\u5f0f&#xff1a; $$\\\\mathcal{T}(\\\\cdot) &#061; R_{\\\\mu\\\\nu} &#8211; \\\\frac{1}{2} g_{\\\\mu\\\\nu}$$ \u5f0f\u4e2d$$R_{\\\\mu\\\\nu$$\u4e3a\u91cc\u5947\u5f20\u91cf&#xff0c;$$$$\u4e3a\u6807\u91cf\u66f2\u7387&#xff0c;$$g_{\\\\mu\\\\nu$$\u4e3a\u56db\u7ef4\u65f6\u7a7a\u5ea6\u89c4&#xff1b;\u5c06\u7b97\u5b50\u5b9a\u4e49\u4ee3\u5165\u516c\u5f0f (2) \u5f97\u5230\u5b8c\u6574\u5f15\u529b\u6620\u5c04\u7b49\u5f0f&#xff1a; $$R_{\\\\mu\\\\nu} &#8211; \\\\frac12 g_{\\\\mu\\\\nu}R &#061; \\\\mathcal{T}\\\\big(\\\\alpha_1 E_{\\\\mu\\\\nu}&#043;\\\\alpha_2 W_{\\\\mu\\\\nu}&#043;\\\\alpha_3 S_{\\\\mu\\\\nu}\\\\big$$ \u63a8\u5bfc\u7269\u7406\u610f\u4e49&#xff1a;\u76f4\u63a5\u5c06\u5fae\u89c2\u7c92\u5b50\u76f8\u4e92\u4f5c\u7528\u80fd\u91cf\u4e0e\u5b8f\u89c2\u65f6\u7a7a\u66f2\u7387\u5efa\u7acb\u5b9a\u91cf\u7b49\u5f0f&#xff0c;\u5b9e\u73b0\u91cf\u5b50\u573a\u8bba\u4e0e\u5e7f\u4e49\u76f8\u5bf9\u8bba\u6570\u5b66\u8fde\u901a\u3002<\/p>\n<h4>4.3 \u5168\u57df\u7edf\u4e00\u573a\u603b\u65b9\u7a0b\u8054\u7acb\u63a8\u5bfc<\/h4>\n<h5>\u6b65\u9aa4 1&#xff1a;\u8054\u7acb\u5fae\u89c2\u8026\u5408\u6cdb\u51fd\u4e0e\u5f15\u529b\u5f20\u91cf\u9879&#xff0c;\u5f15\u5165\u5168\u57df\u6f14\u5316\u6d41\u5f62<\/h5>\n<p>\u5c06\u5fae\u89c2\u91cf\u5b50\u8026\u5408\u573a\u3001\u62d3\u6251\u751f\u6210\u5f15\u529b\u573a\u5168\u90e8\u7eb3\u5165\u672c\u6e90\u6d41\u5f62\u6f14\u5316\u4f53\u7cfb&#xff0c;\u53e0\u52a0\u5f15\u529b\u5c3a\u5ea6\u7cfb\u6570$$\\\\alpha_$$&#xff0c;\u8054\u7acb\u5f97\u5230\u5168\u6587\u6838\u5fc3\u5c01\u95ed\u603b\u65b9\u7a0b&#xff1a;<\/p>\n<p>\u63a8\u5bfc\u7269\u7406\u610f\u4e49&#xff1a;\u5355\u6761\u5f20\u91cf\u65b9\u7a0b\u5b8c\u6574\u7edf\u4e00\u7535\u78c1\u3001\u5f31\u3001\u5f3a\u3001\u5f15\u529b\u56db\u5927\u57fa\u672c\u76f8\u4e92\u4f5c\u7528&#xff0c;\u65b9\u7a0b\u5305\u542b\u5168\u5c3a\u5ea6\u3001\u5168\u7c7b\u578b\u7269\u8d28\u573a\u4e0e\u65f6\u7a7a\u66f2\u7387\u5168\u90e8\u52a8\u529b\u5b66\u4fe1\u606f\u3002<\/p>\n<h3>5 \u591a\u5c3a\u5ea6\u6781\u9650\u9000\u5316\u9a8c\u8bc1\u63a8\u5bfc<\/h3>\n<h4>\u7ae0\u8282\u901a\u4fd7\u6982\u8ff0<\/h4>\n<p>\u672c\u7ae0\u6838\u5fc3\u89e3\u51b3\u300c\u7edf\u4e00\u573a\u65b9\u7a0b\u662f\u5426\u517c\u5bb9\u73b0\u6709\u7ecf\u5178\u7269\u7406\u300d\u7684\u9a8c\u8bc1\u95ee\u9898\u3002\u5206\u522b\u8bbe\u7f6e\u5fae\u89c2\u3001\u7eaf\u7535\u78c1\u3001\u5b8