{"id":49891,"date":"2024-04-21T11:01:22","date_gmt":"2024-04-21T03:01:22","guid":{"rendered":"https:\/\/swarma.org\/?p=49891"},"modified":"2024-04-21T11:01:22","modified_gmt":"2024-04-21T03:01:22","slug":"%e5%b9%bf%e4%b9%89%e5%af%b9%e7%a7%b0%e6%80%a7%ef%bc%9a%e8%81%94%e7%bb%93%e9%ab%98%e8%83%bd%e7%90%86%e8%ae%ba%e3%80%81%e5%87%9d%e8%81%9a%e6%80%81%e7%90%86%e8%ae%ba%e4%b8%8e%e6%95%b0%e5%ad%a6%e7%9a%84","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=49891","title":{"rendered":"\u5e7f\u4e49\u5bf9\u79f0\u6027\uff1a\u8054\u7ed3\u9ad8\u80fd\u7406\u8bba\u3001\u51dd\u805a\u6001\u7406\u8bba\u4e0e\u6570\u5b66\u7684\u65b0\u6982\u5ff5"},"content":{"rendered":"
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\u4e0e\u6b64\u76f8\u53cd\uff0c\u8bfa\u7279\u5b9a\u7406\u4e2d\u7684\u5bf9\u79f0\u6027\u8981\u6c42\u03bb\u4e0e\u65f6\u7a7a\u5750\u6807\u65e0\u5173\uff0c\u5373\u5bf9\u5e94\u4e8e \u201c\u5168\u5c40\u5bf9\u79f0\u6027\u201d<\/span>\uff08global symmetry\uff09<\/span>\u3002\u672c\u6587\u4e2d\u63d0\u5230\u7684\u201c\u5bf9\u79f0\u6027\u201d\u9ed8\u8ba4\u90fd\u6307\u7684\u662f\u5168\u5c40\u5bf9\u79f0\u6027\u3002<\/span><\/span><\/section>\n

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\u56de\u5230\u4e4b\u524d\u7684\u95ee\u9898\uff1a\u7535\u8377\u5b88\u6052\u662f\u7531\u4ec0\u4e48\u8fde\u7eed\u5bf9\u79f0\u6027\u5f97\u5230\u7684\u5462\uff1f<\/span><\/section>\n

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\u7b54\u6848\u662f\uff1a\u5168\u5c40\u89c4\u8303\u5bf9\u79f0\u6027\uff01\u7535\u8377\u662f\u4ee4\u89c4\u8303\u53c2\u6570\u03bb\u4e0e\u65f6\u7a7a\u5750\u6807\u65e0\u5173\u540e\uff0c\u5e94\u7528\u8bfa\u7279\u5b9a\u7406\u63a8\u51fa\u7684\u5b88\u6052\u91cf\u3002<\/span><\/section>\n


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\u5bf9\u79f0\u6027\u80cc\u540e\u7684\u6570\u5b66\u2014\u2014\u7fa4<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


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\u7fa4\u662f\u753119\u4e16\u7eaa\u6570\u5b66\u5929\u624d\u4f3d\u7f57\u74e6<\/span>\uff08\u00c9variste Galois\uff09<\/span>\u3001\u963f\u8d1d\u5c14<\/span>\uff08Niels Henrik Abel\uff09<\/span>\u7b49\u4eba\u63d0\u51fa\u7684\u4ee3\u6570\u7ed3\u6784\uff0c\u5b83\u4f5c\u4e3a\u63cf\u8ff0\u5bf9\u79f0\u6027\u7684\u57fa\u672c\u6570\u5b66\u6846\u67b6\uff0c\u5177\u6709\u9ad8\u5ea6\u7684\u7f8e\u611f\u3002<\/span><\/span><\/section>\n

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\u7b80\u800c\u8a00\u4e4b\uff0c\u7fa4\u662f\u4e00\u4e2a\u96c6\u5408\uff0c\u4e00\u79cd\u88ab\u989d\u5916\u8d4b\u4e88\u7684\u4ee3\u6570\u7ed3\u6784\uff0c\u5373\u5143\u7d20\u4e4b\u95f4\u7684\u7fa4\u8fd0\u7b97a\u00b7b<\/span>\uff08\u4e5f\u53ef\u79f0\u4e3a\u7fa4\u4e58\u6cd5\u3001\u7fa4\u52a0\u6cd5\uff09<\/span>\u3002\u7fa4\u8fd0\u7b97\u9700\u8981\u6ee1\u8db3<\/span><\/span><\/p>\n

(1) \u7ed3\u5408\u5f8ba\u00b7(b\u00b7c)=(a\u00b7b)\u00b7c\uff1b<\/span><\/p>\n

(2) \u53ef\u9006\u6027\uff0c\u5373\u7fa4\u4e2d\u6709\u552f\u4e00\u7684\u5355\u4f4d\u5143e\uff0c\u4f7f\u5f97\u5bf9\u4efb\u4f55\u5143\u7d20a\uff0c\u5b58\u5728\u5b83\u7684\u9006\u5143\u7d20a<\/span>-1<\/sup><\/span>\uff0ca\u00b7a<\/span>-1<\/sup><\/span>= a<\/span>-1<\/sup><\/span>\u00b7a=e\u3002<\/span><\/span><\/section>\n

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\u6b64\u5b9a\u4e49\u6bd4\u8f83\u62bd\u8c61\uff0c\u4f46\u4ece\u5bf9\u79f0\u6027\u53d8\u6362\u7684\u89d2\u5ea6\u6765\u7406\u89e3\u5c31\u663e\u5f97\u975e\u5e38\u81ea\u7136\u3002\u4e00\u4e2a\u7fa4\u7684\u5143\u7d20\u5bf9\u5e94\u67d0\u79cd\u5bf9\u79f0\u6027\u53d8\u6362\uff0c\u7fa4\u4e58\u6cd5\u5219\u8868\u793a\u4e24\u6b21\u63a5\u66ff\u7684\u53d8\u6362\uff0c\u800c\u5355\u4f4d\u5143\u5bf9\u5e94\u4e8e\u4e0d\u53d8\u6362\uff0c\u9006\u5143\u5bf9\u5e94\u4e8e\u9006\u53d8\u6362\u3002<\/span><\/section>\n

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\u7528\u7fa4\u6765\u8868\u793a\u524d\u6587\u63d0\u5230\u7684\u5bf9\u79f0\u6027\u4f8b\u5b50\uff1a<\/span><\/p>\n

(1) \u65f6\u95f4\u5e73\u79fb\u5bf9\u79f0\u6027\u2014\u2014\u5b9e\u6570\u4e0a\u7684\u52a0\u6cd5\u7fa4R\uff1b<\/span><\/p>\n

(2) \u7a7a\u95f4\u5e73\u79fb\u5bf9\u79f0\u6027\u2014\u2014\u4e09\u4e2a\u72ec\u7acb\u5b9e\u6570\u7684\u52a0\u6cd5\u7fa4R<\/span>3<\/sup>\uff1b<\/span><\/span><\/p>\n

(3) \u7a7a\u95f4\u65cb\u8f6c\u5bf9\u79f0\u6027\u2014\u2014\u674e\u7fa4SO(3)\uff0c\u6bcf\u4e00\u4e2a\u7fa4\u5143\u7d20\u53ef\u4ee5\u7528\u4e09\u4e2a\u201c\u6b27\u62c9\u89d2\u201d\u6765\u63cf\u8ff0\uff1b<\/span><\/p>\n

(4) \u7535\u78c1\u573a\u7684\u89c4\u8303\u5bf9\u79f0\u6027\u2014\u2014\u674e\u7fa4U(1)\uff0c\u7fa4\u5143\u7d20exp(i\u03bb)\u5bf9\u5e94\u4e0a\u6587\u63d0\u5230\u7684\u76f8\u4f4d\u65cb\u8f6c<\/span>\uff08\u89c4\u8303\u53c2\u6570\uff09<\/span>\uff0c\u5176\u4e2d\u03bb\u7684\u53d6\u503c\u8303\u56f4\u662f0\u52302\u03c0\u3002<\/span><\/span><\/section>\n

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\u5c24\u5176\u7559\u610f\uff0c\u53ef\u9006\u6027\u662f\u7fa4\u7684\u4e00\u4e2a\u91cd\u8981\u5b9a\u4e49\u7279\u5f81\u3002\u5728\u540e\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u7a81\u7834\u7fa4\u7684\u53ef\u9006\u6027\uff0c\u63a2\u8ba8\u201c\u4e0d\u53ef\u9006\u201d\u7684\u5bf9\u79f0\u6027\u3002<\/span><\/section>\n


