{"id":3865,"date":"2013-09-24T21:12:21","date_gmt":"2013-09-24T13:12:21","guid":{"rendered":"http:\/\/lttt.blog.ustc.edu.cn\/?p=3865"},"modified":"2013-09-24T21:12:21","modified_gmt":"2013-09-24T13:12:21","slug":"%e9%87%8f%e5%ad%90%e6%9d%a8%e7%b1%b3%e5%b0%94%e6%96%af%e7%90%86%e8%ae%ba","status":"publish","type":"post","link":"https:\/\/lttt.vanabel.cn\/?p=3865","title":{"rendered":"\u91cf\u5b50\u6768\u7c73\u5c14\u65af\u7406\u8bba"},"content":{"rendered":"

\u8bd1\u81f3Quantum Yang-Mills Theory<\/a>, \u5b83\u662fThe Millennium Prize Problems<\/em>\u4e2d\u7684\u4e00\u4e2a\u95ee\u9898.<\/p>\n

\n

\\title{\u91cf\u5b50\u6768\u7c73\u5c14\u65af\u7406\u8bba}
\n\\author{A. Jaffe & E. Witten}
\n\\date{2006}<\/p>\n

\u7269\u7406\u89c4\u8303\u7406\u8bba<\/h3>\n

\u81f320\u4e16\u7eaa\u65e9\u671f, \u4eba\u4eec\u5df2\u7ecf\u8ba4\u8bc6\u5230\u5728\u4e9a\u539f\u5b50\u5c3a\u5ea6\u4e0b\u63cf\u8ff0\u81ea\u7136\u89c4\u5f8b\u9700\u8981\u91cf\u5b50\u529b\u5b66. \u5728\u91cf\u5b50\u529b\u5b66\u4e2d, \u4e00\u4e2a\u7c92\u5b50\u7684\u4f4d\u7f6e\u548c\u901f\u5ea6\u662f\u4f5c\u7528\u5728Hilbert\u7a7a\u95f4\u7684\u975e\u4ea4\u6362\u7b97\u5b50, \u800c\u4e14\u50cf\u7ecf\u5178\u529b\u5b66\u4e2d\u7684”\u7c92\u5b50\u7684\u8f68\u8ff9”\u4e4b\u7c7b\u7684\u8bf4\u6cd5\u5df2\u7ecf\u6ca1\u6709\u610f\u4e49\u4e86.
\n
\n\u4f46\u662f\u7c92\u5b50\u7684\u91cf\u5b50\u529b\u5b66\u5e76\u4e0d\u662f\u6545\u4e8b\u7684\u5168\u90e8. \u572819\u4e16\u7eaa\u4ee5\u53ca20\u4e16\u7eaa\u65e9\u671f\u7684\u7269\u7406\u5b66\u4e2d, \u81ea\u7136\u754c\u7684\u8bb8\u591a\u73b0\u8c61\u90fd\u7528\u573a\u7684\u8bed\u8a00\u6765\u8868\u8ff0, \u4f8b\u5982Maxwell\u65b9\u7a0b\u4e2d\u7684\u7535\u78c1\u573a, Einstein\u65b9\u7a0b\u523b\u753b\u7684\u91cd\u529b\u573a. \u56e0\u4e3a\u573a\u548c\u7c92\u5b50\u6709\u76f8\u4e92\u4f5c\u7528, \u572820\u4e16\u7eaa20\u5e74\u4ee3\u665a\u671f, \u4eba\u4eec\u5df2\u7ecf\u6e05\u695a\u5730\u610f\u8bc6\u5230, \u4e0e\u7c92\u5b50\u672c\u8eab\u76f8\u5173\u7684\u6027\u8d28\u5e94\u8be5\u50cf\u573a\u4e00\u6837, \u5f15\u5165\u91cf\u5b50\u529b\u5b66\u7684\u6982\u5ff5.<\/p>\n

