{"id":28632,"date":"2021-09-05T22:47:41","date_gmt":"2021-09-05T14:47:41","guid":{"rendered":"https:\/\/swarma.org\/?p=28632"},"modified":"2021-09-05T22:47:41","modified_gmt":"2021-09-05T14:47:41","slug":"%e4%bb%80%e4%b9%88%e6%98%af%e9%87%8d%e6%95%b4%e5%8c%96-%e9%9b%86%e6%99%ba%e7%99%be%e7%a7%91","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=28632","title":{"rendered":"\u4ec0\u4e48\u662f\u91cd\u6574\u5316 | \u96c6\u667a\u767e\u79d1"},"content":{"rendered":"
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\u91cd\u6574\u5316 Renormalization\u662f\u5e94\u7528\u4e8e\u91cf\u5b50\u573a\u8bba Quantum Field Theory\u3001\u573a\u7684\u7edf\u8ba1\u529b\u5b66 Statistical Mechanics\u548c\u81ea\u76f8\u4f3c Self-similar\u51e0\u4f55\u7ed3\u6784\u7406\u8bba\u4e2d\u7684\u4e00\u7c7b\u65b9\u6cd5\u3002\u901a\u8fc7\u91cd\u6574\u5316\uff0c\u53ef\u4ee5\u6539\u53d8\u8ba1\u7b97\u91cf\u7684\u503c\u4ee5\u62b5\u6d88\u5176\u81ea\u76f8\u4e92\u4f5c\u7528 Self-interaction\uff0c\u8fdb\u800c\u6d88\u9664\u8ba1\u7b97\u91cf\u4e2d\u4ea7\u751f\u7684\u65e0\u7a77\u5927 infinities\u3002\u4f46\u662f\uff0c\u5373\u4f7f\u5728\u91cf\u5b50\u573a\u8bba\u7684\u5708\u56fe loop diagrams\u4e2d\u6ca1\u6709\u51fa\u73b0\u65e0\u7a77\u5927\uff0c\u5bf9\u539f\u62c9\u683c\u6717\u65e5\u573a\u7406\u8bba Lagrangian (Field Theory)\u4e2d\u51fa\u73b0\u7684\u8d28\u91cf\u548c\u573a\u8fdb\u884c\u91cd\u6574\u5316\u4e5f\u662f\u5fc5\u8981\u7684\u3002<\/span>
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\u4f8b\u5982\uff0c\u7535\u5b50 Electron\u7406\u8bba\u4f1a\u5148\u5047\u5b9a\u7535\u5b50\u5177\u6709\u521d\u59cb\u8d28\u91cf\u548c\u7535\u8377\u3002\u5728\u91cf\u5b50\u573a\u8bba\u4e2d\uff0c\u4e00\u4e2a\u7531\u8bf8\u5982\u5149\u5b50 Photon\u3001\u6b63\u7535\u5b50 Positron\u7b49\u865a\u7c92\u5b50 Virtual Particle\u7ec4\u6210\u7684\u4e91\u56e2\u56f4\u7ed5\u7740\u521d\u59cb\u7535\u5b50\u5e76\u4e0e\u4e4b\u76f8\u4e92\u4f5c\u7528\u3002\u8003\u8651\u5230\u5468\u56f4\u7c92\u5b50\u7684\u76f8\u4e92\u4f5c\u7528\uff08\u4f8b\u5982:\u4e0d\u540c\u80fd\u91cf\u7684\u78b0\u649e\uff09\u8868\u660e\u7535\u5b50-\u7cfb\u7edf\u7684\u884c\u4e3a\u5b9b\u5982\u5b83\u6709\u4e0d\u540c\u4e8e\u6700\u521d\u5047\u8bbe\u7684\u8d28\u91cf\u548c\u7535\u8377\u3002\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u91cd\u6574\u5316\u5728\u6570\u5b66\u4e0a\u7528\u5b9e\u9a8c\u89c2\u5bdf\u5230\u7684\u8d28\u91cf\u548c\u7535\u8377\u4ee3\u66ff\u4e86\u6700\u521d\u5047\u8bbe\u7684\u7535\u5b50\u8d28\u91cf\u548c\u7535\u8377\u3002\u6570\u5b66\u548c\u5b9e\u9a8c\u8bc1\u660e\uff0c\u6b63\u7535\u5b50\u548c\u8d28\u5b50 Proton\u7b49\u8d28\u91cf\u66f4\u5927\u7684\u7c92\u5b50\uff0c\u5373\u4f7f\u5b58\u5728\u66f4\u5f3a\u70c8\u7684\u76f8\u4e92\u4f5c\u7528\u548c\u66f4\u5bc6\u96c6\u7684\u865a\u7c92\u5b50\u4e91\uff0c\u5176\u7535\u8377\u4e5f\u4e0e\u7535\u5b50\u5b8c\u5168\u76f8\u540c\u3002<\/span><\/p>\n


