[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/4089#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/4089","headline":"\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f – Wikipedia","name":"\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f – Wikipedia","description":"\u539f\u6587\u3068\u6bd4\u3079\u305f\u7d50\u679c\u3001\u3053\u306e\u8a18\u4e8b\u306b\u306f\u591a\u6570\uff08\u5c11\u306a\u304f\u3068\u30825\u500b\u4ee5\u4e0a\uff09\u306e\u8aa4\u8a33\u304c\u3042\u308b\u3053\u3068\u304c\u5224\u660e\u3057\u3066\u3044\u307e\u3059\u3002\u60c5\u5831\u306e\u5229\u7528\u306b\u306f\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u6b63\u78ba\u306a\u8868\u73fe\u306b\u6539\u8a33\u3067\u304d\u308b\u65b9\u3092\u6c42\u3081\u3066\u3044\u307e\u3059\u3002 \u5834\u306e\u91cf\u5b50\u8ad6\u306b\u304a\u3044\u3066\u3001\u5206\u914d\u95a2\u6570\u306e\u9593\u306e\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f(Ward\u2013Takahashi identity)\u306f\u3001\u7406\u8ad6\u306e\u5927\u57df\u7684\u5bfe\u79f0\u6027\u3084\u5c40\u6240\u7684\u5bfe\u79f0\u6027\u304b\u3089\u5f93\u3044\u3001\u7e70\u308a\u8fbc\u307f\u306e\u5f8c\u3067\u3082\u6709\u52b9\u3068\u306a\u308b\u7b49\u5f0f\u3067\u3042\u308b\u3002 \u91cf\u5b50\u96fb\u78c1\u529b\u5b66\u306e\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f\u306f\u3001\u5143\u3005\u306f\u30b8\u30e7\u30f3\u30fb\u30af\u30ea\u30fc\u30f4\u30fb\u30a6\u30a9\u30fc\u30c9\uff08\u82f1\u8a9e\u7248\uff09(John Clive Ward)\u3068\u9ad8\u6a4b\u5eb7(Yasushi Takahashi)\u306b\u3088\u308a\u96fb\u5b50\u306e\u6ce2\u52d5\u51fd\u6570\u7e70\u308a\u8fbc\u307f\uff08\u82f1\u8a9e\u7248\uff09(wave function renormalization)\u3068\u5f62\u72b6\u56e0\u5b50 F1(0) \u3068\u3092\u95a2\u4fc2\u3065\u3051\u308b\u305f\u3081\u306b\u4f7f\u308f\u308c\u3001\u6442\u52d5\u8ad6\u306e\u3059\u3079\u3066\u306e\u6b21\u6570\u306b\u304a\u3044\u3066\u7d2b\u5916\u767a\u6563\uff08\u82f1\u8a9e\u7248\uff09(ultraviolet divergence)\u304c\u76f8\u6bba\u3059\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3059\u308b\u3002\u305d\u306e\u5f8c\u3001\u6442\u52d5\u8ad6\u306e\u5168\u3066\u306e\u6b21\u6570\u306b\u304a\u3051\u308b\u30b4\u30fc\u30eb\u30c9\u30b9\u30c8\u30fc\u30f3\u306e\u5b9a\u7406\u306e\u8a3c\u660e\u306e\u62e1\u5f35\u306a\u3069\u306b\u3082\u7528\u3044\u3089\u308c\u305f\u3002 \u3088\u308a\u4e00\u822c\u306b\u306f\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f\u306f\u3001\u53e4\u5178\u8ad6\u306b\u304a\u3044\u3066\u30cd\u30fc\u30bf\u30fc\u306e\u5b9a\u7406\u306b\u3088\u308a\u9023\u7d9a\u5bfe\u79f0\u6027\u304b\u3089\u30ab\u30ec\u30f3\u30c8\u306e\u4fdd\u5b58\u5247\u304c\u5f93\u3046\u3053\u3068\u306e\u91cf\u5b50\u8ad6\u306b\u304a\u3051\u308b\u30d0\u30fc\u30b8\u30e7\u30f3\u3067\u3042\u308b\u3002\u5834\u306e\u91cf\u5b50\u8ad6\u3067\u306f\u305d\u306e\u3088\u3046\u306a\u5bfe\u79f0\u6