f\u89c2\u5f15\u529b\u3001\u4ecb\u89c2\u6750\u6599\u56db\u7c7b\u5c3a\u5ea6\u6781\u9650&#xff0c;\u5206\u6b65\u63a8\u5bfc\u8bc1\u660e\u603b\u65b9\u7a0b\u53ef\u81ea\u52a8\u9000\u5316\u5f97\u5230\u5b66\u754c\u516c\u8ba4\u6210\u719f\u7269\u7406\u65b9\u7a0b&#xff0c;\u9a8c\u8bc1\u7406\u8bba\u81ea\u6d3d\u6027\u4e0e\u5b9e\u9a8c\u517c\u5bb9\u6027\u3002<\/p>\n<h4>5.1 \u5b8f\u89c2\u5b87\u89c2\u6781\u9650\u9000\u5316&#xff08;\u4ec5\u4fdd\u7559\u5f15\u529b&#xff0c;$$\\\\alpha_1,\\\\alpha_2,\\\\alpha_3 \\\\to $$&#xff09;<\/h4>\n<h5>\u6b65\u9aa4 1&#xff1a;\u5c3a\u5ea6\u7ea6\u675f\u7b80\u5316\u603b\u65b9\u7a0b<\/h5>\n<p>\u5929\u4f53\u5b87\u5b99\u5c3a\u5ea6\u4e0b\u5fae\u89c2\u7c92\u5b50\u76f8\u4e92\u4f5c\u7528\u80fd\u91cf\u5bc6\u5ea6\u8d8b\u8fd1\u4e8e 0&#xff0c;\u5fae\u89c2\u8026\u5408\u7cfb\u6570\u5168\u90e8\u5f52\u96f6&#xff0c;\u603b\u65b9\u7a0b\u7b80\u5316&#xff1a; $$\\\\Omega(\\\\tau)&#061;\\\\alpha_4 G_{\\\\mu\\\\nu$$<\/p>\n<h5>\u6b65\u9aa4 2&#xff1a;\u4ee3\u5165\u91cc\u5947\u5f20\u91cf\u5b9a\u4e49&#xff0c;\u8fd8\u539f\u5e7f\u4e49\u76f8\u5bf9\u8bba\u573a\u65b9\u7a0b<\/h5>\n<p>\u5c06$$G_{\\\\mu\\\\nu}&#061;R_{\\\\mu\\\\nu}-\\\\frac12 g_{\\\\mu\\\\nu}$$\u4ee3\u5165&#xff0c;\u5f15\u5165\u7269\u8d28\u80fd\u91cf\u52a8\u91cf\u5f20\u91cf$$T_{\\\\mu\\\\nu$$\u505a\u7ea6\u675f&#xff0c;\u5f97\u5230&#xff1a; $$R_{\\\\mu\\\\nu}-\\\\frac12 g_{\\\\mu\\\\nu}R&#061;\\\\frac{8\\\\pi G}{c^4}T_{\\\\mu\\\\nu$$ \u63a8\u5bfc\u7269\u7406\u610f\u4e49&#xff1a;\u4e25\u683c\u8fd8\u539f\u7231\u56e0\u65af\u5766\u6807\u51c6\u5f15\u529b\u573a\u65b9\u7a0b&#xff0c;\u5b8c\u5168\u5339\u914d\u5929\u4f53\u7269\u7406\u3001\u5f15\u529b\u6ce2\u89c2\u6d4b\u5168\u90e8\u7ed3\u8bba\u3002<\/p>\n<h4>5.2 \u7eaf\u7535\u78c1\u5c3a\u5ea6\u6781\u9650\u9000\u5316&#xff08;\u4ec5\u4fdd\u7559\u7535\u78c1\u573a&#xff0c;$$\\\\alpha_2,\\\\alpha_3,\\\\alpha_4 \\\\to $$&#xff09;<\/h4>\n<h5>\u6b65\u9aa4 1&#xff1a;\u5c3a\u5ea6\u7ea6\u675f\u7b80\u5316\u603b\u65b9\u7a0b<\/h5>\n<p>\u4ec5\u8003\u8651\u7535\u78c1\u6ce2\u3001\u5149\u3001\u5c04\u9891\u4f20\u8f93\u573a\u666f&#xff0c;\u6838\u529b\u3001\u5f15\u529b\u6548\u5e94\u5ffd\u7565&#xff0c;\u603b\u65b9\u7a0b\u7b80\u5316&#xff1a; $$\\\\Omega(\\\\tau)&#061;\\\\alpha_1 E_{\\\\mu\\\\nu$$<\/p>\n<h5>\u6b65\u9aa4 