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\u9ad8\u5f62\u5f0f\u5bf9\u79f0\u6027<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

\u5728\u4f20\u7edf\u7684\u5c40\u57df\u91cf\u5b50\u573a\u8bba\u4e2d\uff0c\u4eba\u4eec\u7814\u7a76\u7684\u7126\u70b9\u901a\u5e38\u662f\u5c40\u57df\u573a\u7b97\u7b26\uff0c\u5b83\u4eec\u88ab\u5b9a\u4e49\u5728\u65f6\u7a7a\u4e2d\u7684\u67d0\u4e2a0\u7ef4\u7684\u70b9\u4e0a\u3002\u4f20\u7edf\u7684\u5bf9\u79f0\u6027\u4e3b\u8981\u4f5c\u7528\u5728\u8fd9\u4e9b\u5c40\u57df\u573a\u7b97\u7b26\u4e0a\u3002<\/span><\/section>\n

<\/section>\n
\u7136\u800c\uff0c\u91cf\u5b50\u573a\u8bba\u4e2d\u540c\u6837\u5b58\u5728\u7740\u9ad8\u7ef4\u7684\u975e\u5c40\u57df\u7b97\u7b26\u3002\u4ee5\u9ea6\u514b\u65af\u97e6\u7535\u78c1\u5b66\u7406\u8bba\u4e3a\u4f8b\uff0c\u6211\u4eec\u53ef\u4ee5\u56f4\u7ed5\u4e00\u4e2a\u4e00\u7ef4\u7684\u5708\u4e0a\u5bf9\u89c4\u8303\u573aA\u505a\u79ef\u5206\uff0c\u4ece\u800c\u5b9a\u4e49\u51fa<\/sub><\/span>\u8fd9\u4e00\u5728\u89c4\u8303\u5bf9\u79f0\u6027\u53d8\u6362\u4e0b\u4e0d\u53d8\u7684\u201c\u5a01\u5c14\u900a\u5708\u201d<\/span>\uff08Wilson loop\uff09<\/span>\u7b97\u7b26\u3002<\/span><\/span><\/section>\n

<\/section>\n
\u5728\u5e7f\u4e49\u5bf9\u79f0\u6027\u6d6a\u6f6e\u7684\u65e9\u671f\uff0c\u5960\u57fa\u6027\u5de5\u4f5c\u201cGeneralized global symmetri<\/span><\/span>es\u201d[1]\u9996\u5148<\/span><\/span>\u63d0\u51fa\u4e86\u4e00\u79cd\u88ab\u79f0\u4e3a\u9ad8\u5f62\u5f0f\u5bf9\u79f0\u6027<\/span>\uff08Higher-form symmetry\uff09<\/span>\u7684\u65b0\u9896\u6982\u5ff5\uff0c\u4f5c\u7528\u5728\u573a\u8bba\u4e2d\u7684\u9ad8\u5f62\u5f0f\u7b97\u7b26\u4e0a\u3002<\/span><\/span><\/section>\n

<\/section>\n
\u4f8b\u5982\u5bf9\u4e8e\u4e0d\u5b58\u5728\u5e26\u7535\u7c92\u5b50\u7684\u9ea6\u514b\u65af\u97e6\u7535\u78c1\u5b66\u7406\u8bba\uff0c\u53ef\u4ee5\u5b9a\u4e49\u4e00\u79cd\u62d3\u6251\u7b97\u7b26\u2014\u2014\u7535\u901a\u91cf\u7b97\u7b26<\/span>\uff08electric flux\uff09<\/span>\u4f5c\u7528\u4e8e\u5a01\u5c14\u900a\u5708\u4e0a\uff0c\u5f62\u5f0f\u662f\u5c06\u5176\u4e58\u4e0a\u4e00\u4e2a\u989d\u5916\u7684U(1)\u76f8\u4f4d\u56e0\u5b50<\/span>\uff08\u89c1\u4e0b\u56fe\uff09<\/span>\u3002\u6b64\u79cd\u5168\u5c40\u5bf9\u79f0\u6027\u88ab\u79f0\u4f5c<\/span>\uff08\u7535\u7684\uff09<\/span>\u201c1-\u5f62\u5f0f\u5bf9\u79f0\u6027\u201d<\/span>\uff081-form symmetry\uff09<\/span>\u3002<\/span><\/span><\/section>\n

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\u9ad8\u5f62\u5f0f\u5bf9\u79f0\u6027\u540c\u6837\u6ee1\u8db3\u8bfa\u7279\u5b9a\u7406\uff0c\u4e0a\u6587\u4e2d1-\u5f62\u5f0f\u5bf9\u79f0\u6027\u5bf9\u5e94\u7684\u5b88\u6052\u91cf\u5373\u662f\u7535\u901a\u91cf\u3002\u7531\u4e8e\u6211\u4eec\u5047\u8bbe\u4e0d\u5b58\u5728\u5e26\u7535\u7c92\u5b50\uff0c\u7535\u901a\u91cf\u7684\u786e\u662f\u5b88\u6052\u7684\u3002<\/span><\/section>\n

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\u7c7b\u4f3c\u5730\uff0c\u5f53\u7406\u8bba\u4e2d\u4e0d\u5b58\u5728\u78c1\u8377\u65f6\uff0c\u78c1\u901a\u91cf\u4e5f\u662f\u4e00\u4e2a\u5b88\u6052\u91cf\uff0c\u5bf9\u5e94\u4e8e\u78c1\u76841-\u5f62\u5f0f\u5bf9\u79f0\u6027\u3002<\/span><\/section>\n

<\/section>\n
\u66f4\u4e00\u822c\u5730\u8bf4\uff0c\u4ee5\u4e0a\u56fe\u4e2d\u62d3\u6251\u65b9\u5f0f\u4f5c\u7528\u5728p\u7ef4\u975e\u5c40\u57df\u7b97\u7b26\u4e0a\u7684\u5bf9\u79f0\u6027\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3ap-\u5f62\u5f0f\u5bf9\u79f0\u6027\u3002\u8fd9\u4e2a\u547d\u540d\u6765\u6e90\u4e8e\u5b9a\u4e49\u8fd9\u4e9b\u62d3\u6251\u7b97\u7b26\u7684\u6570\u5b66\u5de5\u5177\u2014\u2014\u5fae\u5206\u5f62\u5f0f\u3002\u5728\u8fd9\u79cd\u8bed\u8a00\u4e0b\uff0c\u9ad8\u5f62\u5f0f\u5bf9\u79f0\u6027\u53ef\u4ee5\u81ea\u7136\u5730\u5728\u5f2f\u66f2\u65f6\u7a7a\u4e2d\u8fdb\u884c\u5b9a\u4e49\u3002<\/span><\/section>\n

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\u9ad8\u5f62\u5f0f\u5bf9\u79f0\u6027\u4e0e\u7981\u95ed<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u5728\u57fa\u7840\u7269\u7406\u5b66\u4e2d\uff0c\u4e00\u4e2a\u91cd\u5927\u95ee\u9898\u662f\u89e3\u91ca\u91cf\u5b50\u8272\u52a8\u529b\u5b66\u4e2d\u7684\u5938\u514b\u7981\u95ed\u73b0\u8c61\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u4e3a\u4ec0\u4e48\u5938\u514b\u5728\u957f\u8ddd\u79bb<\/span>\uff08\u4f4e\u80fd\u6807\uff09<\/span>\u4e0b\u4f1a\u7ec4\u5408\u6210\u8d28\u5b50\u3001\u4e2d\u5b50\u548c\u5176\u4ed6\u7c92\u5b50\uff0c\u800c\u6211\u4eec\u65e0\u6cd5\u76f4\u63a5\u89c2\u6d4b\u5230\u88f8\u5938\u514b\u5462\uff1f\u8fd9\u4e2a\u95ee\u9898\u5728\u6570\u5b66\u4e0a\u5bf9\u5e94\u7740\u514b\u96f7\u6570\u5b66\u7814\u7a76\u6240\u5343\u79a7\u5e74\u4e03\u5927\u6570\u5b66\u95ee\u9898\u4e4b\u4e00\uff0c\u5373\u6768\u2014\u7c73\u5c14\u65af\u95ee\u9898\u3002<\/span><\/span><\/section>\n