027\u306f(\u307b\u3068\u3093\u3069)\u5e38\u306b\u3053\u306e\u3088\u3046\u306b\u4e00\u822c\u5316\u3055\u308c\u305f\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f\u3092\u610f\u5473\u3057\u3001\u91cf\u5b50\u632f\u5e45\u306e\u30ec\u30d9\u30eb\u3067\u306e\u5bfe\u79f0\u6027\u3092\u8ab2\u3059\u3002\u3053\u3053\u3067\u4e00\u822c\u5316\u3055\u308c\u305f\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f\u3068\u547c\u3093\u3067\u3044\u308b\u3082\u306e\u3068\u672c\u6765\u306e\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f\u3068\u306f\u3001\u4f8b\u3048\u3070\u3001\u30df\u30ab\u30a8\u30eb\u30fb\u30da\u30b9\u30ad\u30f3\uff08\u82f1\u8a9e\u7248\uff09(Michael Peskin)\u3068\u30c0\u30cb\u30a8\u30eb\u30fb\u30b7\u30e5\u30ec\u30fc\u30c0\u30fc\uff08\u82f1\u8a9e\u7248\uff09(Daniel Schroeder)\u306e\u6559\u79d1\u66f8 An Introduction to Quantum Field","datePublished":"2018-05-30","dateModified":"2018-05-30","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/b\/b2\/Blue_question_mark.svg\/30px-Blue_question_mark.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/b\/b2\/Blue_question_mark.svg\/30px-Blue_question_mark.svg.png","height":"30","width":"30"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/4089","about":["Wiki"],"wordCount":5007,"articleBody":"\u539f\u6587\u3068\u6bd4\u3079\u305f\u7d50\u679c\u3001\u3053\u306e\u8a18\u4e8b\u306b\u306f\u591a\u6570\uff08\u5c11\u306a\u304f\u3068\u30825\u500b\u4ee5\u4e0a\uff09\u306e\u8aa4\u8a33\u304c\u3042\u308b\u3053\u3068\u304c\u5224\u660e\u3057\u3066\u3044\u307e\u3059\u3002\u60c5\u5831\u306e\u5229\u7528\u306b\u306f\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u6b63\u78ba\u306a\u8868\u73fe\u306b\u6539\u8a33\u3067\u304d\u308b\u65b9\u3092\u6c42\u3081\u3066\u3044\u307e\u3059\u3002\u5834\u306e\u91cf\u5b50\u8ad6\u306b\u304a\u3044\u3066\u3001\u5206\u914d\u95a2\u6570\u306e\u9593\u306e\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f(Ward\u2013Takahashi identity)\u306f\u3001\u7406\u8ad6\u306e\u5927\u57df\u7684\u5bfe\u79f0\u6027\u3084\u5c40\u6240\u7684\u5bfe\u79f0\u6027\u304b\u3089\u5f93\u3044\u3001\u7e70\u308a\u8fbc\u307f\u306e\u5f8c\u3067\u3082\u6709\u52b9\u3068\u306a\u308b\u7b49\u5f0f\u3067\u3042\u308b\u3002\u91cf\u5b50\u96fb\u78c1\u529b\u5b66\u306e\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f\u306f\u3001\u5143\u3005\u306f\u30b8\u30e7\u30f3\u30fb\u30af\u30ea\u30fc\u30f4\u30fb\u30a6\u30a9\u30fc\u30c9\uff08\u82f1\u8a9e\u7248\uff09(John Clive Ward)\u3068\u9ad8\u6a4b\u5eb7(Yasushi Takahashi)\u306b\u3088\u308a\u96fb\u5b50\u306e\u6ce2\u52d5\u51fd\u6570\u7e70\u308a\u8fbc\u307f\uff08\u82f1\u8a9e\u7248\uff09(wave function renormalization)\u3068\u5f62\u72b6\u56e0\u5b50 F1(0) \u3068\u3092\u95a2\u4fc2\u3065\u3051\u308b\u305f\u3081\u306b\u4f7f\u308f\u308c\u3001\u6442\u52d5\u8ad6\u306e\u3059\u3079\u3066\u306e\u6b21\u6570\u306b\u304a\u3044\u3066\u7d2b\u5916\u767a\u6563\uff08\u82f1\u8a9e\u7248\uff09(ultraviolet