\u4e00\u65e6\u8fd9\u6837\u505a\u4e4b\u540e, \u8bf8\u5982\u7535\u573a\u5728\u7a7a\u65f6\u4e2d\u4e0d\u540c\u7684\u70b9\u7684\u5206\u91cf\u8fd9\u6837\u7684\u91cf, \u53d8\u6210\u4e86\u4e0d\u53ef\u4ea4\u6362\u7684\u7b97\u5b50. \u5f53\u4eba\u4eec\u8bd5\u7740\u53bb\u6784\u9020\u8fd9\u4e9b\u7b97\u5b50\u4f5c\u7528\u7684Hilbert\u7a7a\u95f4\u65f6, \u4f1a\u53d1\u73b0\u5f88\u591a\u6709\u8da3\u7684\u4e8b\u60c5. \u5173\u4e8e\u573a\u4e0e\u7c92\u5b50\u7684\u533a\u522b\u4e0d\u518d\u6709\u610f\u4e49, \u56e0\u4e3a\u91cf\u5b50\u573a\u7684\u8fd9\u4e2aHilbert\u7a7a\u95f4\u662f\u7528\u7c92\u5b50\u6fc0\u53d1\u7684\u65b9\u5f0f\u6784\u9020\u7684. \u4f20\u7edf\u7684\u4f8b\u5b50, \u4f8b\u5982\u7535\u5b50, \u91cd\u65b0\u89e3\u91ca\u4e3a\u91cf\u5b50\u5316\u573a\u7684\u72b6\u6001. \u5728\u8fd9\u4e00\u8fc7\u7a0b\u4e2d, \u4eba\u4eec\u9884\u6d4b\u5230”\u53cd\u7269\u8d28”\u7684\u5b58\u5728\u6027; \u5bf9\u6bcf\u4e2a\u7c92\u5b50, \u4e00\u5b9a\u5b58\u5728\u4e0e\u4e4b\u76f8\u5bf9\u4e8e\u7684\u53cd\u7c92\u5b50, \u5b83\u548c\u539f\u7c92\u5b50\u5177\u6709\u76f8\u540c\u7684\u8d28\u91cf\u4f46\u662f\u76f8\u53cd\u7684\u7535\u8377. \u5728 P.A.M. Dirac (\u5373\u4fdd\u7f57\u00b7\u72c4\u62c9\u514b)\u57fa\u4e8e\u91cf\u5b50\u529b\u5b66\u9884\u6d4b\u53cd\u7269\u8d28\u7684\u5b58\u5728\u6027\u4e0d\u4e45, \u5728\u5b87\u5b99\u5c04\u7ebf\u4e2d\u53d1\u73b0\u4e86”\u6b63\u7535\u5b50”\u6216\u8005\u79f0\u4e3a\u7535\u5b50\u7684\u53cd\u7c92\u5b50.<\/p>\n

\u8c8c\u4f3c\u57fa\u672c\u7c92\u5b50\u7269\u7406\u5b66\u6700\u91cd\u8981\u7684\u91cf\u5b50\u573a\u8bba(QFTs)\u662f\u89c4\u8303\u7406\u8bba. \u7ecf\u5178\u7684\u89c4\u8303\u7406\u8bba\u662fMaxwell\u7684\u7535\u78c1\u7406\u8bba, \u5176\u89c4\u8303\u5bf9\u79f0\u7fa4\u662fAbel\u7fa4$U(1)$. \u5982\u679c\u8bb0$A$\u4e3a$U(1)$\u89c4\u8303\u8054\u7edc, \u5728\u5c40\u90e8\u5b83\u662f\u7a7a\u65f6\u4e0a\u7684\u4e00\u4e2a1\u5f62\u5f0f, \u5219\u4e0e\u4e4b\u76f8\u5bf9\u7684\u66f2\u7387\u6216\u8005\u7535\u78c1\u573a\u5f20\u91cf\u662f2\u5f62\u5f0f$F=dA$, \u800c\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u5728\u6ca1\u6709\u7535\u8377\u548c\u7535\u6d41\u7684\u60c5\u51b5\u4e0b\u5c31\u662f$0=dF=d\\ast F$. \u8fd9\u91cc$\\ast$\u4e3aHodge\u5bf9\u5076\u7b97\u5b50; \u4e8b\u5b9e\u4e0a, Hodge\u6b63\u662f\u5c06Maxwell\u65b9\u7a0b\u7684\u89e3\u63a8\u5e7f\u5230\u8c03\u548c\u5f62\u5f0f\u800c\u5efa\u7acb\u4e86\u8457\u540d\u7684Hodge\u7406\u8bba. Maxwell\u65b9\u7a0b\u63cf\u8ff0\u7684\u662f\u5927\u8303\u56f4\u7684\u7535\u78c1\u573a\u4ee5\u53ca, \u6b63\u5982Maxwell\u53d1\u73b0\u7684\u90a3\u6837, \u5149\u6ce2\u4ee5\u4e00\u4e2a\u5178\u578b\u7684\u901f\u5ea6\u4f20\u64ad, \u5373\u5149\u901f.<\/p>\n