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\u91cd\u6574\u5316\u6700\u65e9\u53d1\u5c55\u4e8e\u91cf\u5b50\u7535\u52a8\u529b\u5b66 Quantum Electrodynamics\uff0c\u4ee5\u89e3\u91ca\u5fae\u6270\u7406\u8bba Perturbation Theory\u4e2d\u7684\u65e0\u7a77\u79ef\u5206\u3002\u91cd\u6574\u5316\u6700\u521d\u88ab\u4eba\u8ba4\u4e3a\u662f\u4e00\u4e2a\u5b58\u7591\u7684\u4e34\u65f6\u7a0b\u5e8f\uff0c\u751a\u81f3\u5305\u62ec\u5b83\u7684\u4e00\u4e9b\u53d1\u660e\u8005\u3002\u5373\u4fbf\u5982\u6b64\uff0c\u91cd\u6574\u5316\u6700\u7ec8\u4f5c\u4e3a\u4e00\u4e2a\u91cd\u8981\u7684\u4e14\u81ea\u6d3d Self-consistent\u7684\u5b9e\u9645\u5c3a\u5ea6\u7269\u7406\u673a\u5236\u88ab\u7269\u7406\u5b66 Physics \u548c\u6570\u5b66 Mathematics\u7684\u51e0\u4e2a\u9886\u57df\u6240\u63a5\u53d7\u3002<\/span><\/p>\n


\u4eca\u5929\uff0c\u89c2\u70b9\u53d1\u751f\u4e86\u8f6c\u53d8: \u57fa\u4e8e\u5c3c\u53e4\u62c9\u00b7\u535a\u6208\u67f3\u535a\u592b\u548c Kenneth Wilson \u5bf9\u91cd\u6574\u5316\u7fa4 Renormalization Group\u7684\u7a81\u7834\u6027\u89c1\u89e3\uff0c\u5173\u6ce8\u70b9\u6210\u4e3a\u8fde\u7eed\u5c3a\u5ea6\u95f4\u7269\u7406\u91cf\u7684\u53d8\u5316\uff0c\u800c\u76f8\u9694\u8f83\u8fdc\u7684\u5c3a\u5ea6\u901a\u8fc7\u201c\u6709\u6548\u7684\u201c\u63cf\u8ff0\u5f7c\u6b64\u76f8\u5173\u3002\u5e7f\u6cdb\u6765\u8bf4\uff0c\u6240\u6709\u5c3a\u5ea6\u90fd\u4ee5\u7cfb\u7edf\u7684\u65b9\u5f0f\u8054\u7cfb\u5728\u4e00\u8d77\u3002\u540c\u65f6\uff0c\u4e0e\u6bcf\u4e2a\u5c3a\u5ea6\u76f8\u5173\u7684\u5b9e\u9645\u7269\u7406\u5b66\u88ab\u9002\u5408\u4e8e\u6bcf\u4e2a\u5c3a\u5ea6\u7684\u7279\u5b9a\u8ba1\u7b97\u6280\u672f\u63d0\u53d6\u51fa\u6765\u3002\u5a01\u5c14\u900a\u9610\u660e\u4e86\u7cfb\u7edf\u4e2d\u54ea\u4e9b\u53d8\u91cf\u662f\u81f3\u5173\u91cd\u8981\u7684\uff0c\u800c\u54ea\u4e9b\u53c8\u662f\u5197\u4f59\u7684\u3002<\/span><\/p>\n


\u91cd\u6574\u5316\u4e0d\u540c\u4e8e\u6b63\u5219\u5316 Regularization\uff0c\u540e\u8005\u662f\u53e6\u4e00\u79cd\u901a\u8fc7\u5047\u8bbe\u65b0\u5c3a\u5ea6\u4e2d\u5b58\u5728\u65b0\u7684\u672a\u77e5\u7684\u7269\u7406\u5b66\u4ee5\u63a7\u5236\u65e0\u7a77\u5927\u7684\u6280\u672f\u3002<\/span><\/p>\n