divergence)\u304c\u76f8\u6bba\u3059\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3059\u308b\u3002\u305d\u306e\u5f8c\u3001\u6442\u52d5\u8ad6\u306e\u5168\u3066\u306e\u6b21\u6570\u306b\u304a\u3051\u308b\u30b4\u30fc\u30eb\u30c9\u30b9\u30c8\u30fc\u30f3\u306e\u5b9a\u7406\u306e\u8a3c\u660e\u306e\u62e1\u5f35\u306a\u3069\u306b\u3082\u7528\u3044\u3089\u308c\u305f\u3002\u3088\u308a\u4e00\u822c\u306b\u306f\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f\u306f\u3001\u53e4\u5178\u8ad6\u306b\u304a\u3044\u3066\u30cd\u30fc\u30bf\u30fc\u306e\u5b9a\u7406\u306b\u3088\u308a\u9023\u7d9a\u5bfe\u79f0\u6027\u304b\u3089\u30ab\u30ec\u30f3\u30c8\u306e\u4fdd\u5b58\u5247\u304c\u5f93\u3046\u3053\u3068\u306e\u91cf\u5b50\u8ad6\u306b\u304a\u3051\u308b\u30d0\u30fc\u30b8\u30e7\u30f3\u3067\u3042\u308b\u3002\u5834\u306e\u91cf\u5b50\u8ad6\u3067\u306f\u305d\u306e\u3088\u3046\u306a\u5bfe\u79f0\u6027\u306f(\u307b\u3068\u3093\u3069)\u5e38\u306b\u3053\u306e\u3088\u3046\u306b\u4e00\u822c\u5316\u3055\u308c\u305f\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f\u3092\u610f\u5473\u3057\u3001\u91cf\u5b50\u632f\u5e45\u306e\u30ec\u30d9\u30eb\u3067\u306e\u5bfe\u79f0\u6027\u3092\u8ab2\u3059\u3002\u3053\u3053\u3067\u4e00\u822c\u5316\u3055\u308c\u305f\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f\u3068\u547c\u3093\u3067\u3044\u308b\u3082\u306e\u3068\u672c\u6765\u306e\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f\u3068\u306f\u3001\u4f8b\u3048\u3070\u3001\u30df\u30ab\u30a8\u30eb\u30fb\u30da\u30b9\u30ad\u30f3\uff08\u82f1\u8a9e\u7248\uff09(Michael Peskin)\u3068\u30c0\u30cb\u30a8\u30eb\u30fb\u30b7\u30e5\u30ec\u30fc\u30c0\u30fc\uff08\u82f1\u8a9e\u7248\uff09(Daniel Schroeder)\u306e\u6559\u79d1\u66f8 An Introduction to Quantum Field Theory\uff08\u53c2\u8003\u6587\u732e\u53c2\u7167\uff09\u306e\u3088\u3046\u306a\u6587\u732e\u3092\u8aad\u3080\u969b\u306b\u306f\u3001\u533a\u5225\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f[\u7de8\u96c6]\u904b\u52d5\u91cf\u7a7a\u9593(momentum space)\u306b\u304a\u3051\u308b\u76f8\u95a2\u51fd\u6570\u306e\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f\u306f\u3001\u5916\u7dda\u306e\u904b\u52d5\u91cf\u304c\u5fc5\u305a\u3057\u3082\u30aa\u30f3\u30b7\u30a7\u30eb\u3067\u306a\u3044\u5834\u5408\u306b\u9069\u7528\u3055\u308c\u308b\u3002M(k;p1\u22efpn;q1\u22efqn)=\u03f5\u03bc(k)M\u03bc(k;p1\u22efpn;q1\u22efqn){displaystyle {mathcal {M}}(k;p_{1}cdots p_{n};q_{1}cdots q_{n})=epsilon _{mu }(k){mathcal {M}}^{mu }(k;p_{1}cdots p_{n};q_{1}cdots q_{n})}\u3092\u3001\u904b\u52d5\u91cf k \u3092\u6301\u3064\u5916\u7dda\u5149\u5b50(\u3053\u3053\u306b \u03f5\u03bc(k){displaystyle !epsilon _{mu }(k)} \u306f\u5149\u5b50\u306e\u504f\u5149\uff08\u82f1\u8a9e\u7248\uff09(polarization)\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308a\u3001\u03bc{displaystyle mu }=0,…,3\u306b\u6e21\u3063\u3066\u548c\u3092\u3068\u3063\u3066\u3044\u308b)\u3001\u904b\u52d5\u91cf p1\u22efpn{displaystyle p_{1}cdots p_{n}} \u3092\u6301\u3064n \u500b\u306e\u96fb\u5b50\u304b\u3089\u306a\u308b\u521d\u671f\u72b6\u614b\u3001\u53ca\u3073\u904b\u52d5\u91cf q1\u22efqn{displaystyle q_{1}cdots q_{n}} \u3092\u6301\u3064n \u500b\u306e\u96fb\u5b50\u304b\u3089\u306a\u308b\u7d42\u72b6\u614b\u306b\u3064\u3044\u3066\u306e\u91cf\u5b50\u96fb\u78c1\u529b\u5b66(QED)\u3067\u306e\u76f8\u95a2\u51fd\u6570\u3068\u3059\u308b\u3002\u3055\u3089\u306b\u3001M0{displaystyle {mathcal {M}}_{0}} \u3092\u5143\u306e\u632f\u5e45\u304b\u3089\u904b\u52d5\u91cf k \u3092\u3082\u3064\u5149\u5b50\u3092\u53d6\u308a\u9664\u304f\u3053\u3068\u306b\u3088\u308a\u5f97\u3089\u308c\u308b\u3088\u308a\u5358\u7d14\u306a\u632f\u5e45(amplitude)\u3068\u3059\u308b\u3002\u3059\u308b\u3068\u3001\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f\u306f\u3001k\u03bcM\u03bc(k;p1\u22efpn;q1\u22efqn)=e\u2211i[M0(p1\u22efpn;q1\u22ef(qi\u2212k)\u22efqn){displaystyle k_{mu }{mathcal {M}}^{mu }(k;p_{1}cdots p_{n};q_{1}cdots q_{n})=esum _{i}left[{mathcal {M}}_{0}(p_{1}cdots p_{n};q_{1}cdots (q_{i}-k)cdots q_{n})right.}\u2212M0(p1\u22ef(pi+k)\u22efpn;q1\u22efqn)]{displaystyle left.-{mathcal {M}}_{0}(p_{1}cdots (p_{i}+k)cdots p_{n};q_{1}cdots q_{n})right]}\u3068\u306a\u308b\u3002\u3053\u3053\u306b e \u306f\u96fb\u5b50\u306e\u96fb\u8377\u3067\u3042\u308a\u8ca0\u306e\u5024\u3092\u3068\u308b\u3002M{displaystyle {mathcal {M}}} \u306e\u5916\u7dda\u96fb\u5b50\u306e\u904b\u52d5\u91cf\u304c\u30aa\u30f3\u30b7\u30a7\u30eb\u306e\u5834\u5408\u306b\u306f\u3001\u3053\u306e\u7b49\u5f0f\u306e\u53f3\u8fba\u306e\u632f\u5e45\u306f\u305d\u308c\u305e\u308c\u30aa\u30d5\u30b7\u30a7\u30eb\u306e\u5916\u7dda\u7c92\u5b50\u3092\uff11\u3064\u6301\u3061\u3001\u5f93\u3063\u3066\u3001S-\u884c\u5217\u8981\u7d20\u306b\u5bc4\u4e0e\u3057\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3002\u30a6\u30a9\u30fc\u30c9\u306e\u6052\u7b49\u5f0f[\u7de8\u96c6]\u30a6\u30a9\u30fc\u30c9\u306e\u6052\u7b49\u5f0f\u306f\u3001\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f\u3092S-\u884c\u5217\u8981\u7d20\u3078\u7279\u6b8a\u5316\u3057\u305f\u6052\u7b49\u5f0f\u3067\u3042\u308a\u3001\u7269\u7406\u7684\u306b\u53ef\u80fd\u306a\u6563\u4e71\u904e\u7a0b\u3092\u8a18\u8ff0\u3059\u308b\u306e\u3067\u3001\u3059\u3079\u3066\u306e\u304c\u5916\u90e8\u7c92\u5b50\u306e\u30aa\u30f3\u30b7\u30a7\u30eb\u3092\u6301\u3064\u3002\u7e70\u308a\u8fd4\u3059\u304c\u3001M(k)=\u03f5\u03bc(k)M\u03bc(k){displaystyle {mathcal {M}}(k)=epsilon _{mu }(k){mathcal {M}}^{mu }(k)} \u3092\u3001\u904b\u52d5\u91cf k{displaystyle !k} \u306e\u5916\u90e8\u5149\u5b50\u3092\u6301\u3064 QED \u904e\u7a0b\u306e\u632f\u5e45\u3068\u3059\u308b\u3002\u3053\u3053\u306b \u03f5\u03bc(k){displaystyle !epsilon _{mu }(k)} \u306f\u3001\u5149\u5b50\u306e\u504f\u5149\uff08\u82f1\u8a9e\u7248\uff09(polarization)\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308b\u3002\u3059\u308b\u3068\u3001\u30a6\u30a9\u30fc\u30c9\u306e\u6052\u7b49\u5f0f\u306f\u3001k\u03bcM\u03bc(k)=0{displaystyle k_{mu }{mathcal {M}}^{mu }(k)=0}\u3067\u3042\u308b\u3002\u7269\u7406\u7684\u306b\u306f\u3001\u3053\u306e\u6052\u7b49\u5f0f\u306e\u610f\u5473\u306f\u3001\u30e9\u30f3\u30c0\u30a6\u30b2\u30fc\u30b8\u3067\u8d77\u304d\u308b\u5149\u5b50\u306e\u7e26\u65b9\u5411\u306e\u504f\u5149\u306f\u7269\u7406\u7684\u3067\u306f\u306a\u304f\u3001S-\u884c\u5217\u304b\u3089\u6d88\u3048\u308b\u3002\u3053\u306e\u4f7f\u3044\u65b9\u306e\u4f8b\u306f\u3001QED \u306e\u771f\u7a7a\u504f\u6975\u3068\u96fb\u5b50\u306e\u9802\u70b9\u51fd\u6570\u306e\u30c6\u30f3\u30bd\u30eb\u69cb\u9020\u3092\u62d8\u675f\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002\u7d4c\u8def\u7a4d\u5206\u3067\u306e\u5c0e\u51fa[\u7de8\u96c6]\u7d4c\u8def\u7a4d\u5206\u306e\u5b9a\u5f0f\u5316\u306b\u304a\u3044\u3066\u3001\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f\u306f\u3001\u30b2\u30fc\u30b8\u5909\u63db\u306e\u4e0b\u3067\u306e\u6c4e\u51fd\u6570\u6e2c\u5ea6\u306e\u4e0d\u5909\u91cf\u306e\u53cd\u6620\u3067\u3042\u308b\u3002\u8a73\u3057\u304f\u8a00\u3046\u3068\u3001\u03b4\u03f5{displaystyle delta _{epsilon }} \u3067 \u03b5 \u306b\u3088\u308b\u30b2\u30fc\u30b8\u5909\u63db\u3092\u8868\u3059\u3068\uff08\u52a0\u3048\u3066\u3001\u03b5 \u3092\u7cfb\u306e\u7269\u7406\u7684\u5bfe\u79f0\u6027\u304c\u5927\u57df\u7684\u3067\u3042\u308b\u5834\u5408\u3084\u5927\u57df\u7684\u5bfe\u79f0\u6027\u304c\u5b58\u5728\u3057\u306a\u3044\u5834\u5408\u3067\u3082\u3001\u6c4e\u51fd\u6570\u6e2c\u5ea6\u306e\u4e0d\u5909\u6027\u306b\u3064\u3044\u3066\u306e\u307f\u5fc3\u914d\u3059\u308b\u3060\u3051\u3067\u3088\u3044\uff09\u3001\u222b\u03b4\u03f5(FeiS)D\u03d5=0{displaystyle int delta _{epsilon }left({mathcal {F}}e^{iS}right){mathcal {D}}phi =0}\u306f\u3001\u6c4e\u51fd\u6570\u6e2c\u5ea6\u306e\u4e0d\u5909\u6027\u3092\u8868\u3059\u3002\u3053\u3053\u306b S \u306f\u4f5c\u7528\u3067\u3042\u308a\u3001F{displaystyle {mathcal {F}}} \u306f\u91cf\u5b50\u5834\u306e\u6c4e\u51fd\u6570\u3067\u3042\u308b\u3002\u30b2\u30fc\u30b8\u5909\u63db\u304c\u7406\u8ad6\u306e\u5927\u57df\u7684\u5bfe\u79f0\u6027\u306b\u5bfe\u5fdc\u3059\u308b\u3068\u3001\uff08\u5834 \u03c6 \u306e\u6c4e\u51fd\u6570\u3068\u3057\u3066\uff09\u3042\u308b\u30ab\u30ec\u30f3\u30c8\uff08\u82f1\u8a9e\u7248\uff09(current) J \u306b\u5bfe\u3057\u3001\u66f2\u9762\u9805\uff08\u82f1\u8a9e\u7248\uff09(surface term)\u3092\u7121\u8996\u3059\u308b\u3053\u3068\u3092\u4eee\u5b9a\u3057\u305f\u90e8\u5206\u7a4d\u5206\u306b\u3088\u308a\u3001\u03b4\u03f5S=\u222b(\u2202\u03bc\u03f5)J\u03bcddx=\u2212\u222b\u03f5\u2202\u03bcJ\u03bcddx{displaystyle