\u89c4\u8303\u7406\u8bba\u7684\u601d\u60f3\u6e90\u81f3Hermann Weyl\u7684\u5de5\u4f5c, \u8bf7\u53c2\u80031<\/a>\u4e2d\u5173\u4e8e\u89c4\u8303\u5bf9\u79f0\u4e0e\u53d1\u73b0\u6768\u7c73\u5c14\u65af\u7406\u8bba\u7684\u4e00\u4e2a\u6709\u8da3\u7684\u8ba8\u8bba, \u5173\u4e8e\u6768\u7c73\u5c14\u65af\u7406\u8bba\u7684\u53d1\u73b0\u53c2\u80032<\/a>, \u5b83\u4e5f\u79f0\u4e3a”\u975e\u4ea4\u6362\u7684\u89c4\u8303\u7406\u8bba”. \u5728\u7ecf\u5178\u7684\u7406\u8bba\u4e2d, \u5c06\u7535\u78c1\u573a\u7684\u89c4\u8303\u7fa4$U(1)$\u6362\u6210\u4e00\u822c\u7684\u7d27\u89c4\u8303\u7fa4$G$. \u7531\u8054\u7edc\u5b9a\u4e49\u66f2\u7387\u7684\u5f0f\u5b50\u8fd9\u65f6\u5fc5\u987b\u6539\u6210$F=dA+A\\wedge A$, \u800cMaxwell\u65b9\u7a0b\u7531Yang-Mills\u65b9\u7a0b$0=d_Af=d_A\\ast F$\u53d6\u4ee3, \u5176\u4e2d$d_A$\u662f\u5916\u5fae\u5206\u7b97\u5b50\u7684\u89c4\u8303\u5171\u53d8\u5ef6\u62d3.
\n
\n\u7ecf\u5178\u7684\u6768\u7c73\u5c14\u65af\u65b9\u7a0b\u53ef\u4ee5\u770b\u4f5c\u662f\u5982\u4e0b\u7684Yang-Mills\u6cdb\u51fd\u7684\u53d8\u5206\u65b9\u7a0b:\n<\/p>\n

$$\\begin{equation}\\label{eq:1}
\nL=\\frac{1}{4g^2}\\int \\tr F\\wedge\\ast F,
\n\\end{equation}$$
\n\u5176\u4e2d$\\tr$\u662f$G$\u7684\u674e\u4ee3\u6570\u4e0a\u7684\u4e00\u4e2a\u4e0d\u53d8\u7684\u4e8c\u6b21\u578b. Yang-Mills\u65b9\u7a0b\u662f\u975e\u7ebf\u6027\u7684, \u8fd9\u4e0d\u540c\u4e8eMaxwell\u65b9\u7a0b. \u50cf\u91cd\u529b\u573a\u7684Einstein\u65b9\u7a0b\u4e00\u6837, Yang-Mills\u65b9\u7a0b\u53ea\u77e5\u9053\u6781\u5c11\u6570\u3001\u6781\u5c11\u6570\u7684\u663e\u793a\u89e3. \u4f46\u662f\u6768\u7c73\u5c14\u65af\u65b9\u7a0b\u6bd5\u7adf\u8fd8\u662f\u548cMaxwell\u65b9\u7a0b\u6709\u5171\u6027: \u7279\u522b\u662f, \u4ece\u4ed6\u4eec\u90fd\u53ef\u4ee5\u8bc1\u660e”\u65e0\u8d28\u91cf\u7684\u6ce2\u4ee5\u5149\u901f\u4f20\u64ad”\u8fd9\u4e00\u7ecf\u5178\u4e8b\u5b9e. <\/p>\n