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\u5e26\u7535\u7c92\u5b50\u7684\u8d28\u91cf\u5e94\u5305\u62ec\u5176\u9759\u7535\u573a(\u7535\u78c1\u8d28\u91cf)\u4e2d\u7684\u8d28\u80fd\u3002\u5047\u8bbe\u8fd9\u4e2a\u7c92\u5b50\u662f\u4e00\u4e2a\u5e26\u7535\u7684\u534a\u5f84\u4e3are\u7684\u7403\u58f3\u3002\u573a\u4e2d\u7684\u8d28\u80fd\u662f\uff1a<\/span><\/p>\n

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\u5f53\u65f6re \u2192 0\uff0c\u5b83\u4f1a\u53d8\u5f97\u65e0\u7a77\u5927\u3002\u8fd9\u610f\u5473\u7740\u70b9\u7c92\u5b50\u5177\u6709\u65e0\u7a77\u5927\u7684\u60ef\u6027 Inertia\uff0c\u4f7f\u5b83\u65e0\u6cd5\u88ab\u52a0\u901f\u3002\u987a\u5e26\u4e00\u63d0\uff0c\u4f7f\u5f97mem\u7b49\u4e8e\u7535\u5b50\u8d28\u91cf\u7684\u8fd9\u4e2a\u503cre\u88ab\u79f0\u4e3a\u7535\u5b50\u7ecf\u5178\u534a\u5f84 Classical Electron Radius\uff0c\u5b83(\u8bbe\u7f6eq=e\u4ee5\u53cac\u548c\u03b50\u7684\u8fd8\u539f\u56e0\u5b50)\u88ab\u8bc1\u660e\u662f\uff1a<\/span><\/p>\n

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\u5176\u4e2d\u03b1\u22481\/137\u662f\u7cbe\u7ec6\u7ed3\u6784\u5e38\u6570 Fine-structure Constant\u7cbe\u7ec6\u7ed3\u6784\u5e38\u6570\uff0c\u210f\/(mec) \u662f\u7535\u5b50\u7684\u5eb7\u666e\u987f\u6ce2\u957f\u3002<\/span><\/p>\n


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\u91cd\u6574\u5316: \u7403\u5f62\u5e26\u7535\u7c92\u5b50\u7684\u603b\u6709\u6548\u8d28\u91cf\u5305\u62ec\u7403\u58f3\u7684\u5b9e\u9645\u88f8\u8d28\u91cf(\u5728\u4e0a\u8ff0\u4e0e\u5176\u7535\u573a\u76f8\u5173\u7684\u8d28\u91cf\u4e4b\u4e0a)\u3002\u5982\u679c\u5141\u8bb8\u58f3\u4f53\u7684\u88f8\u8d28\u91cf\u5141\u8bb8\u4e3a\u8d1f\u503c\uff0c\u5219\u53ef\u80fd\u53d6\u4e00\u4e2a\u4e00\u81f4\u7684\u70b9\u6781\u9650\u3002\u8fd9\u5c31\u662f\u6240\u8c13\u7684\u91cd\u6574\u5316\uff0c\u6d1b\u4f26\u5179\u548c\u4e9a\u4f2f\u62c9\u7f55\u8bd5\u56fe\u7528\u8fd9\u79cd\u65b9\u5f0f\u53d1\u5c55\u51fa\u7535\u5b50\u7684\u7ecf\u5178\u7406\u8bba\u3002\u8fd9\u9879\u65e9\u671f\u7684\u5de5\u4f5c\u542f\u53d1\u4e86\u540e\u6765\u5728\u91cf\u5b50\u573a\u8bba\u4e2d\u6b63\u5219\u5316\u548c\u91cd\u6574\u5316\u7684\u5c1d\u8bd5\u3002<\/span><\/p>\n


(\u5047\u8bbe\u5728\u5c0f\u5c3a\u5ea6\u4e0a\u5b58\u5728\u65b0\u7684\u7269\u7406\u5b66\uff0c\u53e6\u89c1\u6b63\u5219\u5316\u4ece\u8fd9\u4e2a\u7ecf\u5178\u95ee\u9898\u4e2d\u53bb\u9664\u65e0\u7a77\u5927\u7684\u66ff\u4ee3\u65b9\u6cd5\u3002)<\/span><\/p>\n