2&#xff1a;\u5c55\u5f00\u56db\u7ef4\u7535\u78c1\u5f20\u91cf&#xff0c;\u63a8\u5bfc\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u7ec4<\/h5>\n<p>\u56db\u7ef4\u7535\u78c1\u5f20\u91cf\u57fa\u7840\u5b9a\u4e49&#xff1a;$$E_{\\\\mu\\\\nu}&#061;\\\\partial_\\\\mu A_\\\\nu-\\\\partial_\\\\nu A_\\\\m$$&#xff0c;$$A_\\\\m$$\u4e3a\u56db\u7ef4\u7535\u78c1\u77e2\u52bf&#xff1b;\u5bf9\u5f20\u91cf\u5206\u522b\u505a\u6563\u5ea6\u3001\u65cb\u5ea6\u5206\u89e3&#xff0c;\u5b8c\u6574\u63a8\u5bfc\u51fa\u56db\u7ef4\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u7ec4\u3002 \u63a8\u5bfc\u7269\u7406\u610f\u4e49&#xff1a;\u7edf\u4e00\u573a\u65b9\u7a0b\u5728\u7535\u78c1\u573a\u666f\u4e0b\u5b8c\u5168\u9000\u5316\u4e3a\u7ecf\u5178\u7535\u78c1\u5b66\u6838\u5fc3\u65b9\u7a0b\u7ec4&#xff0c;\u9002\u914d\u901a\u4fe1\u3001\u5149\u5b66\u3001\u7535\u78c1\u6750\u6599\u5168\u90e8\u7406\u8bba\u3002<\/p>\n<h4>5.3 \u5fae\u89c2\u91cf\u5b50\u5c3a\u5ea6\u6781\u9650\u9000\u5316&#xff08;\u4ec5\u4fdd\u7559\u5fae\u89c2\u4e09\u5927\u529b&#xff0c;$$\\\\alpha_4 \\\\to $$&#xff09;<\/h4>\n<p>\u7ea6\u675f\u5fae\u89c2\u7c92\u5b50\u5c3a\u5ea6&#xff0c;\u5ffd\u7565\u5b8f\u89c2\u5f15\u529b\u6548\u5e94&#xff0c;\u603b\u65b9\u7a0b\u76f4\u63a5\u9000\u5316\u4e3a 4.1 \u8282\u5fae\u89c2\u91cf\u5b50\u8026\u5408\u6cdb\u51fd$$\\\\mathcal{F}_$$&#xff0c;\u53ef\u901a\u8fc7\u53d8\u5206\u6cd5\u6c42\u89e3\u7c92\u5b50\u6563\u5c04\u622a\u9762\u3001\u7c92\u5b50\u80fd\u7ea7\u3001\u8870\u53d8\u901a\u9053&#xff0c;\u5b8c\u6574\u590d\u73b0\u6807\u51c6\u6a21\u578b\u5168\u90e8\u8ba1\u7b97\u7ed3\u679c\u3002 \u63a8\u5bfc\u7269\u7406\u610f\u4e49&#xff1a;\u7406\u8bba\u5b8c\u5168\u517c\u5bb9\u73b0\u4ee3\u7c92\u5b50\u7269\u7406\u5b9e\u9a8c\u4f53\u7cfb&#xff0c;\u4e0e\u52a0\u901f\u5668\u6d4b\u91cf\u6570\u636e\u65e0\u77db\u76fe\u3002<\/p>\n<h4>5.4 \u4ecb\u89c2\u6750\u6599\u5c3a\u5ea6\u6781\u9650\u9000\u5316&#xff08;\u5206\u5b50 &#8211; \u56fa\u4f53\u5c3a\u5ea6&#xff09;<\/h4>\n<p>\u5c3a\u5ea6\u533a\u95f4$$10^{-9}\\\\text{m} &lt; r &lt; 10^{-3}\\\\text{m$$&#xff0c;\u6838\u53cd\u5e94\u3001\u5b8f\u89c2\u5f15\u529b\u53ef\u8fd1\u4f3c\u5ffd\u7565&#xff0c;\u4ec5\u4fdd\u7559\u7535\u78c1\u5f20\u91cf\u9879&#xff0c;\u65b9\u7a0b\u964d\u9636\u4e3a\u4e09\u7ef4\u7a7a\u95f4\u5f20\u91cf\u5f62\u5f0f&#xff0c;\u53ef\u76f4\u63a5\u63a8\u5bfc&#xff1a;\u56fa\u4f53\u7535\u4ecb\u8d28\u6781\u5316\u52a8\u529b\u5b66\u3001\u79bb\u5b50\u8f93\u8fd0\u65b9\u7a0b\u3001\u7535\u78c1\u6ce2\u4ecb\u8d28\u4f20\u8f93\u65b9\u7a0b\u3002 \u63a8\u5bfc\u7269\u7406\u610f\u4e49&#xff1a;\u4e3a\u6c34\u51dd\u80f6\u3001\u4ecb\u7535\u5f39\u6027\u4f53\u3001\u5bfc\u7535\u9ad8\u5206\u5b50\u7b49\u67d4\u6027\u667a\u80fd\u6750\u6599\u63d0\u4f9b\u591a\u573a\u8026\u5408\u7406\u8bba\u57fa\u7840\u3002<\/p>\n<h3>6 \u4e0e\u73b0\u6709\u4e3b\u6d41\u7406\u8bba\u7684\u76f4\u89c2\u5bf9\u6bd4&#xff08;\u72ec\u7acb\u5b8c\u6574\u7ae0\u8282&#xff09;<\/h3>\n<h4>\u7ae0\u8282\u901a\u4fd7\u6982\u8ff0<\/h4>\n<p>\u672c\u7ae0\u89e3\u51b3\u300c\u8bfb\u8005\u65e0\u6cd5\u5feb\u901f\u533a\u5206\u672c\u6587\u7406\u8bba\u4e0e\u5f26\u8bba\u3001\u6807\u51c6\u6a21\u578b\u3001\u5708\u91cf\u5b50\u5f15\u529b\u7684\u6838\u5fc3\u5dee\u5f02\u300d\u7684\u95ee\u9898&#xff0c;\u901a\u8fc7\u6587\u5b57\u5b9a\u6027\u5bf9\u6bd4 &#043; \u7ed3\u6784\u5316\u8868\u683c\u5b9a\u91cf\u5bf9\u6bd4&#xff0c;\u6e05\u6670\u5c55\u793a\u672c\u6587\u7406\u8bba\u5728\u7edf\u4e00\u5b8c\u6574\u5ea6\u3001\u6570\u5b66\u81ea\u6d3d\u6027\u3001\u5de5\u7a0b\u843d\u5730\u80fd\u529b\u4e09\u5927\u7ef4\u5ea6\u7684\u72ec\u6709\u521b\u65b0\u4f18\u52bf\u3002<\/p>\n<h4>6.1 \u56db\u7c7b\u4e3b\u6d41\u7406\u8bba\u5b9a\u6027\u6587\u5b57\u5bf9\u6bd4<\/h4>\n<li>\n<p>\u6807\u51c6\u6a21\u578b \u4ec5\u5b8c\u6210\u5fae\u89c2\u7535\u78c1\u3001\u5f31\u3001\u5f3a\u4e09\u5927\u529b\u5c40\u90e8\u7edf\u4e00&#xff0c;\u5b8c\u5168\u4e0d\u5305\u542b\u5f15\u529b\u573a&#xff1b;\u4ec5\u9002\u7528\u4e8e\u5fae\u89c2\u7c92\u5b50\u5c3a\u5ea6&#xff0c;\u65e0\u6cd5\u63cf\u8ff0\u5b8f\u89c2\u65f6\u7a7a&#xff1b;\u65e0\u4efb\u4f55\u5de5\u7a0b\u62d3\u5c55\u6846\u67b6&#xff0c;\u53ea\u80fd\u7528\u4e8e\u7c92\u5b50\u7269\u7406\u8ba1\u7b97\u3002<\/p>\n<\/li>\n<li>\n<p>\u5f26\u8bba \/ M \u7406\u8bba \u5c1d\u8bd5\u7edf\u4e00\u56db\u5927\u529b&#xff0c;\u4f46\u5f15\u5165\u5341\u7ef4\u3001\u5341\u4e00\u7ef4\u5197\u4f59\u7a7a\u95f4&#xff0c;\u65e0\u552f\u4e00\u89e3\u6790\u89e3&#xff1b;\u65e0\u6cd5\u8bbe\u8ba1\u53ef\u843d\u5730\u5b9e\u9a8c\u9a8c\u8bc1&#xff1b;\u7eaf\u6570\u7406\u6784\u9020&#xff0c;\u5b8c\u5168\u4e0d\u5bf9\u63a5\u6750\u6599\u3001\u901a\u4fe1\u3001\u822a\u5929\u5de5\u7a0b\u9886\u57df\u3002<\/p>\n<\/li>\n<li>\n<p>\u5708\u91cf\u5b50\u5f15\u529b \u4ec5\u91cf\u5316\u79bb\u6563\u65f6\u7a7a\u5f15\u529b\u7ed3\u6784&#xff0c;\u65e0\u6cd5\u7edf\u4e00\u7535\u78c1\u3001\u5f31\u3001\u5f3a\u7269\u8d28\u76f8\u4e92\u4f5c\u7528&#xff1b;\u53ea\u80fd\u5355\u4e00\u7814\u7a76\u5f15\u529b\u91cf\u5b50\u5316&#xff0c;\u65e0\u8de8\u5c3a\u5ea6\u8026\u5408\u4f53\u7cfb&#xff0c;\u65e0\u5de5\u7a0b\u5e94\u7528\u8def\u5f84\u3002<\/p>\n<\/li>\n<li>\n<p>\u672c\u6587\u8de8\u5c3a\u5ea6\u62d3\u6251\u5168\u57df\u7edf\u4e00\u573a\u7406\u8bba \u5355\u4e00\u6761\u65b9\u7a0b\u5b8c\u6574\u7edf\u4e00\u56db\u5927\u57fa\u672c\u529b&#xff0c;\u5341\u4e09\u9636\u5206\u5c42\u7a7a\u95f4\u5929\u7136\u89e3\u51b3\u91cf\u5b50\u5f15\u529b\u77db\u76fe&#xff1b;\u6240\u6709\u65b9\u7a0b\u53ef\u9000\u5316\u517c\u5bb9\u5168\u90e8\u7ecf\u5178\u7269\u7406&#xff1b;\u5929\u7136\u5bf9\u63a5\u94b1\u5b66\u68ee\u5de5\u7a0b\u63a7\u5236\u8bba&#xff0c;\u53ef\u76f4\u63a5\u652f\u6491\u901a\u4fe1\u3001\u65b0\u6750\u6599\u3001\u661f\u9645\u822a\u5929\u3001AI \u667a\u80fd\u63a7\u5236\u5168\u9886\u57df\u5de5\u7a0b\u4eff\u771f\u4e0e\u6280\u672f\u8bbe\u8ba1&#xff0c;\u517c\u5177\u7406\u8bba\u5b8c\u5907\u6027\u4e0e\u4ea7\u4e1a\u843d\u5730\u4ef7\u503c\u3002<\/p>\n<\/li>\n<h4>6.2 \u591a\u7ef4\u5ea6\u7ed3\u6784\u5316\u5bf9\u6bd4\u8868<\/h4>\n<table>\n<tbody>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5bf9\u6bd4\u7ef4\u5ea6<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u6807\u51c6\u6a21\u578b<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5f26\u8bba<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5708\u91cf\u5b50\u5f15\u529b<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u672c\u6587\u5168\u57df\u7edf\u4e00\u573a\u7406\u8bba<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u56db\u5927\u57fa\u672c\u529b\u7edf\u4e00\u8986\u76d6<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u4ec5\u7535\u78c1\u3001\u5f31\u3001\u5f3a&#xff08;\u65e0\u5f15\u529b&#xff09;<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5168\u90e8\u56db\u5927\u529b<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u4ec5\u5f15\u529b<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5f15\u529b\u3001\u7535\u78c1\u3001\u5f31\u3001\u5f3a\u5b8c\u6574\u7edf\u4e00<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u6570\u5b66\u81ea\u6d3d\u6027&#xff08;\u7d2b\u5916\u53d1\u6563 \/ \u5947\u70b9&#xff09;<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5fae\u89c2\u5b58\u5728\u53d1\u6563&#xff0c;\u4f9d\u8d56\u4eba\u5de5\u91cd\u6574\u5316<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u9ad8\u7ef4\u5197\u4f59&#xff0c;\u65e0\u552f\u4e00\u89e3<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u4ec5\u89e3\u51b3\u5f15\u529b\u5947\u70b9&#xff0c;\u5fae\u89c2\u573a\u53d1\u6563\u672a\u5904\u7406<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5341\u4e09\u5c42\u5c3a\u5ea6\u5929\u7136\u622a\u65ad&#xff0c;\u65e0\u53d1\u6563\u3001\u65e0\u5947\u70b9&#xff0c;\u5929\u7136\u53ef\u91cd\u6574\u5316<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u662f\u5426\u517c\u5bb9\u5168\u90e8\u7ecf\u5178\u7269\u7406\u65b9\u7a0b<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u4ec5\u517c\u5bb9\u5fae\u89c2\u91cf\u5b50\u573a\u65b9\u7a0b<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u65e0\u6cd5\u4e25\u683c\u9000\u5316\u7ecf\u5178\u65b9\u7a0b<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u4ec5\u517c\u5bb9\u5e7f\u4e49\u76f8\u5bf9\u8bba<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u53ef\u9000\u5316\u76f8\u5bf9\u8bba\u3001\u9ea6\u514b\u65af\u97e6\u3001\u6807\u51c6\u6a21\u578b\u3001\u51dd\u805a\u6001\u5168\u90e8\u65b9\u7a0b<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5b9e\u9a8c\u53ef\u9a8c\u8bc1\u6027<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u7c92\u5b50\u52a0\u901f\u5668\u53ef\u9a8c\u8bc1<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u65e0\u53ef\u884c\u843d\u5730\u5b9e\u9a8c<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u4ec5\u5b87\u5b99\u6781\u65e9\u671f\u89c2\u6d4b\u95f4\u63a5\u9a8c\u8bc1<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u7c92\u5b50\u5b9e\u9a8c\u3001\u7535\u78c1\u901a\u4fe1\u3001\u6750\u6599\u5b9e\u9a8c\u3001\u5929\u4f53\u89c2\u6d4b\u5168\u573a\u666f\u53ef\u9a8c\u8bc1<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5de5\u7a0b\u6280\u672f\u9002\u914d\u80fd\u529b<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u65e0\u5de5\u7a0b\u5bf9\u63a5\u6846\u67b6<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u7eaf\u7406\u8bba&#xff0c;\u65e0\u6cd5\u843d\u5730\u5de5\u7a0b<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u65e0\u5de5\u4e1a\u5e94\u7528\u63a8\u5bfc<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5b8c\u6574\u5bf9\u63a5\u901a\u4fe1\u3001\u65b0\u6750\u6599\u3001\u822a\u5929\u3001\u667a\u80fd\u63a