\u572820\u4e16\u7eaa50\u5e74\u4ee3, \u5f53Yang-Mills\u7406\u8bba\u521b\u7acb\u4e4b\u524d, \u4eba\u4eec\u5df2\u7ecf\u77e5\u9053\u91cf\u5b50\u7248\u672c\u7684Maxwell\u7406\u8bba, \u90a3\u65f6\u79f0\u4e4b\u4e3a\u91cf\u5b50\u7535\u52a8\u529b\u5b66\u6216\u8005QED, \u5b83\u5bf9\u7535\u78c1\u573a\u4e0e\u7535\u78c1\u529b\u6709\u51c6\u786e\u7684\u63cf\u8ff0. \u4e8b\u5b9e\u4e0a, QED\u5c06\u65e9\u671f\u91cf\u5b50\u7406\u8bba\u7684\u9884\u6d4b\u63d0\u793a\u4e86\u597d\u51e0\u4e2a\u6570\u91cf\u7ea7, \u800c\u4e14\u8fd8\u9884\u6d4b\u4e86\u65b0\u7684\u8dc3\u8fc1\u80fd\u7ea7.<\/p>\n

\u56e0\u6b64, \u5f88\u81ea\u7136\u7684\u95ee\u9898\u662f:\u662f\u5426\u975e\u4ea4\u6362\u7684\u89c4\u8303\u7406\u8bba\u80fd\u591f\u63cf\u8ff0\u81ea\u7136\u754c\u4e2d\u5176\u4ed6\u7684\u529b, \u7279\u522b\u662f\u5f31\u4f5c\u7528\u529b(\u662f\u653e\u5c04\u6027\u5f62\u6210\u7684\u539f\u56e0\u4e4b\u4e00) \u4ee5\u53ca\u5f3a\u4f5c\u7528\u529b\u6216\u8005\u6838\u529b (\u662f\u4f7f\u5f97\u8d28\u5b50\u548c\u4e2d\u5b50\u5f62\u6210\u539f\u5b50\u6838\u7684\u539f\u56e0\u4e4b\u4e00). \u7ecf\u5178Yang-Mills\u7406\u8bba\u7684\u96f6\u8d28\u91cf\u6027\u662f\u5c06\u5176\u5e94\u7528\u5230\u5176\u4ed6\u529b\u7684\u4e3b\u8981\u969c\u788d\u4e4b\u4e00, \u56e0\u4e3a\u5f31\u4f5c\u7528\u529b\u548c\u5f3a\u4f5c\u7528\u529b\u90fd\u662f\u77ed\u7a0b\u529b\u800c\u5927\u91cf\u7684\u7c92\u5b50\u90fd\u662f\u6709\u8d28\u91cf\u7684. \u56e0\u6b64\u8fd9\u4e9b\u73b0\u8c61\u5728\u63cf\u8ff0\u65e0\u8d28\u91cf\u7c92\u5b50\u7684\u957f\u7a0b\u573a\u65f6\u5e76\u4e0d\u4f1a\u51fa\u73b0.<\/p>\n

\u572820\u4e16\u7eaa\u516d\u4e03\u5341\u5e74\u4ee3, \u7269\u7406\u5b66\u5bb6\u514b\u670d\u4e86\u5173\u4e8e\u975e\u4ea4\u6362\u7fa4\u7684\u89c4\u8303\u573a\u7684\u7269\u7406\u89e3\u91ca\u8fd9\u4e00\u7269\u7406\u969c\u788d. \u5728\u5f31\u4f5c\u7528\u529b\u7684\u60c5\u5f62, \u8fd9\u5c31\u662fGlashow-Salam-Weinberg\u7684\u7535\u5f31\u7406\u8bba3<\/a>4<\/a>(electroweak theory), \u5176\u89c4\u8303\u7fa4\u662f$H=SU(2)\\times U(1)$. \u901a\u8fc7\u989d\u5916\u7684\u52a0\u4e00\u4e2a”Higgs\u573a”\u6765\u89e3\u51b3\u7ecf\u5178Yang-Mills\u6ce2\u7684\u96f6\u8d28\u91cf\u6027. Higgs\u573a\u4f5c\u7528\u4e8e$H$\u7684\u4e00\u4e2a$2$\u7ef4\u8868\u793a\u4e0a; \u5b83\u662f\u975e\u96f6\u7684\u800c\u4e14\u5728\u771f\u7a7a\u6001\u4e2d\u8d8b\u4e8e\u5e38\u503c, \u8fd9\u65f6\u5c06\u7ed3\u6784\u7fa4\u4ece$H$\u7ea6\u5316\u5230$U(1)$\u7684\u4e00\u4e2a\u5b50\u7fa4 (\u5bf9\u89d2\u5d4c\u5165\u5230$SU(2)\\times U(1)$\u4e2d). \u8fd9\u4e00\u7406\u8bba\u4ee5\u4e00\u79cd\u57fa\u672c\u7edf\u4e00\u7684\u65b9\u5f0f\u63cf\u8ff0\u4e86\u7535\u78c1\u529b\u548c\u5f31\u4f5c\u7528\u529b; \u7531\u4e8e\u7ed3\u6784\u7fa4\u7ea6\u5316\u4e3a$U(1)$, \u957f\u7a0b\u573a\u53ea\u6709\u7535\u78c1\u529b, \u6b63\u5982\u6211\u4eec\u5728\u81ea\u7136\u754c\u89c2\u5bdf\u5230\u7684\u90a3\u6837.<\/p>\n