\u5728\u8ba1\u7b97\u5e26\u7535 Electric Charged\u7c92\u5b50\u7684\u7535\u78c1 electromagnetic\u76f8\u4e92\u4f5c\u7528\u65f6\uff0c\u4eba\u4eec\u5f88\u5bb9\u6613\u5ffd\u7565\u7c92\u5b50\u81ea\u8eab\u7684\u573a\u5bf9\u81ea\u5df1\u7684\u53cd\u4f5c\u7528 Back-reaction\u3002(\u7c7b\u4f3c\u4e8e\u7535\u8def\u5206\u6790\u7684\u53cd\u7535\u52a8\u52bf Back-EMF)\u3002\u4f46\u662f\u8fd9\u79cd\u53cd\u4f5c\u7528\u5bf9\u4e8e\u89e3\u91ca\u5e26\u7535\u7c92\u5b50\u53d1\u5c04\u8f90\u5c04\u65f6\u7684\u6469\u64e6\u662f\u5fc5\u8981\u7684\u3002\u5982\u679c\u5047\u8bbe\u7535\u5b50\u662f\u4e00\u4e2a\u70b9\uff0c\u53cd\u4f5c\u7528\u7684\u503c\u5c31\u4f1a\u53d1\u6563\uff0c\u8fd9\u548c\u8d28\u91cf\u53d1\u6563\u7684\u539f\u56e0\u662f\u4e00\u6837\u7684\uff0c\u56e0\u4e3a\u573a\u662f\u5448\u5e73\u65b9\u53cd\u6bd4 Inverse-square\u7684\u3002<\/span><\/p>\n


\u4e9a\u4f2f\u62c9\u7f55-\u6d1b\u4f26\u5179\u7406\u8bba\u6709\u4e00\u4e2a\u975e\u56e0\u679c\u7684\u201c\u9884\u52a0\u901f\u5ea6\u201d\u3002\u6709\u65f6\uff0c\u7535\u5b50\u5728\u65bd\u52a0\u529b\u4e4b\u524d\u5c31\u5f00\u59cb\u79fb\u52a8\u4e86\u3002\u8fd9\u662f\u70b9\u6781\u9650\u4e0d\u4e00\u81f4\u7684\u6807\u5fd7\u3002<\/span><\/p>\n


\u8fd9\u4e2a\u95ee\u9898\u5728\u7ecf\u5178\u573a\u8bba\u4e2d\u6bd4\u5728\u91cf\u5b50\u573a\u8bba\u4e2d\u66f4\u4e25\u91cd\uff0c\u56e0\u4e3a\u5728\u91cf\u5b50\u573a\u8bba\u4e2d\uff0c\u7531\u4e8e\u865a\u7c92\u5b50-\u53cd\u7c92\u5b50\u5bf9\u7684\u5e72\u6d89\uff0c\u5e26\u7535\u7c92\u5b50\u7ecf\u5386\u4e86 Zitterbewegung\uff0c\u4ece\u800c\u6709\u6548\u5730\u62b9\u53bb\u4e86\u4e00\u4e2a\u53ef\u4ee5\u4e0e\u5eb7\u666e\u987f\u6ce2\u957f\u76f8\u6bd4\u7684\u533a\u57df\u4e0a\u7684\u7535\u8377\u3002\u5728\u5c0f\u8026\u5408\u7684\u91cf\u5b50\u7535\u52a8\u529b\u5b66\u4e2d\uff0c\u7535\u78c1\u8d28\u91cf\u53ea\u968f\u7740\u7c92\u5b50\u534a\u5f84\u7684\u5bf9\u6570\u53d1\u6563\u3002<\/span><\/p>\n


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\u91cf\u5b50\u7535\u52a8\u529b\u5b66\u4e2d\u7684\u53d1\u6563<\/span><\/strong><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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(a) Vacuum polarization, a.k.a.\u7535\u8377\u5c4f\u853d\u3002<\/span><\/p>\n

\u8fd9\u4e2a\u73af\u6709\u4e00\u4e2a\u5bf9\u6570\u7684\u7d2b\u5916\u8f90\u6563\u3002<\/span><\/p>\n

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(b)\u91cf\u5b50\u7535\u52a8\u529b\u5b66\u4e2d\u7684\u81ea\u80fd\u56fe\u3002<\/span><\/p>\n

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(c)\u201c\u4f01\u9e45\u201d\u56fe\u793a\u4f8b\u5b50\u3002<\/span><\/p>\n


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\u572820\u4e16\u7eaa30\u5e74\u4ee3\u53d1\u5c55\u91cf\u5b50\u7535\u52a8\u529b\u5b66\u65f6\uff0c\u9a6c\u514b\u65af\u00b7\u4f2f\u6069\u3001\u7ef4\u5c14\u7eb3\u00b7\u6d77\u68ee\u5821\u3001\u5e15\u65af\u5938\u5c14\u00b7\u4e54\u4e39\u548c\u4fdd\u7f57\u00b7\u72c4\u62c9\u514b\u53d1\u73b0\uff0c\u5728\u5fae\u6270\u4fee\u6b63\u4e2d\uff0c\u8bb8\u591a\u79ef\u5206\u662f\u53d1\u6563\u7684(\u89c1\u65e0\u7a77\u5927\u95ee\u9898)\u3002<\/span><\/p>\n