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\u5728\u6b64\u7406\u8bba\u4e2d\uff0c\u5a01\u5c14\u900a\u5708\u626e\u6f14\u7740\u91cd\u8981\u7684\u89d2\u8272\uff0c\u56e0\u4e3a\u5f53\u5706\u5708\u7684\u5c3a\u5bf8\u8d8b\u4e8e\u65e0\u7a77\u5927\u65f6\uff0c\u5176\u884c\u4e3a\u5bf9\u5e94\u4e8e\u91cf\u5b50\u8272\u52a8\u529b\u5b66\u5728\u957f\u8ddd\u79bb\u4e0b\u7684\u884c\u4e3a\u3002\u6709\u4ee5\u4e0b\u4e24\u79cd\u53ef\u80fd\u7684\u60c5\u51b5\uff1a<\/span><\/section>\n

<\/span><\/section>\n
(1) \u5a01\u5c14\u900a\u5708\u7684\u53d6\u503c<\/span>\uff08\u771f\u7a7a\u671f\u671b\u503c\uff09<\/span>\u5448exp(-A)\u7684\u5f62\u5f0f\uff0c\u4e0e\u5706\u5708\u7684\u9762\u79ef\u76f8\u5173\uff0c\u88ab\u79f0\u4e3a\u9762\u79ef\u5f8b\u3002\u5f53\u5706\u5708\u5c3a\u5bf8\u8d8b\u4e8e\u65e0\u7a77\u65f6\uff0c\u5a01\u5c14\u900a\u5708\u7684\u771f\u7a7a\u671f\u671b\u503c\u8d8b\u4e8e\u96f6\uff0c\u7406\u8bba\u5904\u4e8e\u7981\u95ed\u72b6\u6001\u3002<\/span><\/span><\/section>\n

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(2) \u5a01\u5c14\u900a\u5708\u7684\u53d6\u503c<\/span>\uff08\u771f\u7a7a\u671f\u671b\u503c\uff09<\/span>\u5448exp(-L)\u7684\u5f62\u5f0f\uff0c\u4e0e\u5706\u5708\u7684\u5468\u957f\u76f8\u5173\uff0c\u88ab\u79f0\u4e3a\u5468\u957f\u5f8b\u3002\u8fd9\u65f6\u5f53\u5706\u5708\u5c3a\u5bf8\u8d8b\u4e8e\u65e0\u7a77\u65f6\uff0c\u5a01\u5c14\u900a\u5708\u7684\u771f\u7a7a\u671f\u671b\u503c\u53ef\u5728\u52a0\u5c40\u57df\u62b5\u6d88\u9879\u540e\u4e0d\u7b49\u4e8e\u96f6\uff0c\u800c\u7406\u8bba\u5904\u4e8e\u89e3\u7981\u95ed\u72b6\u6001\u3002<\/span><\/span><\/section>\n

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\u5bf9\u4e8e\u53ea\u6709\u89c4\u8303\u573a<\/span>\uff08\u80f6\u5b50\uff09<\/span>\uff0c\u6ca1\u6709\u7269\u8d28\u573a<\/span>\uff08\u5938\u514b\uff09<\/span>\u7684\u6768\u2014\u7c73\u5c14\u65af\u573a\u8bba\uff0c\u5176\u4e2d\u8574\u542b\u7740\u79bb\u6563\u76841-\u5f62\u5f0f\u5bf9\u79f0\u6027\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u8ba8\u8bba\u5176\u4e2d\u80f6\u5b50\u7684\u7981\u95ed\u884c\u4e3a\u3002\u4e0a\u9762\u63d0\u5230\u7684\u9762\u79ef\u5f8b\uff081\uff09\u5bf9\u5e94\u4e8e1-\u5f62\u5f0f\u5bf9\u79f0\u6027\u672a\u53d1\u751f\u81ea\u53d1\u5bf9\u79f0\u7834\u7f3a\u7684\u60c5\u51b5\uff0c\u5373\u7981\u95ed\u72b6\u6001\uff1b\u800c\u5468\u957f\u5f8b\uff082\uff09\u5219\u8868\u660e1-\u5f62\u5f0f\u5bf9\u79f0\u6027\u53d1\u751f\u4e86\u81ea\u53d1\u5bf9\u79f0\u7834\u7f3a\uff0c\u5373\u89e3\u7981\u95ed\u72b6\u6001\u3002<\/span><\/span><\/section>\n

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\u5728\u5e7f\u4e49\u5bf9\u79f0\u6027\u7684\u7814\u7a76\u4e2d\uff0c\u4e00\u4e2a\u7ec8\u6781\u76ee\u6807\u662f\u627e\u5230\u9002\u7528\u4e8e\u771f\u5b9e\u4e16\u754c\u7684\u91cf\u5b50\u8272\u52a8\u529b\u5b66\u7684\u5e7f\u4e49\u5bf9\u79f0\u6027\uff0c\u7814\u7a76\u5176\u5bf9\u79f0\u6027\u81ea\u53d1\u7834\u7f3a\uff0c\u6700\u7ec8\u7406\u89e3\u7981\u95ed\u4e0e\u89e3\u7981\u95ed\u76f8\u4e4b\u95f4\u7684\u76f8\u53d8\u8fc7\u7a0b\u7b49\u7269\u7406\u95ee\u9898\u3002\u8fd9\u662f\u4e00\u4e2a\u957f\u8fdc\u800c\u5bcc\u6709\u6311\u6218\u6027\u7684\u7814\u7a76\u95ee\u9898\u3002<\/span><\/section>\n


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\u91cf\u5b50\u53cd\u5e38\uff0c\u53cd\u5e38\u7406\u8bba\u4e0eSPT<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u91cf\u5b50\u4e16\u754c\u662f\u4e00\u4e2a\u795e\u79d8\u4e14\u4e0e\u7ecf\u5178\u4e16\u754c\u622a\u7136\u4e0d\u540c\u7684\u9886\u57df\uff0c\u5176\u8bb8\u591a\u65b9\u9762\u96be\u4ee5\u7528\u65e5\u5e38\u7ecf\u9a8c\u7406\u89e3\u3002\u5728\u5bf9\u79f0\u6027\u65b9\u9762\uff0c\u7ecf\u5178\u573a\u8bba\u4e2d\u5177\u6709\u7684\u5bf9\u79f0\u6027\u4e5f\u6709\u53ef\u80fd\u5728\u91cf\u5b50\u6c34\u5e73\u4e0b\u88ab\u7834\u574f\u3002\u8fd9\u79cd\u7269\u7406\u73b0\u8c61\u88ab\u79f0\u4e3a\u91cf\u5b50\u53cd\u5e38<\/span>\uff08\u6216\u53cd\u5e38\uff0canomaly\uff09<\/span><\/span>[5]<\/span>\u3002<\/span><\/span><\/section>\n

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\u5177\u4f53\u800c\u8a00\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u91cf\u5b50\u7406\u8bba\u7684\u914d\u5206\u51fd\u6570\u662f\u5426\u4f9d\u7136\u62e5\u6709\u539f\u5bf9\u79f0\u6027\u3002\u91cf\u5b50\u53cd\u5e38\u53ef\u5206\u4e3a\u4e24\u79cd\u4e3b\u8981\u7c7b\u578b\uff1a<\/span><\/section>\n

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(1) \u89c4\u8303\u5bf9\u79f0\u6027\u7684\u91cf\u5b50\u53cd\u5e38\uff1b\u5b83\u7684\u5b58\u5728\u8868\u660e\u91cf\u5b50\u89c4\u8303\u573a\u8bba\u672c\u8eab\u662f\u4e0d\u81ea\u6d3d\u7684\uff0c\u56e0\u800c\u9700\u8981\u7528\u67d0\u4e9b\u7269\u7406\u673a\u5236\u6765\u62b5\u6d88<\/span>\uff08\u4f8b\u5982Green-Schwarz\u673a\u5236\uff09<\/span>\u3002<\/span><\/span><\/section>\n

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(2) \u5168\u5c40\u5bf9\u79f0\u6027\u7684\u91cf\u5b50\u53cd\u5e38\uff0c\u5373\u2019t Hooft\u53cd\u5e38\uff1b\u5b83\u7684\u5b58\u5728\u672c\u8eab\u5e76\u4e0d\u4f1a\u63a8\u7ffb\u7406\u8bba\uff0c\u4f46\u5982\u679c\u60f3\u5c06\u5168\u5c40\u5bf9\u79f0\u6027\u53d8\u4e3a\u6709\u52a8\u529b\u5b66\u7684\u89c4\u8303\u5bf9\u79f0\u6027\uff0c\u5373\u8fdb\u884c\u89c4\u8303\u5316\uff0c\u2019t Hooft\u53cd\u5e38\u5c06\u963b\u788d\u8fd9\u4e00\u8fc7\u7a0b\u7684\u53d1\u751f\u3002<\/span><\/section>\n