\u5173\u4e8e\u5f3a\u76f8\u4e92\u4f5c\u7528\u529b\u7684Yang-Mills\u96f6\u8d28\u91cf\u6027\u7684\u4fee\u6b63\u6709\u7740\u672c\u8d28\u7684\u4e0d\u540c. \u8fd9\u91cc\u7684\u4fee\u6b63\u4e0d\u662f\u65b0\u52a0\u4e00\u4e2a\u573a\u5230Yang-Mills\u573a\u4e0a, \u800c\u662f\u53d1\u73b0\u4e86\u5173\u4e8e\u91cf\u5b50Yang-mills\u7406\u8bba\u672c\u8eab\u7684\u4e00\u4e2a\u91cd\u8981\u6027\u8d28, \u5373\u5b83\u7684\u7ecf\u5178\u62c9\u683c\u6717\u65e5\u7b26\u53f7\u662f\u6709$\\eqref{eq:1}$\u7ed9\u51fa\u7684. \u8fd9\u4e00\u6027\u8d28\u79f0\u4e3a”\u6e10\u8fd1\u81ea\u7531”5<\/a>6<\/a>. \u521d\u7565\u6765\u8bb2, \u8fd9\u610f\u5473\u7740, \u5728\u77ed\u8ddd\u79bb\u65f6, \u573a\u7684\u91cf\u5b50\u884c\u4e3a\u548c\u7ecf\u5178\u7406\u8bba\u7684\u91cf\u5b50\u884c\u4e3a\u7c7b\u4f3c, \u4f46\u5728\u957f\u8ddd\u79bb\u65f6, \u7ecf\u5178\u7684\u7406\u8bba\u5df2\u7ecf\u4e0d\u8db3\u4ee5\u5f15\u5bfc\u8fd9\u4e2a\u573a\u7684\u91cf\u5b50\u884c\u4e3a\u4e86.
\n
\n\u6e10\u8fd1\u81ea\u7531, \u4ee5\u53ca\u572820\u4e16\u7eaa\u516d\u4e03\u5341\u5e74\u4ee3\u53d1\u73b0\u7684\u5b9e\u9a8c\u6027\u548c\u7406\u8bba\u6027\u7684\u7ed3\u679c, \u4f7f\u5f97\u5229\u7528\u975e\u4ea4\u6362\u89c4\u8303\u7406\u8bba\u6765\u63cf\u8ff0\u6838\u529b\u6210\u4e3a\u53ef\u80fd, \u8fd9\u65f6\u89c4\u8303\u7fa4\u662f$G=SU(3)$. \u8f85\u52a9\u7684\u573a\u63cf\u8ff0, \u5728\u7ecf\u5178\u6c34\u5e73, “\u5938\u514b”\u662f\u548c\u7535\u5b50\u7c7b\u4f3c\u7684$1\/2$\u81ea\u65cb\u5bf9\u8c61, \u4f46\u4f5c\u7528\u5728$SU(3)$\u7684\u57fa\u672c\u8868\u793a\u4e0a. \u5f3a\u529b\u7684\u975e\u4ea4\u6362\u89c4\u8303\u573a\u8bba\u53c8\u79f0\u4e3a\u91cf\u5b50\u8272\u52a8\u529b\u5b66(QCD).<\/p>\n