delta _{epsilon }S=int left(partial _{mu }epsilon right)J^{mu }mathrm {d} ^{d}x=-int epsilon partial _{mu }J^{mu }mathrm {d} ^{d}x}\u3068\u306a\u308b\u3002\u3059\u308b\u3068\u3001\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f\u306f\u3001\u27e8\u03b4\u03f5F\u27e9\u2212i\u222b\u03f5\u27e8F\u2202\u03bcJ\u03bc\u27e9ddx=0{displaystyle langle delta _{epsilon }{mathcal {F}}rangle -iint epsilon langle {mathcal {F}}partial _{mu }J^{mu }rangle mathrm {d} ^{d}x=0}\u3068\u306a\u308b\u3002\u3053\u306e\u7b49\u5f0f\u306e\u30cd\u30fc\u30bf\u30fc\u306e\u9023\u7d9a\u65b9\u7a0b\u5f0f\u306e QFT \u306b\u304a\u3051\u308b\u985e\u4f3c\u7269\u306f \u2202\u03bcJ\u03bc=0{displaystyle partial _{mu }J^{mu }=0} \u3067\u3042\u308b\u3002\u30b2\u30fc\u30b8\u5909\u63db\u304c\u5b9f\u969b\u306e\u30b2\u30fc\u30b8\u5bfe\u79f0\u6027\u306b\u5bfe\u5fdc\u3059\u308b\u3068\u3001\u222b\u03b4\u03f5(Fei(S+Sgf))D\u03d5=0{displaystyle int delta _{epsilon }left({mathcal {F}}e^{ileft(S+S_{gf}right)}right){mathcal {D}}phi =0}\u3068\u306a\u308b\u3002\u3053\u3053\u306b S \u306f\u30b2\u30fc\u30b8\u4e0d\u5909\u306f\u4f5c\u7528\u3067\u3042\u308a\u3001Sgf \u306f\u30b2\u30fc\u30b8\u4e0d\u5909\u3067\u306f\u306a\u3044\u30b2\u30fc\u30b8\u56fa\u5b9a\uff08\u82f1\u8a9e\u7248\uff09(gauge fixing)\u9805\u3067\u3042\u308b\u3002\u3057\u304b\u3057\u3001\u305f\u3068\u3048\u5927\u57df\u7684\u5bfe\u79f0\u6027\u304c\u5b58\u5728\u3057\u306a\u3044\uff08\u5bfe\u79f0\u6027\u304c\u7834\u308c\u3066\u3044\u308b\uff09\u5834\u5408\u3067\u3082\u3001\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f\u306f\u30c1\u30e3\u30fc\u30b8\u306e\u975e\u4fdd\u5b58\u306e\u7387\u3092\u8a18\u8ff0\u3059\u308b\u3002\u6c4e\u51fd\u6570\u6e2c\u5ea6\u304c\u30b2\u30fc\u30b8\u4e0d\u5909\u3067\u306a\u3044\u304c\u3001\u03bb \u3092\u5834 \u03c6 \u306e\u6c4e\u51fd\u6570\u3068\u3057\u305f\u3068\u304d\u306b\u306f\u222b\u03b4\u03f5(FeiS)D\u03d5=\u222b\u03f5\u03bbFeiSddx{displaystyle int delta _{epsilon }left({mathcal {F}}e^{iS}right){mathcal {D}}phi =int epsilon lambda {mathcal {F}}e^{iS}mathrm {d} ^{d}x}\u3092\u6e80\u3059\u3068\u3059\u308b\u3068\u3001\u30a2\u30ce\u30de\u30ea\u30fc\u30a6\u30a9\u30fc\u30c9\uff1d\u9ad8\u6a4b\u6052\u7b49\u5f0f\u3092\u5f97\u308b\u3002\u3053\u306e\u3053\u3068\u306e\u4f8b\u306f\u30ab\u30a4\u30e9\u30eb\u30a2\u30ce\u30de\u30ea\u30fc\uff08\u82f1\u8a9e\u7248\uff09(chiral anomaly)\u304c\u3042\u308b\u5834\u5408\u3067\u3042\u308b\u3002\u53c2\u8003\u6587\u732e[\u7de8\u96c6]Y. Takahashi, Nuovo Cimento, Ser 10, 6 (1957) 370.J.C. Ward, Phys. Rev. 78, (1950) 182For a pedagogical derivation, see section 7.4 of Michael E. Peskin and Daniel V. Schroeder (1995). An Introduction to Quantum Field Theory. 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