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\u5728\u6709\u2019t Hooft\u53cd\u5e38\u7684\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u901a\u5e38\u53ef\u4ee5\u5f15\u5165\u4e00\u4e2a\u9ad8\u4e00\u7ef4\u65f6\u7a7a\u4e2d\u7684\u201c\u53cd\u5e38\u7406\u8bba\u201d<\/span>\uff08anomaly theory\uff09<\/span>\uff0c\u4e0e\u539f\u6765\u7684\u7269\u7406\u4f53\u7cfb\u76f8\u8026\u5408\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u539f\u6765d\u7ef4\u7684\u7269\u7406\u4f53\u7cfb\u53ef\u4ee5\u88ab\u8ba4\u4e3a\u5b58\u5728\u4e8e\u67d0\u4e2a(d+1)\u7ef4\u5e26\u8fb9\u6d41\u5f62\u7684\u8fb9\u754c\u4e0a\u3002\u53cd\u5e38\u7406\u8bba\u662f\u4e00\u4e2a\u62d3\u6251\u91cf\u5b50\u573a\u8bba\uff0c\u5176\u89c4\u8303\u53d8\u6362\u6b63\u597d\u4e0ed\u7ef4\u7269\u7406\u7406\u8bba\u4e2d\u7684\u2019t Hooft\u53cd\u5e38\u76f8\u62b5\u6d88\uff0c\u8fd9\u6837\u7ec4\u5408\u4e4b\u540e\u7684\u5927\u4f53\u7cfb\u5c31\u6ca1\u6709\u53cd\u5e38\uff0c\u89c1\u4e0b\u56fe\u3002<\/span><\/span><\/section>\n

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\u5728\u51dd\u805a\u6001\u7269\u7406\u4e2d\uff0c\u4e00\u4e2a\u91cd\u8981\u7684\u7814\u7a76\u8bfe\u9898\u662f\u63a2\u7d22\u548c\u5206\u7c7b\u7269\u7406\u4f53\u7cfb\u4e2d\u7684\u5404\u79cd\u76f8\uff0c\u7279\u522b\u662f\u88ab\u4f53\u7cfb\u7684\u62d3\u6251\u6027\u8d28\u6240\u4fdd\u62a4\u7684\u201c\u62d3\u6251\u5e8f\u201d<\/span>\uff08topological order\uff09<\/span>\u3002\u524d\u8ff0\u7684\u53cd\u5e38\u7406\u8bba\u7684\u7269\u7406\u56fe\u50cf\u6b63\u597d\u5bf9\u5e94\u4e8e\u6587\u5c0f\u521a\u8001\u5e08\u7b49\u4eba\u63d0\u51fa\u7684\u5bf9\u79f0\u6027\u4fdd\u62a4\u62d3\u6251\u5e8f<\/span>\uff08SPT\uff0cSymmetry Protected Topological order\uff09<\/span><\/span>[6]\u3002<\/span>\u4ee5\u4e0a\u7684\u8ba8\u8bba\u4e5f\u53ef\u81ea\u7136\u9002\u7528\u5230\u9ad8\u5f62\u5f0f\u5bf9\u79f0\u6027\u7684\u60c5\u51b5\uff0c\u4e3a\u7406\u89e3\u91cf\u5b50\u4f53\u7cfb\u4e2d\u7684\u5bf9\u79f0\u6027\u548c\u62d3\u6251\u6027\u8d28\u63d0\u4f9b\u4e86\u65b0\u89c6\u89d2\u3002<\/span><\/span><\/section>\n


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\u6b63\u5982\u524d\u6587\u6240\u8ff0\uff0c\u7fa4\u662f\u4e00\u79cd\u63cf\u8ff0\u5bf9\u79f0\u6027\u7684\u81ea\u7136\u7ed3\u6784\uff0c\u4f46\u662f\u5426\u63cf\u8ff0\u5bf9\u79f0\u6027\u4e00\u5b9a\u8981\u7528\u7fa4\u5462\uff1f\u968f\u7740\u5f62\u5f0f\u5316\u91cf\u5b50\u573a\u8bba\u7684\u53d1\u5c55\u548c\u9ad8\u5f62\u5f0f\u5bf9\u79f0\u6027\u7684\u63d0\u51fa\uff0c\u4eba\u4eec\u610f\u8bc6\u5230\u5728\u573a\u8bba\u4e2d\u9700\u8981\u5173\u6ce8\u9ad8\u7ef4\u7269\u4f53\u548c\u9ad8\u7ef4\u7b97\u7b26\uff0c\u4f8b\u5982\u88abp-\u5f62\u5f0f\u5bf9\u79f0\u6027\u4f5c\u7528\u7684p\u7ef4\u7b97\u7b26\u3002\u4f46\u662f\uff0c\u6211\u4eec\u80fd\u5426\u63cf\u8ff0\u4e0d\u540c\u9ad8\u5f62\u5f0f\u5bf9\u79f0\u6027\u4e4b\u95f4\u7684\u6df7\u5408\u5462\uff1f\u4ee5\u53ca\u9700\u8981\u7528\u4ec0\u4e48\u6837\u7684\u6570\u5b66\u7ed3\u6784\u6765\u63cf\u8ff0\u5462\uff1f<\/span><\/section>\n

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\u7b54\u6848\u662f\uff1a\u73b0\u4ee3\u6570\u5b66\u7684\u7075\u9b42\u2014\u2014\u8303\u7574\u3002<\/span><\/section>\n

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\u8303\u7574\u662f\u96c6\u5408\u8bba\u7684\u63a8\u5e7f\u4e0e\u96c6\u5927\u6210\uff0c\u540c\u65f6\u4e5f\u662f\u6570\u5b66\u7684\u4e00\u4e2a\u91cd\u8981\u524d\u6cbf\u9886\u57df\u3002\u4e00\u4e2a\u4e00\u9636\u8303\u7574\u5305\u542b\u4e86\u4e00\u4e9b\u5bf9\u8c61<\/span>\uff08object\uff09<\/span>\u548c\u5bf9\u8c61\u4e4b\u95f4\u7684\u5173\u7cfb<\/span>\uff08\u88ab\u79f0\u4e3a\u201c\u6001\u5c04\u201d\uff0c1-morphism\uff09<\/span>\u3002\u8fdb\u4e00\u6b65\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u4e8c\u9636\u8303\u7574<\/span>\uff082-category\uff09<\/span>\uff0c\u5176\u4e2d\u5305\u542b\u5173\u7cfb\u4e4b\u95f4\u7684\u5173\u7cfb<\/span>\uff082-morphism\uff09<\/span>\uff0c\u4e09\u9636\u8303\u7574\u5305\u542b\u5173\u7cfb\u7684\u5173\u7cfb\u7684\u5173\u7cfb<\/span>\uff083-morphism\uff09<\/span>\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u751a\u81f3\u5230\u65e0\u7a77\u8303\u7574\u3002<\/span><\/span><\/section>\n

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\u5728\u62d3\u6251\u5b66\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u7a7a\u95f4\u4e0a\u7684\u6bcf\u4e2a\u70b9\u770b\u6210\u5bf9\u8c61\uff0c\u4e24\u4e2a\u70b9\u4e4b\u95f4\u7684\u8def\u5f84\u770b\u6210\u5bf9\u8c61\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u4e24\u4e2a\u8def\u5f84\u4e4b\u95f4\u5f20\u6210\u7684\u9762\u770b\u6210\u5173\u7cfb\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u7b49\u7b49\u3002\u56e0\u6b64\uff0c\u53ef\u4ee5\u770b\u51fa\u8303\u7574\u8bba\u65e9\u671f\u7684\u53d1\u5c55\u4e0e\u4ee3\u6570\u62d3\u6251\u4e2d\u7684\u540c\u4f26\u8bba<\/span>\uff08homotopy theory\uff09<\/span>\u5b58\u5728\u5bc6\u5207\u7684\u8054\u7cfb\u3002<\/span><\/span><\/section>\n

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\u5728\u4ee3\u6570\u4e2d\uff0c\u6211\u4eec\u540c\u6837\u53ef\u4ee5\u7528\u8303\u7574\u7684\u8bed\u8a00\u5b9a\u4e49\u4ee3\u6570\u7ed3\u6784\u3002\u4f8b\u5982\uff0c\u7fa4\u53ef\u4ee5\u88ab\u770b\u4f5c\u662f\u53ea\u6709\u4e00\u4e2a\u5bf9\u8c61\u201c\u2022\u201d\u7684\u4e00\u9636\u8303\u7574\uff0c\u5176\u4e2d\u6bcf\u4e2a\u7fa4\u5143\u7d20\u5bf9\u5e94\u201c\u2022\u201d\u5230\u81ea\u5df1\u7684\u4e00\u4e2a1-morphism\u3002\u5f53\u7136\uff0c\u5bf9\u4e8e\u7fa4\u6765\u8bf4\uff0c\u8fd9\u4e9b1-morphism\u90fd\u662f\u53ef\u9006\u7684\uff0c\u5e76\u4e14\u9700\u8981\u6ee1\u8db3\u7ed3\u5408\u5f8b\u3002<\/span><\/section>\n