\u5229\u7528QCD\u6765\u63cf\u8ff0\u5f3a\u529b\u662f20\u4e16\u7eaa\u516d\u4e03\u5341\u5e74\u4ee3\u4e00\u7cfb\u5217\u5b9e\u9a8c\u4e0e\u7406\u8bba\u7a81\u7834\u7684\u7ed3\u679c. \u540c\u65f6\u8fd8\u6d89\u53ca\u5f3a\u76f8\u4e92\u4f5c\u7528\u7684\u5bf9\u79f0\u6027\u4e0e\u9ad8\u80fd\u6001\u884c\u4e3a. \u4f46\u662f\u7ecf\u5178\u7684\u975e\u4ea4\u6362\u89c4\u8303\u573a\u8bba\u548c\u73b0\u5b9e\u4e16\u754c\u89c2\u5bdf\u5230\u7684\u5f3a\u76f8\u4e92\u4f5c\u7528\u662f\u5f88\u4e0d\u540c\u7684; \u4e3a\u4e86\u4f7f\u5f97QCD\u80fd\u591f\u6210\u529f\u5730\u63cf\u8ff0\u5f3a\u76f8\u4e92\u4f5c\u7528\u529b, \u5b83\u5fc5\u987b\u5177\u5907\u5982\u4e0b\u4e09\u6761\u63cf\u8ff0\u91cf\u5b50\u884c\u4e3a\u7684\u57fa\u672c\u6027\u8d28, \u5b83\u4eec\u6bcf\u6761\u90fd\u548c\u7ecf\u5178\u7406\u8bba\u7684\u884c\u4e3a\u6709\u5f88\u5927\u4e0d\u540c:<\/p>\n

    \n
  1. \u5b83\u5fc5\u987b\u6709”\u8d28\u91cf\u95f4\u9699”, \u5373\u5b58\u5728\u5e38\u6570$\\Delta>0$, \u4f7f\u5f97\u6bcf\u4e2a\u771f\u7a7a\u4e2d\u7684\u6fc0\u53d1\u6001\u81f3\u5c11\u5177\u6709\u80fd\u91cf$\\Delta$.<\/li>\n
  2. \u5b83\u5fc5\u987b\u6709”\u5938\u514b\u7981\u95ed”\u73b0\u8c61, \u5373\u5c3d\u7ba1\u8be5\u7406\u8bba\u662f\u7531\u57fa\u672c\u573a\u6765\u63cf\u8ff0\u7684, \u4f8b\u5982\u5938\u514b\u573a, \u4f46\u5728$SU(3)$\u4e0b\u7684\u4f5c\u7528\u662f\u975e\u5e73\u51e1\u7684, \u800c\u7269\u7406\u7c92\u5b50\u6001, \u4f8b\u5982\u8d28\u5b50, \u4e2d\u5b50\u548c\u4ecb\u5b50\u662f$SU(3)$\u4e0d\u53d8\u7684.<\/li>\n
  3. \u5b83\u5fc5\u987b\u5177\u5907”\u624b\u5f81\u5bf9\u79f0\u7834\u7f3a”, \u8fd9\u610f\u5473\u7740\u771f\u7a7a\u53ea\u6709\u5728\u4f5c\u7528\u5728\u5938\u514b\u573a\u7684\u5168\u5bf9\u79f0\u7fa4\u7684\u5b50\u7fa4\u4e0b\u624d\u662f\u52bf\u4e0d\u53d8\u7684(\u5728\u624b\u5f81\u6027\u7684\u6781\u9650\u60c5\u5f62, \u5938\u514b\u672c\u8eab\u7684\u8d28\u91cf\u4e3a\u96f6). <\/li>\n<\/ol>\n

    \u7b2c\u4e00\u70b9\u662f\u5fc5\u8981\u7684, \u5b83\u89e3\u91ca\u4e86\u6838\u529b\u662f\u5f3a\u529b\u4f46\u662f\u662f\u77ed\u7a0b\u7684; \u7b2c\u4e8c\u70b9\u89e3\u91ca\u4e86\u4e3a\u4ec0\u4e48\u5938\u514b\u603b\u662f\u6210\u5bf9\u51fa\u73b0; \u7b2c\u4e09\u6761\u4e5f\u662f\u5fc5\u987b\u7684, \u56e0\u4e3a\u5b83\u89e3\u91ca\u4e8620\u4e16\u7eaa60\u5e74\u7684\u53d1\u5c55\u7684\u8f6f$\\pi$\u4ecb\u5b50(soft pions)\u7684”\u6d41\u4ee3\u6570”(current algebra)\u7406\u8bba. <\/p>\n