\u4e00\u79cd\u63cf\u8ff0\u5fae\u6270\u7406\u8bba\u4fee\u6b63\u53d1\u6563\u7684\u65b9\u6cd5\u662f\u7531Hans Kramers\uff0cHans Bethe \uff0cJulian Schwinger\uff0cRichard Feynman\u548cShin’ichiro Tomonaga\uff0cand systematized Freeman Dyson in 1949.\u57281947-49\u5e74\u53d1\u73b0\u7684\uff0c\u5e76\u57281949\u5e74\u88abFreeman Dyson\u7cfb\u7edf\u5316\u3002\u53d1\u6563\u51fa\u73b0\u5728\u542b\u865a\u7c92\u5b50\u95ed\u73af\u7684\u8d39\u66fc\u56fe\u7684\u8f90\u5c04\u6821\u6b63\u4e2d\u3002<\/span><\/p>\n


\u865a\u7c92\u5b50\u9075\u5faa\u80fd\u91cf\u548c\u52a8\u91cf\u5b88\u6052\uff0c\u5b83\u4eec\u53ef\u4ee5\u6709\u4efb\u4f55\u80fd\u91cf\u548c\u52a8\u91cf\uff0c\u751a\u81f3\u662f\u89c2\u6d4b\u5230\u7684\u7c92\u5b50\u8d28\u91cf\u7684\u76f8\u5bf9\u80fd\u91cf\u548c\u52a8\u91cf\u5173\u7cfb\u6240\u4e0d\u5141\u8bb8\u7684\u80fd\u91cf\u548c\u52a8\u91cf(\u5373\uff0cE^2-p^2\u4e0d\u4e00\u5b9a\u662f\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\u7c92\u5b50\u8d28\u91cf\u7684\u5e73\u65b9\uff0c\u4f8b\u5982\uff0c\u5bf9\u4e8e\u5149\u5b50\u5b83\u53ef\u80fd\u662f\u975e\u96f6\u7684)\u3002\u8fd9\u6837\u7684\u7c92\u5b50\u53eb\u505a\u79bb\u58f3\u7c92\u5b50\u3002\u5f53\u6709\u4e00\u4e2a\u5708\u65f6\uff0c\u53c2\u4e0e\u5708\u7684\u7c92\u5b50\u7684\u52a8\u91cf\u4e0d\u662f\u552f\u4e00\u7531\u5165\u5c04\u548c\u8f93\u51fa\u7c92\u5b50\u7684\u80fd\u91cf\u548c\u52a8\u91cf\u51b3\u5b9a\u7684\u3002\u5708\u4e2d\u4e00\u4e2a\u7c92\u5b50\u80fd\u91cf\u7684\u53d8\u5316\u53ef\u4ee5\u88ab\u5708\u4e2d\u53e6\u4e00\u4e2a\u7c92\u5b50\u80fd\u91cf\u76f8\u7b49\u800c\u76f8\u53cd\u7684\u53d8\u5316\u6240\u5e73\u8861\uff0c\u800c\u4e0d\u5f71\u54cd\u8fdb\u5165\u548c\u6d41\u51fa\u7684\u7c92\u5b50\u3002\u56e0\u6b64\uff0c\u6709\u8bb8\u591a\u53d8\u5316\u662f\u53ef\u80fd\u7684\u3002\u56e0\u6b64\uff0c\u4e3a\u4e86\u627e\u5230\u5708\u8fc7\u7a0b\u7684\u632f\u5e45\uff0c\u5fc5\u987b\u5bf9\u6240\u6709\u53ef\u80fd\u7684\u80fd\u91cf\u548c\u52a8\u91cf\u7684\u7ec4\u5408\u8fdb\u884c\u79ef\u5206\uff0c\u8fd9\u4e9b\u7ec4\u5408\u53ef\u80fd\u5728\u5708\u4e2d\u4f20\u64ad\u3002<\/span><\/p>\n


\u8fd9\u4e9b\u79ef\u5206\u901a\u5e38\u662f\u53d1\u6563\u7684\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u5b83\u4eec\u7ed9\u51fa\u65e0\u9650\u7684\u7ed3\u679c\u3002\u5176\u4e2d\u201c\u7d2b\u5916\u201d\u53d1\u6563\u8f83\u4e3a\u663e\u8457\u3002\u7d2b\u5916\u53d1\u6563\u6765\u81ea\u4e8e\u4ee5\u4e0b\u51e0\u79cd\u60c5\u5f62\uff1a<\/span><\/p>\n