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\u63a5\u4e0b\u6765\u5c31\u662f\u5c06\u7fa4\u63a8\u5e7f\u5230\u9ad8\u9636\u7fa4<\/span>\uff08higher-group\uff09<\/span>\uff0c\u4e00\u4e2an\u9636\u7fa4<\/span>\uff08n-group\uff09<\/span>\u88ab\u5b9a\u4e49\u4e3a\u53ea\u6709\u4e00\u4e2a\u5bf9\u8c61\u201c\u2022\u201d\u7684n\u9636\u8303\u7574\u3002\u5728\u8fd9\u4e2an\u9636\u8303\u7574\u4e2d\uff0c\u5305\u62ec\u53ef\u9006\u76841-morphism\u30012-morphism\u76f4\u5230n-morphism\uff0c\u5b83\u4eec\u5728\u7269\u7406\u4e2d\u5bf9\u5e94\u4e8e\u4e0d\u540c\u7684\u5bf9\u79f0\u6027\u53d8\u6362\uff0c\u4f5c\u7528\u5728\u4e0d\u540c\u7ef4\u5ea6\u7684\u7b97\u7b26\u4e0a\u3002<\/span><\/span><\/section>\n

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\u66f4\u7ec6\u81f4\u5730\u8bf4\uff0c\u5bf9\u79f0\u7fa4\u5728\u7269\u7406\u7b97\u7b26\u4e0a\u7684\u4f5c\u7528\u65b9\u5f0f\u662f\u7531\u5176\u201c\u7fa4\u8868\u793a\u201d\u786e\u5b9a\u7684\u3002\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\u662f\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u65cb\u8f6c\u53d8\u6362\uff0c\u5b83\u53ef\u4ee5\u4f5c\u7528\u5728\u4e09\u7ef4\u5750\u6807\u77e2\u91cf\u4e0a\u3002\u5728\u7ebf\u6027\u4ee3\u6570\u4e2d\uff0c\u8fd9\u53ef\u4ee5\u7406\u89e3\u4e3a\u4e00\u4e2a3\u00d73\u7684\u65cb\u8f6c\u77e9\u9635\u53bb\u4e58\u4ee5\u4e00\u4e2a\u4e09\u7ef4\u5217\u77e2\u91cf\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6211\u4eec\u7528\u4e00\u4e2a3\u00d73\u77e9\u9635\u53bb\u201c\u8868\u793a\u201d\u65cb\u8f6c\u5bf9\u79f0\u7fa4\u7684\u5143\u7d20\u3002<\/span><\/section>\n

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\u5bf9\u4e8e\u9ad8\u9636\u7fa4\u7684\u7fa4\u8868\u793a\uff0c\u4e5f\u9700\u8981\u7528\u6240\u8c13\u7684\u201cn\u9636\u77e2\u91cf\u7a7a\u95f4\u201d<\/span>\uff08\u4e00\u4e2an\u9636\u8303\u7574\uff09<\/span>\u53bb\u66ff\u4ee3\u666e\u901a\u7684\u77e2\u91cf\u7a7a\u95f4\u3002\u5728\u6570\u5b66\u9886\u57df\uff0c\u4e00\u822c\u7684\u9ad8\u9636\u7fa4\u4e0e\u8868\u793a\u7406\u8bba\u8fd8\u672a\u88ab\u5b8c\u5168\u5efa\u7acb\uff0c\u800c\u6b64\u95ee\u9898\u5728\u6570\u5b66\u548c\u7269\u7406\u4e2d\u90fd\u5b58\u5728\u8bb8\u591a\u672a\u77e5\u7684\u53ef\u80fd\u6027\uff0c\u4e9f\u5f85\u4eba\u4eec\u6df1\u5165\u63a2\u7d22\u3002<\/span><\/span><\/section>\n


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\u5728\u8303\u7574\u5bf9\u79f0\u6027\u7684\u8ba8\u8bba\u4e2d\uff0c\u6211\u4eec\u4f9d\u7136\u5047\u8bbe\u6240\u6709\u5bf9\u79f0\u53d8\u6362\u90fd\u662f\u53ef\u9006\u7684\u3002\u73b0\u5728\u81ea\u7136\u800c\u7136\u5730\u5f15\u51fa\u4e00\u4e2a\u95ee\u9898\uff1a\u6211\u4eec\u80fd\u5426\u653e\u677e\u5bf9\u53ef\u9006\u6027\u7684\u8981\u6c42\u5462\uff1f<\/span><\/section>\n

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\u5728\u4e00\u822c\u7684\u8303\u7574\u4e2d\uff0c1-morphism\u5f53\u7136\u53ef\u4ee5\u662f\u4e0d\u53ef\u9006\u7684\u3002\u4e00\u4e2a\u7ecf\u5178\u4f8b\u5b50\u662f\u975e\u963f\u8d1d\u5c14\u7fa4\u7684\u8868\u793a\u5f20\u91cf\u8303\u7574<\/span>\uff08representation tensor category\uff09<\/span>\uff0c\u5176\u4e2d\u76841-morphism\u662f\u7fa4\u8868\u793a\uff0c\u800c\u5b83\u4eec\u4e4b\u95f4\u7684\u7ed3\u5408\u5c31\u662f\u7fa4\u8868\u793a\u4e4b\u95f4\u7684\u5f20\u91cf\u4e58\u79ef\u5c55\u5f00\u3002\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\u662fSU(2)\u7fa4\uff0c\u5176\u4e0d\u53ef\u7ea6\u8868\u793a\u53ef\u7528\u81ea\u65cb\u6807\u8bb0\u3002\u4e24\u4e2a\u81ea\u65cb1\/2\u7684\u7c92\u5b50\u7ed3\u5408\uff0c\u53ef\u4ee5\u5f97\u5230\u4e00\u4e2a\u81ea\u65cb\u4e3a1\u7684\u4e09\u91cd\u6001\uff0c\u4ee5\u53ca\u4e00\u4e2a\u81ea\u65cb\u4e3a0\u7684\u5355\u91cd\u6001\uff1a<\/span><\/span><\/section>\n

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\u5728\u8fd9\u4e2a\u4ee3\u6570\u7cfb\u7edf\u4e2d\uff0c\u5355\u4f4d\u5143\u53ef\u4ee5\u88ab\u5b9a\u4e49\u6210\u81ea\u65cb\u4e3a0\u7684\u5355\u91cd\u6001\u3002\u7136\u800c\uff0c\u5bf9\u4e8e\u5f20\u91cf\u79ef\u8fd0\u7b97\u800c\u8a00\uff0c\u4e0d\u5b58\u5728\u9006\u5143\u7684\u6982\u5ff5\u3002<\/span><\/section>\n

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\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u63a2\u8ba8\u7269\u7406\u7cfb\u7edf\u4e2d\u7684\u4e0d\u53ef\u9006\u5bf9\u79f0<\/span>\u6027[3]\u3002<\/span>\u4e00\u822c\u6765\u8bf4\uff0c\u751f\u6210\u4e0d\u53ef\u9006\u5bf9\u79f0\u6027\u7684\u62d3\u6251\u7b97\u7b26\u4e4b\u95f4\u7684\u5f20\u91cf\u79ef\u9700\u8981\u5f62\u6210\u4ee5\u4e0b\u7684\u4e00\u822c\u5f62\u5f0f\uff0c\u5373\u7b49\u5f0f\u53f3\u8fb9\u662f\u82e5\u5e72\u4e2a\u7b97\u7b26\u7684\u76f4\u548c\uff1a<\/span><\/section>\n