    \u81ea20\u4e16\u7eaa\u4e03\u5341\u5e74\u4ee3\u4ee5\u6765\u7684\u5927\u91cf\u5b9e\u9a8c\u548c\u7535\u8111\u6a21\u62df7<\/a>\u8ba9\u4eba\u4eec\u975e\u5e38\u575a\u4fe1QCD\u5177\u6709\u4ee5\u4e0a\u4e09\u6761\u6027\u8d28. \u8fd9\u4e9b\u6027\u8d28\u4e5f\u53ef\u4ee5, \u5728\u67d0\u79cd\u7a0b\u5ea6\u4e0a, \u4ece\u5404\u79cd\u975e\u5e38\u590d\u6742\u7684\u6a21\u578b(\u4f8b\u5982\u5f3a\u8026\u5408\u7684\u683c\u70b9\u89c4\u8303\u7406\u8bba8<\/a>)\u7684\u7406\u8bba\u8ba1\u7b97\u4e2d\u63a8\u5bfc\u51fa\u6765. \u4f46\u662f, \u4ece\u7406\u8bba\u4e0a, \u5b83\u4eec\u8fd8\u6ca1\u6709\u5b8c\u5168\u88ab\u7406\u89e3; \u5373\u8fd8\u6ca1\u6709\u4e00\u4e2a\u4ee4\u4eba\u4fe1\u670d\u7684, \u65e0\u8bba\u662f\u4ece\u6570\u5b66\u4e0a\u5b8c\u5907\u7684\u8bc1\u660e, \u6216\u8005\u7528\u7406\u8bba\u8ba1\u7b97\u6765\u8868\u660e, \u4e0a\u9762\u4e09\u6761\u6027\u8d28\u662f\u5fc5\u4e0d\u53ef\u7f3a\u7684. <\/p>\n

    \u63a2\u6c42\u6570\u5b66\u7684\u7406\u89e3<\/h3>\n

    \u5f85\u7eed…<\/p>\n

    \u53c2\u8003\u6587\u732e<\/h3>\n
    \n
    \n
      \n
    1. C. N. Yang and R. L. Mills, Conservation of isotopic spin and isotopic gauge invariance,
      \nPhys. Rev. 96 (1954), 191\u2013195.       \u21a9<\/a><\/li>\n
    2. L. O\u2019Raifeartaigh, The Dawning of Gauge Theory, Princeton University Press, 1997. \u21a9<\/a><\/li>\n
    3. Salam, Abdus. “Weak and electromagnetic interactions.” (1968): 367-377. \u21a9<\/a><\/li>\n
    4. Weimberg, S. “A Model of Leptons Phys.” Rev. Lett 19 (1967): 1264. \u21a9<\/a><\/li>\n
    5. Gross, David J., and Frank Wilczek. “Ultraviolet behavior of non-abelian gauge theories.” Physical Review Letters 30.26 (1973): 1343-1346. \u21a9<\/a><\/li>\n
    6. Politzer, H. David. “Reliable perturbative results for strong interactions?.” Physical Review Letters 30.26 (1973): 1346-1349. \u21a9<\/a><\/li>\n
    7. Creutz, Michael. “Monte Carlo study of quantized SU (2) gauge theory.” Physical Review D 21.8 (1980): 2308. \u21a9<\/a><\/li>\n
    8. Wilson, Kenneth G. “Quarks and strings on a lattice.” New phenomena in subnuclear physics. Springer US, 1977. 69-142. \u21a9<\/a><\/li>\n<\/ol>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

      \u8bd1\u81f3Quantum Yang-Mills Theory, \u5b83\u662fThe Mille …<\/p>\n

      \u91cf\u5b50\u6768\u7c73\u5c14\u65af\u7406\u8bba<\/span> \u9605\u8bfb\u66f4\u591a »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[710,397,452],"class_list":["post-3865","post","type-post","status-publish","format-standard","hentry","category-mathnotes","tag-710","tag-397","tag-452"],"_links":{"self":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/3865","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3865"}],"version-history":[{"count":0,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/3865\/revisions"}],"wp:attachment":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3865"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3865"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3865"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}