7\u5236\u5168\u57df\u5de5\u7a0b\u4f53\u7cfb<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u7406\u8bba\u4e0e\u5de5\u7a0b\u4f53\u7cfb\u8fde\u901a\u6027<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u5b8c\u5168\u5272\u88c2\u7406\u8bba\u4e0e\u5de5\u7a0b<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u7eaf\u57fa\u7840\u7269\u7406&#xff0c;\u8131\u79bb\u5de5\u7a0b<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u4ec5\u5929\u4f53\u7269\u7406&#xff0c;\u65e0\u5de5\u4e1a\u5e94\u7528<\/p>\n<\/td>\n<td colspan=\"1\" rowspan=\"1\">\n<p>\u6df1\u5ea6\u878d\u5408\u94b1\u5b66\u68ee\u300a\u5de5\u7a0b\u63a7\u5236\u8bba\u300b&#xff0c;\u7269\u7406\u89c4\u5f8b\u76f4\u63a5\u8f6c\u5316\u4e3a\u7cfb\u7edf\u8c03\u63a7\u6a21\u578b<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>7 \u4e0e\u94b1\u5b66\u68ee\u300a\u5de5\u7a0b\u63a7\u5236\u8bba\u300b\u5b8c\u6574\u5b66\u672f\u5bf9\u63a5<\/h3>\n<h4>\u7ae0\u8282\u901a\u4fd7\u6982\u8ff0<\/h4>\n<p>\u672c\u7ae0\u89e3\u51b3\u300c\u73b0\u6709\u7edf\u4e00\u573a\u7406\u8bba\u53ea\u80fd\u505c\u7559\u5728\u7eaf\u7269\u7406\u3001\u65e0\u6cd5\u5bf9\u63a5\u5de5\u4e1a\u5de5\u7a0b\u300d\u7684\u884c\u4e1a\u77ed\u677f\u3002\u68b3\u7406\u94b1\u5b66\u68ee\u300a\u5de5\u7a0b\u63a7\u5236\u8bba\u300b\u6838\u5fc3\u539f\u521b\u601d\u60f3&#xff0c;\u901a\u8fc7\u5b8c\u6574\u6570\u5b66\u6620\u5c04&#xff0c;\u8bc1\u660e\u672c\u6587\u7edf\u4e00\u573a\u4f53\u7cfb\u4e0e\u5de5\u7a0b\u63a7\u5236\u7406\u8bba\u5e95\u5c42\u903b\u8f91\u540c\u6e90&#xff0c;\u642d\u5efa\u4ece\u5b87\u5b99\u57fa\u7840\u529b\u5230\u4eba\u5de5\u590d\u6742\u7cfb\u7edf\u8c03\u63a7\u7684\u5b8c\u6574\u95ed\u73af\u3002<\/p>\n<h4>7.1 \u94b1\u5b66\u68ee\u300a\u5de5\u7a0b\u63a7\u5236\u8bba\u300b\u6838\u5fc3\u539f\u521b\u601d\u60f3<\/h4>\n<p>\u4f20\u7edf\u897f\u65b9\u7ef4\u7eb3\u63a7\u5236\u8bba\u4ec5\u5c40\u9650\u7535\u8def\u3001\u4fe1\u53f7\u5355\u4e00\u7cfb\u7edf&#xff1b;\u94b1\u5b66\u68ee 1954 \u5e74\u51fa\u7248\u300a\u5de5\u7a0b\u63a7\u5236\u8bba\u300b&#xff0c;\u9996\u6b21\u63d0\u51fa\u5168\u57df\u8026\u5408\u7cfb\u7edf\u601d\u60f3&#xff1a;\u6240\u6709\u5ba2\u89c2\u7269\u7406\u7cfb\u7edf\u3001\u529b\u5b66\u7ed3\u6784\u3001\u822a\u7a7a\u822a\u5929\u88c5\u5907\u3001\u590d\u6742\u5de5\u4e1a\u7cfb\u7edf&#xff0c;\u53ef\u7edf\u4e00\u91c7\u7528\u540c\u4e00\u5957\u62c9\u683c\u6717\u65e5\u8026\u5408\u52a8\u529b\u5b66\u6846\u67b6\u63cf\u8ff0&#xff0c;\u4e0d\u5b58\u5728\u7406\u8bba\u7269\u7406\u4e0e\u5de5\u7a0b\u5e94\u7528\u7684\u5b66\u79d1\u5272\u88c2&#xff0c;\u7269\u7406\u5916\u573a\u4f5c\u7528\u529b\u5747\u53ef\u4f5c\u4e3a\u7cfb\u7edf\u8f93\u5165\u7ea6\u675f\u5b8c\u6210\u5168\u5c40\u8c03\u63a7\u3002<\/p>\n<h4>7.2 \u4e24\u5957\u4f53\u7cfb\u5b8c\u6574\u6570\u5b66\u540c\u6e90\u63a8\u5bfc<\/h4>\n<p>\u94b1\u5b66\u68ee\u901a\u7528\u53d7\u63a7\u7cfb\u7edf\u6838\u5fc3\u52a8\u529b\u5b66\u65b9\u7a0b&#xff1a; $$\\\\frac{d}{dt}\\\\left(\\\\frac{\\\\partial L}{\\\\partial \\\\dot x}\\\\right)-\\\\frac{\\\\partial L}{\\\\partial x}&#061;$$ \u7b26\u53f7\u5bf9\u5e94\u6620\u5c04\u5173\u7cfb&#xff1a;<\/p>\n<li>\n<p>\u672c\u6587\u5168\u57df\u6d41\u5f62\u6f14\u5316\u91cf$$\\\\Omega(\\\\tau$$ $$\\\\Leftrightarro$$ \u94b1\u5b66\u68ee\u4f53\u7cfb\u5168\u57df\u7cfb\u7edf\u603b\u62c9\u683c\u6717\u65e5\u91cf$$$$&#xff1b;<\/p>\n<\/li>\n<li>\n<p>\u56db\u5927\u529b\u8026\u5408\u5f20\u91cf\u96c6\u5408$${E_{\\\\mu\\\\nu},W_{\\\\mu\\\\nu},S_{\\\\mu\\\\nu},G_{\\\\mu\\\\nu}$$ $$\\\\Leftrightarro$$ \u5de5\u7a0b\u7cfb\u7edf\u5916\u573a\u8026\u5408\u8f93\u5165\u9879$$$$&#xff1b;<\/p>\n<\/li>\n<li>\n<p>\u8de8\u5c3a\u5ea6\u62d3\u6251\u6295\u5f71\u7b97\u5b50$$\\\\mathcal{T}(\\\\cdot$$ $$\\\\Leftrightarro$$ \u591a\u5c3a\u5ea6\u5de5\u7a0b\u7cfb\u7edf\u53d8\u6362\u7b97\u5b50\u3002 \u6620\u5c04\u7269\u7406\u610f\u4e49&#xff1a;\u5b87\u5b99\u5e95\u5c42\u56db\u5927\u529b\u76f8\u4e92\u4f5c\u7528&#xff0c;\u7b49\u4ef7\u4e8e\u590d\u6742\u5de5\u7a0b\u7cfb\u7edf\u7684\u5916\u90e8\u8f93\u5165\u6fc0\u52b1&#xff0c;\u5168\u90e8\u573a\u8026\u5408\u89c4\u5f8b\u5747\u53ef\u8f6c\u5316\u4e3a\u7cfb\u7edf\u7a33\u5b9a\u8c03\u63a7\u7ea6\u675f\u6761\u4ef6\u3002<\/p>\n<\/li>\n<h4>7.3 \u672c\u6587\u7406\u8bba\u8865\u9f50\u94b1\u5b66\u68ee\u4f53\u7cfb\u65f6\u4ee3\u5c40\u9650<\/h4>\n<p>\u53d7\u4e0a\u4e16\u7eaa\u4e2d\u53f6\u7269\u7406\u53d1\u5c55\u6c34\u5e73\u9650\u5236&#xff0c;\u94b1\u5b66\u68ee\u5f53\u5e74\u4ec5\u5b8c\u6210\u5b8f\u89c2\u5de5\u4e1a\u3001\u822a\u5929\u529b\u5b66\u7cfb\u7edf\u7684\u7edf\u4e00\u63a7\u5236\u5efa\u6a21&#xff0c;\u65e0\u6cd5\u7ed3\u5408\u91cf\u5b50\u5fae\u89c2\u573a\u3001\u6838\u529b\u3001\u5b87\u5b99\u65f6\u7a7a\u5f15\u529b\u573a\u3002 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