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\u4e00\u4e2a\u5177\u6709\u4e0d\u53ef\u9006\u5bf9\u79f0\u6027\u7684\u7269\u7406\u5b9e\u4f8b\u53ef\u7531\u4ee5\u4e0b\u65b9\u6cd5\u6784\u9020\uff1a<\/span>\u8003\u8651\u4e00\u4e2a\u5177\u6709\u79bb\u6563\u975e\u963f\u8d1d\u5c14\u7fa4G\u5bf9\u79f0\u6027\u7684\u573a\u8bba\u6a21\u578b\uff0c\u6211\u4eec\u5c06\u8fd9\u4e2a\u5bf9\u79f0\u6027\u89c4\u8303\u5316\uff0c\u53d8\u6210\u4e00\u4e2a\u89c4\u8303\u7fa4\u4e3aG\u7684\u89c4\u8303\u573a\u8bba\u3002\u53ef\u4ee5\u8bc1\u660e\uff0c\u65b0\u7684\u4f53\u7cfb\u4f1a\u5177\u6709\u4e00\u4e2a\u65b0\u7684\u5bf9\u79f0\u6027G\u2019\uff0c\u5176\u5bf9\u79f0\u6027\u4ee3\u6570\u4e3aG\u7684Pontryagin\u5bf9\u5076\uff0c\u4e5f\u5c31\u662fG\u7684\u8868\u793a\u5f20\u91cf\u8303\u7574\u3002\u7531\u4e8e\u975e\u963f\u8d1d\u5c14\u7fa4\u7684\u8868\u793a\u5728\u5f20\u91cf\u4e58\u79ef\u8fd0\u7b97\u4e0b\u4e0d\u53ef\u9006\uff0c\u6211\u4eec\u56e0\u6b64\u6784\u9020\u51fa\u4e86\u4e00\u4e2a\u5e26\u6709\u4e0d\u53ef\u9006\u5bf9\u79f0\u6027\u7684\u7269\u7406\u4f53\u7cfb\u3002<\/span><\/span><\/section>\n

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\u6211\u4eec\u8fd8\u53ef\u4ee5\u7814\u7a76\u6700\u4e00\u822c\u7684\uff0c\u7531n\u9636\u5f20\u91cf\u8303\u7574\u63cf\u8ff0\u7684\u9ad8\u9636\u8303\u7574\u5bf9\u79f0\u6027\uff0c\u8fd9\u4e9b\u9ad8\u9636\u8303\u7574\u5bf9\u79f0\u6027\u7684\u5b9a\u4e49\u548c\u6027\u8d28\u4e0e\u666e\u901a\u5bf9\u79f0\u6027\u5927\u4e0d\u76f8\u540c\u3002\u5982\u4f55\u7814\u7a76\u5b83\u4eec\u7684\u8868\u793a\u8bba\u3001\u91cf\u5b50\u53cd\u5e38\u3001\u5bf9\u79f0\u6027\u7834\u7f3a\u7b49\u95ee\u9898\u90fd\u662f\u6570\u5b66\u7269\u7406\u4e2d\u7684\u524d\u6cbf\u8bfe\u9898\u3002<\/span><\/section>\n


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\u5982\u4f55\u7406\u89e3\u975e\u5fae\u6270\u3001\u5f3a\u8026\u5408\u3001\u5f3a\u5173\u8054\u7cfb\u7edf\u662f\u7269\u7406\u5b66\u4e2d\u7684\u57fa\u672c\u96be\u9898\uff0c\u4e5f\u662f\u6570\u5b66\u7269\u7406\u7684\u7ec8\u6781\u95ee\u9898\u4e4b\u4e00\u3002\u7531\u4e8e\u4e00\u822c\u7684\u975e\u5fae\u6270\u91cf\u5b50\u573a\u8bba\u8fc7\u4e8e\u590d\u6742\uff0c\u4eba\u4eec\u4f1a\u5c1d\u8bd5\u8ba8\u8bba\u4e00\u4e9b\u5177\u6709\u66f4\u9ad8\u5bf9\u79f0\u6027\u7684\u6a21\u578b\u3002<\/span><\/section>\n

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\u5176\u4e00\u662f\u63a2\u8ba8\u5177\u6709\u6807\u5ea6\u4e0d\u53d8\u6027\u7684\u201c\u5171\u5f62\u573a\u8bba\u201d\u3002\u8fd9\u4e9b\u7406\u8bba\u5728\u7edf\u8ba1\u7269\u7406\u4e2d\u7528\u4e8e\u63cf\u8ff0\u4e34\u754c\u73b0\u8c61\uff0c\u540c\u65f6\u4e5f\u80fd\u63cf\u8ff0\u91cf\u5b50\u573a\u8bba\u5728\u6781\u9650\u77ed\u8ddd\u79bb<\/span>\uff08\u7d2b\u5916\uff09<\/span>\u6216\u6781\u9650\u957f\u8ddd\u79bb<\/span>\uff08\u7ea2\u5916\uff09<\/span>\u4e0b\u7684\u201c\u4e0d\u52a8\u70b9\u7406\u8bba\u201d\u3002<\/span><\/span><\/section>\n

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\u5176\u4e8c\u662f\u5f15\u5165\u4e00\u79cd\u65b0\u7684\u5bf9\u79f0\u6027\u2014\u2014\u8d85\u5bf9\u79f0\uff0c\u8981\u6c42\u7406\u8bba\u4e2d\u7684\u73bb\u8272\u5b50\u4e0e\u8d39\u7c73\u5b50\u4e24\u4e24\u914d\u5bf9\u3002\u8d85\u5bf9\u79f0\u53ef\u7b80\u5316\u3001\u51cf\u5c11\u91cf\u5b50\u573a\u8bba\u4e2d\u7684\u91cf\u5b50\u4fee\u6b63\u3002<\/span><\/section>\n

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\u5171\u5f62\u573a\u8bba\u4e0e\u8d85\u5bf9\u79f0\u91cf\u5b50\u573a\u8bba\u4e00\u76f4\u4ee5\u6765\u90fd\u662f\u5f62\u5f0f\u5316\u9ad8\u80fd\u7406\u8bba\u7684\u91cd\u70b9\u7814\u7a76\u9886\u57df\uff0c\u5b83\u4eec\u80cc\u540e\u8574\u542b\u7740\u4e30\u5bcc\u7684\u6570\u5b66\u7ed3\u6784\u3002\u4f8b\u5982\u56db\u7ef4N=2\u8d85\u5bf9\u79f0\u573a\u8bba\u7684Seiberg-Witten\u7406\u8bba\u3001\u56db\u7ef4N=4\u8d85\u5bf9\u79f0\u573a\u8bba\u7684\u6563\u5c04\u632f\u5e45\u7ed3\u6784\uff0c\u4ee5\u53ca\u5404\u79cd\u5bf9\u5076\u6027\u7b49\u90fd\u662f\u6df1\u53d7\u5173\u6ce8\u7684\u7814\u7a76\u65b9\u5411\u3002<\/span><\/section>\n

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\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u6709\u4e9b\u91cf\u5b50\u573a\u8bba\u540c\u65f6\u5177\u5907\u8d85\u5bf9\u79f0\u6027\u548c\u5171\u5f62\u4e0d\u53d8\u6027\uff0c\u5b83\u4eec\u88ab\u79f0\u4e3a\u201c\u8d85\u5bf9\u79f0\u5171\u5f62\u573a\u8bba\u201d<\/span>\uff08superconformal field theory\uff09<\/span>\u3002\u8fd9\u7c7b\u7406\u8bba\u5f88\u591a\u90fd\u662f\u975e\u5fae\u6270\u7684\uff0c\u751a\u81f3\u6ca1\u6709\u7ecf\u5178\u62c9\u6c0f\u91cf\u8fd1\u4f3c\u63cf\u8ff0\u3002\u8457\u540d\u7684\u4f8b\u5b50\u5305\u62ec\u56db\u7ef4\u7684\u201cArgyres-Douglas\u201d\u7406\u8bba\uff0c\u4ee5\u53ca\u4f17\u591a\u7684\u4e94\u7ef4\u3001\u516d\u7ef4\u65f6\u7a7a\u4e2d\u7684\u8d85\u5bf9\u79f0\u5171\u5f62\u573a<\/span><\/span>\u8bba\u7b49[7, 8]\u3002<\/span><\/section>\n

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\u6211\u4eec\u53ef\u4ee5\u5728\u5f26\u8bba\u6846\u67b6\u4e2d\u7cfb\u7edf\u5730\u6784\u9020\u8bb8\u591a\u8d85\u5bf9\u79f0\u5171\u5f62\u573a\u8bba\uff0c\u8fd9\u4e5f\u88ab\u79f0\u4e3a\u201c\u51e0\u4f55\u5de5\u7a0b\u201d<\/span>\uff08geometric engineering\uff09<\/span>\u3002\u5f26\u8bba\u662f\u4e00\u79cd\u81ea\u4e0a\u4e16\u7eaa70\u5e74\u4ee3\u4ee5\u6765\u53d1\u5c55\u8d77\u6765\u7684\u91cf\u5b50\u5f15\u529b\u5019\u9009\u7406\u8bba\uff0c\u65e8\u5728\u7edf\u4e00\u91cf\u5b50\u573a\u8bba\u4e0e\u5e7f\u4e49\u76f8\u5bf9\u8bba\u3002\u8bf8\u591a\u73b0\u4ee3\u6570\u5b66\u5206\u652f\u4e5f\u968f\u7740\u5f26\u8bba\u7684\u8fdb\u5c55\u800c\u4e00\u540c\u5f97\u5230\u53d1\u5c55\uff0c\u5982\u590d\u4ee3\u6570\u51e0\u4f55\u3001\u955c\u50cf\u5bf9\u79f0\u3001\u8ba1\u6570\u51e0\u4f55\u3001\u5171\u5f62\u573a\u8bba\u76f8\u5173\u7684\u7b97\u5b50\u4ee3\u6570\uff0c\u7b49\u7b49\u3002<\/span><\/span><\/section>\n

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\u4eba\u4eec\u901a\u5e38\u4f7f\u7528\u7684\u5f26\u8bba\u7248\u672c\u662f10\u7ef4\u7684IIA\/IIB\u8d85\u5f26\u7406\u8bba\uff0c\u6216\u800511\u7ef4\u7684M-\u7406\u8bba\u3001\u201c12\u7ef4\u201d\u7684F-\u7406\u8bba\u7b49\u3002\u4e3a\u4e86\u83b7\u5f97\u6211\u4eec\u6240\u9700\u7684\u4f4e\u7ef4\u7406\u8bba\uff0c\u6211\u4eec\u9700\u8981\u628a\u5176\u4e2d\u4e00\u4e9b\u989d\u5916\u7684\u65f6\u7a7a\u7ef4\u6570\u7f6e\u4e8e\u6ee1\u8db3\u4e00\u5b9a\u6570\u5b66\u6761\u4ef6\u7684\u51e0\u4f55\u7a7a\u95f4\u4e0a\uff0c\u6bd4\u5982\u8457\u540d\u7684\u5361\u62c9\u6bd4-\u4e18\u6d41\u5f62\u3002<\/span><\/section>\n

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\u5f53\u6211\u4eec\u5e0c\u671b\u6784\u9020\u4e0d\u542b\u5f15\u529b\u90e8\u5206\u7684\u8d85\u5bf9\u79f0\u5171\u5f62\u573a\u8bba\u65f6\uff0c\u9009\u53d6\u7684\u51e0\u4f55\u7a7a\u95f4\u9700\u8981\u6ee1\u8db3\u4ee5\u4e0b\u7684\u6027\u8d28\uff1a<\/span><\/section>\n

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(1) \u51e0\u4f55\u7a7a\u95f4\u7684\u4f53\u79ef\u8d8b\u4e8e\u65e0\u7a77\uff0c\u4f7f\u5f97\u4f4e\u7ef4\u7406\u8bba\u7684\u725b\u987f\u5f15\u529b\u5e38\u6570\u8d8b\u4e8e\u96f6\uff0c\u5373\u5f15\u529b\u76f8\u4e92\u4f5c\u7528\u53ef\u88ab\u5ffd\u7565\uff1b<\/span><\/section>\n

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(2) \u51e0\u4f55\u7a7a\u95f4\u5305\u542b\u4e00\u4e2a\u5947\u5f02\u70b9\uff0c\u5373\u5448\u73b0\u4e0b\u56fe\u7684\u9525\u5f62\u7ed3\u6784\u3002\u8d85\u5bf9\u79f0\u5171\u5f62\u573a\u8bba\u4e2d\u7684\u7269\u7406\u81ea\u7531\u5ea6\u5c31\u9690\u85cf\u5728\u8fd9\u4e2a\u5947\u5f02\u70b9\u5f53\u4e2d\u3002<\/span><\/section>\n

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\u5177\u4f53\u800c\u8a00\uff0c\u5728\u8d85\u5f26\/M-\u7406\u8bba\u4e2d\u90fd\u5b58\u5728\u7740\u5947\u5f02\u7684\u9ad8\u7ef4\u201c\u819c\u201d\u7269\u4f53\uff0c\u5982\u8d85\u5f26\u4e2d\u7684D\u819c\u548cM-\u7406\u8bba\u4e2d\u7684M2\u3001M5\u819c\u3002\u901a\u8fc7\u5c06\u8fd9\u4e9b\u819c\u7f20\u7ed5\u5728\u4e00\u4e9b\u7279\u5b9a\u7684\u5b50\u7a7a\u95f4\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u6784\u9020\u51fa\u5e7f\u4e49\u5bf9\u79f0\u6027\u4f5c\u7528\u7684\u9ad8\u7ef4\u7269\u7406\u5bf9\u8c61\uff01\u4f8b\u5982\uff0c\u7b14\u8005\u4e0e\u5408\u4f5c\u8005\u9996\u6b21\u901a\u8fc7\u8fd9\u79cd\u65b9\u6cd5\u8ba1\u7b97\u4e86\u56db\u7ef4\u201cArgyres-Douglas\u201d\u7406\u8bba\u53ca\u5176\u63a8\u5e7f\u7406\u8bba\u7684\u9ad8\u5f62\u5f0f\u5bf9<\/span>\u79f0\u6027[9]<\/span>\u3002<\/span><\/section>\n

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(1) \u5f2f\u66f2\u7684\u53cd\u5fb7\u897f\u7279<\/span>\uff08Anti de-Sitter \uff0cAdS\uff09<\/span>\u65f6\u7a7a\u4e2d\u7684\u91cf\u5b50\u5f15\u529b\u7406\u8bba\u3002\u8fd9\u91cc\u7684\u53cd\u5fb7\u897f\u7279\u65f6\u7a7a\u53ef\u4ee5\u89c6\u4e3a\u4e00\u79cd\u5177\u6709\u8fb9\u754c\u7684\u8d1f\u66f2\u7387\u53cc\u66f2\u65f6\u7a7a\uff1b<\/span><\/span><\/p>\n

(2) \u5728AdS\u65f6\u7a7a\u8fb9\u754c\u4e0a\u5b9a\u4e49\u7684\u4e00\u4e2a\u91cf\u5b50\u573a\u8bba\uff0c\u8be5\u573a\u8bba\u4e2d\u6ca1\u6709\u5f15\u529b\u76f8\u4e92\u4f5c\u7528\u3002<\/span><\/section>\n

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\u56e0\u6b64\uff0c\u4e3a\u4e86\u7814\u7a76AdS\/CFT\u6846\u67b6\u4e0b\u8fb9\u754c\u91cf\u5b50\u573a\u8bba\u7684\u5e7f\u4e49\u5bf9\u79f0\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u53bb\u5bfb\u627eAdS\u91cf\u5b50\u5f15\u529b\u4e2d\u662f\u5426\u5b58\u5728\u5408\u9002\u7684\u89c4\u8303\u573a\u3002\u8bfb\u8005\u53ef\u80fd\u4f1a\u53d1\u73b0\uff0c\u6b64\u7269\u7406\u56fe\u50cf\u4e0e\u4e0a\u6587\u4e2d\u8bb2\u7684\u53cd\u5e38\u7406\u8bba\u4e0eSPT\u7684\u56fe\u50cf\u975e\u5e38\u76f8\u4f3c\u3002\u5b9e\u9645\u4e0a\uff0c\u8fb9\u754c\u91cf\u5b50\u573a\u8bba\u7684\u2019t Hooft\u53cd\u5e38\u6b63\u597d\u5bf9\u5e94\u4e8eAdS\u4e2d\u91cf\u5b50\u5f15\u529b\u7684\u62d3\u6251\u9879\uff01\u5728\u8fd1\u5e74\uff0c\u7b14\u8005\u4e0e\u5408\u4f5c\u8005\u5229\u7528M-\u7406\u8bba\u7684\u51e0\u4f55\u6846\u67b6\u6210\u529f\u8ba1\u7b97\u4e86\u8457\u540d\u7684\u4e09\u7ef4ABJ\/ABJM\u7406\u8bba\u7684\u2019t Hooft\u53cd\u5e38\uff0c\u4ee5\u53ca\u5176\u4ed6\u4e09\u7ef4\u8d85\u5bf9\u79f0\u5171\u5f62\u573a\u8bba\u7684\u60c5<\/span>\u5f62[11]<\/span>\u3002<\/span><\/section>\n

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\u6700\u540e\uff0c\u8ba9\u6211\u4eec\u7b80\u8981\u5c55\u671b\u4e00\u4e0b\u8fd9\u4e09\u4e2a\u65b9\u5411\u7684\u672a\u6765\u7814\u7a76\u524d\u666f\uff1a<\/span><\/p>\n

(1) \u5728\u9ad8\u80fd\u7406\u8bba\u65b9\u9762\uff0c\u7814\u7a76\u5404\u79cd\u5e7f\u4e49\u5bf9\u79f0\u6027\u7684\u91cf\u5b50\u53cd\u5e38\u3001\u5bf9\u79f0\u6027\u81ea\u53d1\u7834\u7f3a\u7b49\u57fa\u672c\u95ee\u9898\uff0c\u6df1\u5165\u7814\u7a76\u5e7f\u4e49\u5bf9\u79f0\u6027\u5728\u5f26\u8bba\u4e0e\u5f15\u529b-\u5168\u606f\u5bf9\u5076\u4e2d\u7684\u5b9e\u73b0\u5f62\u5f0f\uff0c\u63a2\u7d22\u5728\u7c92\u5b50\u7269\u7406\u3001\u6563\u5c04\u632f\u5e45\u3001\u6a21\u578b\u6784\u9020\u4e2d\u7684\u7269\u7406\u5e94\u7528\u7b49\u3002<\/span><\/p>\n

(2) \u5728\u51dd\u805a\u6001\u7406\u8bba\u65b9\u9762\uff0c\u7528\u5e7f\u4e49\u5bf9\u79f0\u6027\u63cf\u8ff0\u5404\u79cd\u62d3\u6251\u7269\u6001\u3001SPT\uff0c\u5728\u683c\u70b9\u54c8\u5bc6\u987f\u91cf\u6a21\u578b\u4e2d\u5b9e\u73b0\u5e7f\u4e49\u5bf9\u79f0\u6027\uff0c\u5206\u7c7b\u878d\u5408\u8303\u7574\u3001\u9ad8\u9636\u878d\u5408\u8303\u7574<\/span>\uff08higher fusion category\uff09<\/span>\u53ca\u5176\u5bf9\u5e94\u7684\u62d3\u6251\u573a\u8bba\uff0c\u7814\u7a76\u5728\u62d3\u6251\u91cf\u5b50\u8ba1\u7b97\u4e2d\u7684\u6f5c\u5728\u5e94\u7528\u7b49\u3002<\/span><\/span><\/p>\n

(3) \u5728\u6570\u5b66\u9886\u57df\uff0c\u7ec6\u81f4\u5730\u7814\u7a76\u9ad8\u9636\u8303\u7574\u53ca\u5176\u8868\u793a\u8bba\uff0c\u4e25\u683c\u8bc1\u660e\u62d3\u6251\u91cf\u5b50\u573a\u8bba\u3001SPT\u7b49\u9886\u57df\u7684\u7269\u7406\u731c\u60f3\uff0c\u63a8\u52a8\u91cf\u5b50\u573a\u8bba\u7684\u516c\u7406\u5316\uff0c\u4e3a\u7406\u8bba\u7269\u7406\u63d0\u4f9b\u66f4\u4e25\u5bc6\u7684\u6570\u5b66\u57fa\u7840\u3002<\/span><\/section>\n

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\u53c2\u8003\u6587\u732e<\/span><\/strong><\/span><\/section>\n
[1] D. Gaiotto, A. Kapustin, N. Seiberg, B. Willett, Generalized Global Symmetries, JHEP (2015) 02, 172.<\/span><\/section>\n
[2] R. Luo, Q-.R. Wang, Y-.N. Wang, Lecture Notes on Generalized Symmetries and Applications, Physics Report (2024) 1065.<\/span><\/section>\n
[3] L. Bhardwaj, L. E. Bottini, L. Fraser-Taliente, L. Gladden, D. S. Gould, A. Platschorre, H.  Tillim, Lectures on generalized symmetries, Physics Report (2024) 1051.<\/span><\/section>\n
[4] S. Schafer-Nameki, ICTP lectures on (non-) invertible generalized symmetries, Physics Report (2024) 1063.<\/span><\/section>\n
[5] J. A. Harvey, TASI 2003 lectures on anomalies, arXiv: hep-th\/0509097.<\/span><\/section>\n
[6] X. Chen, Z-.C. Gu, Z-.X. Liu, X-.G. Wen, Symmetry protected topological orders and the group cohomology of their symmetry group, Physical Review B, 87(15), 155114.<\/span><\/section>\n
[7] P. Jefferson, S. Katz, H. C. Kim, C. Vafa, On geometric classification of 5d SCFTs, JHEP 04 (2018) 103.<\/span><\/section>\n
[8] J. J. Heckman, D. R. Morrison, T. Rudelius, C. Vafa (2015), Atomic classification of 6D SCFTs. Fortschritte der Physik, 63.7-8 (2015), 468-530.<\/span><\/section>\n
[9] C. Closset, S. Schafer-Nameki, Y-.N. Wang, Coulomb and Higgs Branches from Canonical Singularities: Part 0, JHEP 02 (2021) 003.<\/span><\/section>\n
[10] F. Apruzzi, F. Bonetti, D. S. Gould, S. Schafer-Nameki, Aspects of Categorical Symmetries from Branes: SymTFTs and Generalized Charges, arXiv:2306.16405.<\/span><\/section>\n
[11] D. S. Gould, M. v. Beest, S. Schafer-Nameki, Y. N. Wang, Symmetry TFTs for 3d QFTs from M-theory, JHEP 02 (2023) 226.<\/span><\/section>\n


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<\/span><\/span><\/a><\/section>\n

<\/section>\n
\u8be6\u60c5\u8bf7\u70b9\u51fb\uff1a<\/span><\/section>\n

\u4eba\u4eba\u53ef\u5b66\u7684\u8303\u7574\u8bba\u7b2c\u4e00\u5b63\u2014\u2014\u8de8\u9886\u57df\u7684\u79d1\u5b66\u65b9\u6cd5\u8bba | \u7cbe\u54c1\u5165\u95e8\u7cfb\u5217\u8bfe<\/a><\/span><\/p>\n

\u4eba\u4eba\u53ef\u5b66\u7684\u8303\u7574\u8bba\u7b2c\u4e8c\u5b63\u2014\u2014\u8de8\u5b66\u79d1\u7684\u79d1\u5b66\u65b9\u6cd5\u8bba | \u7cbe\u54c1\u5165\u95e8\u7cfb\u5217\u8bfe<\/a><\/span><\/section>\n


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<\/p>\n<\/section>\n

\n
\n

\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/p>\n

1. <\/strong>\u5bf9\u79f0\u6027\u7834\u7f3a\u4e0e\u6d8c\u73b0\uff1a\u5bf9\u79f0\u6027\u5982\u4f55\u5e2e\u52a9\u7406\u89e3\u751f\u547d\u548c\u667a\u80fd\uff1f<\/a><\/strong><\/span><\/strong><\/section>\n
2. <\/strong>\u91cf\u5b50\u8054\u7ed3\uff1a\u9ad8\u80fd\u7269\u7406\u3001\u51dd\u805a\u6001\u7269\u7406\u548c\u91cf\u5b50\u4fe1\u606f\u4e4b\u95f4\u7684\u8054\u7cfb<\/a><\/strong><\/span><\/strong><\/strong><\/section>\n
3. <\/strong>\u624b\u6027\u5bf9\u79f0\u6027\u7834\u7f3a\uff1a\u624b\u6027\u6574\u5408\u6765\u6e90\u4e8e\u6700\u5c0f\u65f6\u95f4\u81ea\u7531\u80fd\u6d88\u8017<\/a><\/strong><\/span><\/strong>
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4. <\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/strong><\/strong><\/span><\/section>\n
5.<\/strong> \u9f99\u5e74\u5927\u8fd0\u8d77\uff0c\u5b66\u4e60\u6b63\u5f53\u65f6\uff01\u89e3\u9501\u96c6\u667a\u5168\u7ad9\u5185\u5bb9\uff0c\u5f00\u542f\u65b0\u5e74\u5b66\u4e60\u8ba1\u5212<\/a><\/strong><\/strong><\/strong><\/strong><\/span><\/section>\n
6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/section>\n


<\/p>\n


<\/p>\n<\/section>\n

\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfe\u7a0b<\/strong><\/span><\/strong><\/span><\/strong><\/p>\n<\/section>\n<\/section>\n

<\/mp-style-type><\/p>\n

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\u672c\u7bc7\u6587\u7ae0\u6765\u6e90\u4e8e\u5fae\u4fe1\u516c\u4f17\u53f7: \u96c6\u667a\u4ff1\u4e50\u90e8 <\/p>\n<\/blockquote>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

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