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\u4e00\u65b9\u3001\u91cf\u5b50\u30d5\u30a3\u30fc\u30eb\u30c9\u7406\u8ad6\u3092\u8a18\u8ff0\u3059\u308b\u5834\u5408\u3001\u30d1\u30b9\u30a4\u30f3\u30c6\u30b0\u30e9\u30eb\u5f62\u5f0f\u306e\u4e00\u90e8\u3068\u3057\u3066\u3001eichfelder\u306e\u30ad\u30e3\u30ea\u30d6\u30ec\u30fc\u30b7\u30e7\u30f3\u304c\u5fc5\u8981\u3067\u3059\u3002\u305d\u308c\u4ee5\u5916\u306e\u5834\u5408\u3001\u30ad\u30e3\u30ea\u30d6\u30ec\u30fc\u30b7\u30e7\u30f3\u306b\u3088\u3063\u3066\u306e\u307f\u7570\u306a\u308b\u8eab\u4f53\u7684\u306b\u540c\u4e00\u306e\u6761\u4ef6\u306e\u7121\u9650\u306e\u6570\u306b\u308f\u305f\u3063\u3066\u7d71\u5408\u3055\u308c\u308b\u305f\u3081\u3001\u7a4d\u5206\u304c\u660e\u78ba\u306b\u5b9a\u7fa9\u3055\u308c\u306a\u304f\u306a\u308a\u307e\u3059\u3002\u30ad\u30e3\u30ea\u30d6\u30ec\u30fc\u30b7\u30e7\u30f3\u304c\u8a2d\u5b9a\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u3053\u308c\u306f\u30e9\u30b0\u30e9\u30f3\u5bc6\u5ea6\u306b\u8ffd\u52a0\u306e\u5bc4\u4e0e\u3092\u3082\u305f\u3089\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u91cf\u5b50\u30d5\u30a3\u30fc\u30eb\u30c9\u306f\u3069\u3053\u304b\u3089\u3067\u3082\u30e9\u30b0\u30e9\u30f3\u5bc6\u5ea6\u306b\u73fe\u308c\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30d5\u30a3\u30fc\u30eb\u30c9\u306f\u3001Ludwig Faddejew\u3068Wiktor Popow Faddejew-Popow-Speistfelder\u307e\u305f\u306fGhosts of Shorts\u306e\u6700\u521d\u306e\u8aac\u660e\u306b\u5f93\u3063\u3066\u8a00\u53ca\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u5e7d\u970a\u306f\u3001\uff08\u30d2\u30c3\u30b0\u30b9\u30dc\u30bd\u30f3\u306e\u3088\u3046\u306b\uff09\u30b9\u30d4\u30f3-0\u7c92\u5b50\u3067\u3042\u308b\u305f\u3081\u3001\u30b9\u30d4\u30f3\u7d71\u8a08\u306e\u5b9a\u7406\u306b\u5f93\u308f\u306a\u3044\u305f\u3081\u306e\u975e\u7269\u7406\u7684\u306a\u7279\u6027\u3092\u6301\u3063\u3066\u3044\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30b9\u30d4\u30ea\u30c3\u30c8\u306f\u3082\u3068\u3082\u3068\u7406\u8ad6\u306e\u4e00\u90e8\u3067\u306f\u306a\u3044\u305f\u3081\u3001\u30aa\u30fc\u30af\u306e\u5bfe\u79f0\u6027\u306b\u3088\u3063\u3066\u8003\u616e\u3055\u308c\u3066\u3044\u306a\u3044\u305f\u3081\u3001\u30aa\u30fc\u30af\u5bfe\u79f0\u624b\u8853\u306f\u7cbe\u795e\u306e\u5909\u63db\u306e\u6761\u4ef6\u3092\u63d0\u4f9b\u3057\u307e\u305b\u3093\u3002 BRST\u306e\u5bfe\u79f0\u6027\u306f\u3001\u6750\u6599\u5834\u3068eichfelder\u306e\u5909\u63db\u304cEichtransformation\u3068\u6bd4\u8f03\u3057\u3066\u9055\u3044\u306f\u306a\u3044\u3068\u3044\u3046\u70b9\u3067\u3001\u30b9\u30d4\u30ea\u30c3\u30c8\u306e\u5b58\u5728\u3092\u8003\u616e\u3057\u3066\u3044\u307e\u3059\u304c\u3001\u5bfe\u79f0\u6027\u306b\u9055\u53cd\u3059\u308bEichfixiers\u671f\u306e\u8ca2\u732e\u306f\u3001\u30b9\u30d4\u30ea\u30c3\u30c8\u30d5\u30a3\u30fc\u30eb\u30c9\u306b\u3088\u308b\u8ca2\u732e\u306b\u3088\u3063\u3066\u6b63\u78ba\u306b\u88dc\u511f\u3055\u308c\u307e\u3059\u3002 \u306f l {displaystyle {mathcal {l}}} \u30e4\u30f3\u30df\u30eb\u30ba\u7406\u8ad6\u306e\u30e9\u30b0\u30e9\u30f3\u5bc6\u5ea6\u3001\u6b21\u306b\u30e9\u30b0\u30e9\u30f3\u30b8\u30ca\u30a4\u30c8\u5168\u4f53\u304c\u904b\u52d5\u306e\u90e8\u5206\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u30a2\u30a4\u30d2\u30d5\u30a7\u30eb\u30c0\u30fc\u306e\u52d5\u304d\u3068\u305d\u308c\u81ea\u4f53\u3068\u306e\u76f8\u4e92\u4f5c\u7528\u3092\u8868\u3059\u3001\u305d\u308c\u81ea\u4f53\u3068\u306e\u76f8\u4e92\u4f5c\u7528\u3092\u8868\u3059\u3001 L\u89aa\u65cf {displaystyle {mathcal {l}} _ {text {kin}}}} \u3001eichfixierungsterm        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4L\u4fee\u7406 {displaystyle {mathcal {l}} _ {text {fix}}}} \u305d\u3057\u3066\u30b9\u30d4\u30ea\u30c3\u30c8\u30d5\u30a3\u30fc\u30eb\u30c9\u3001 L\u7cbe\u795e {displaystyle {mathcal {l}} _ {text {geist}}}} \u554f\u984c\u306e\u7528\u8a9e\u3068\u529b\u3068\u554f\u984c\u306e\u9593\u306e\u76f8\u4e92\u4f5c\u7528\u3002 eichfelder\u306e\u30aa\u30fc\u30af\u5bfe\u79f0\u6027\u306f\u3001\u7f6e\u304d\u63db\u3048\u306e\u4e0b\u306e\u30e9\u30b0\u30e9\u30f3\u30b8\u30ca\u30a4\u30c8\u304c a m a \u2192 A\u2032m a = a m a + \u2202 m a a + f a b c a b a m c {displaystyle a_ {mu}^{a} to {a ‘} _ {mu}^{a_ {mu}^{a}+partial _ {mu} alpha^{a}+f^{abc} alpha^{b} a_ {mu}^{c}} eichfelder\u306e\u5834\u5408 a {displaystyle a} Invarian\u306e\u907a\u8de1\u3002 a {displaystyle alpha} \u90e8\u5c4b\u3068\u6642\u9593\u306e\u6a5f\u80fd\u306f\u3042\u308a\u307e\u3059\u304b\uff1f f {displaystyle f} \u5bfe\u79f0\u30b0\u30eb\u30fc\u30d7\u306e\u69cb\u9020\u5b9a\u6570\u3067\u3059\u3002 \u91cf\u5b50\u96fb\u6c17\u529b\u5b66\u3067\u306f\u3001\u91cf\u5b50\u30d5\u30a3\u30fc\u30eb\u30c9\u7406\u8ad6\u306b\u3088\u308b\u53e4\u5178\u7684\u306a\u96fb\u6c17\u529b\u5b66\u306e\u4e00\u822c\u5316\u306f\u3001 a {displaystyle a} \u30d9\u30af\u30c8\u30eb\u96fb\u4f4d\u3001\u69cb\u9020\u5b9a\u6570 f = 0 {displaystyle f = 0} \u6307\u5b9a\u3055\u308c\u305f\u5909\u63db\u306f\u3001\u96fb\u6c17\u304a\u3088\u3073\u78c1\u5834\u304c\u5909\u5316\u3057\u306a\u3044\u30d9\u30af\u30c8\u30eb\u96fb\u4f4d\u306e\u53e4\u5178\u7684\u306a\u30aa\u30fc\u30af\u5909\u63db\u3067\u3059\u3002 r \u30d0\u30c4 -\u8f03\u6b63 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] eichfixierungsterme\u304c\u3042\u308a\u307e\u3059 r \u30d0\u30c4 {displaystyle r_ {xi}} -Quantum\u96fb\u6c17\u529b\u5b66\u306e\u5834\u5408\u3001\u96fb\u6c17\u529b\u5b66\u306e\u30de\u30c3\u30af\u30b9\u30a6\u30a7\u30eb\u65b9\u7a0b\u5f0f\u306b\u304a\u3051\u308bLorenz\u306e\u84c4\u7a4d\u3092\u4e00\u822c\u5316\u3059\u308bids Lfix=  –  12\u03be\uff08 \u2202 \u03bca \u03bca\uff09\uff09 2{displaystyle {mathcal {l}} _ {text {fix}} =  –  {frac {1} {2xi}}}\uff08partial^{mu} a_ {mu}^{a}\uff09^{2}}} \u30aa\u30fc\u30af\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3092\u4f7f\u7528 \u30d0\u30c4 {displaystyle xi} \u3002\u30ed\u30fc\u30ec\u30f3\u30c4\u306e\u84c4\u7a4d\u306e\u91cf\u5b50\u78c1\u5834\u306e\u7406\u8ad6\u7684\u540c\u7b49\u7269\u3067\u3042\u308b\u30d5\u30a1\u30a4\u30f3\u30de\u30f3\u65b9\u7a0b\u5f0f\u306f\u3001\u8a2d\u5b9a\u304b\u3089\u751f\u3058\u307e\u3059 \u30d0\u30c4 = \u521d\u3081 {displaystyle xi = 1} \u3002\u5e7d\u970a\u306e\u671f\u9593\u306f\u3067\u3059 LGeist=  –  \uff08 \u2202 \u03bcc\u00afa\uff09\uff09 \uff08 \u2202 \u03bcc a –  f abca \u03bcbc c\uff09\uff09 {displaystyle {mathcal {l}} _ {text {geist}} =  – \uff08partial^{mu} {bar {c}}^{a}\uff09\uff08partial _ {mu} \u30b9\u30d4\u30ea\u30c3\u30c8\u30d5\u30a3\u30fc\u30eb\u30c9\u3067 c {displaystyle c} \u3001\u53cd\u30b9\u30d4\u30ea\u30c3\u30c8\u30d5\u30a3\u30fc\u30eb\u30c9 c\u00af{displaystyle {bar {c}}} \u5bfe\u79f0\u30b0\u30eb\u30fc\u30d7\u306e\u69cb\u9020\u5b9a\u6570 f {displaystyle f} \u3002\u7279\u306b\u3001\u5730\u533a\u30b0\u30eb\u30fc\u30d7\u306e\u5834\u5408 f = 0 {displaystyle f = 0} \u3001\u30b9\u30d4\u30ea\u30c3\u30c8\u30d5\u30a3\u30fc\u30eb\u30c9\u304c\u96fb\u6c17\u529b\u5b66\u3067\u5206\u96e2\u3057\u3001\u8ca2\u732e\u3057\u306a\u3044\u3088\u3046\u306b\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u7528\u8a9e\u3067\u4e0a\u8a18\u3067\u6307\u5b9a\u3055\u308c\u305feich\u5909\u63db\u3092\u633f\u5165\u3059\u308b\u3068\u3001\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u5bc6\u5ea6\u306f \u3044\u3044\u3048 \u3088\u308a\u591a\u304f\u306eeich Invariant\u3002 BRST\u5909\u63db\u306e\u4e0b\u3067\u306e\u4e0d\u5909\u6027\u306f\u3001\u30ad\u30e3\u30ea\u30d6\u30ec\u30fc\u30b7\u30e7\u30f3\u5909\u63db\u3092\u7121\u9650\u5909\u63db\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u306b\u8d77\u56e0\u3057\u307e\u3059 A\u03bca\u2192A\u2032\u03bca=A\u03bca+\u03b8(\u2202\u03bcca+gfabcA\u03bcbcc)c\u00afa\u2192c\u00af\u2032a=c\u00afa+\u03b81\u03be\u2202\u03bcA\u03bcaca\u2192c\u2032a=ca\u221212\u03b8fabccbcc{displayStyle {begin {aligned} a_ {mu}^{a} to {a ‘} _ {mu}^{a}\uff06= a_ {mu}^{a}+theta\uff08partial _ {mu} c^{a}+gf^{{{{{{{{{{{{{{{{{{{{{{{b\uff09 c}}^{a} to {{bar {c}} ‘}^{a}\uff06= {bar {c}}}^{a}+theta {frac {1} {xi}} partial^{mu} a_ {mu}^{a} \\ c^{a} to {a { }  –  {frac {1} {2}} theta f^{abc} c^{b} c^{c} end {aligned}}}} \u7121\u9650\u5909\u63db\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3092\u4f7f\u7528\u3057\u307e\u3059 th {displaystyletheta} \u3001\u305d\u308c\u306b\u3088\u3063\u3066 th {displaystyletheta} Gra\u00dfmann\u756a\u53f7\u3067\u3059\u3002\u3053\u306e\u305f\u3081\u306b\u3001\u7279\u306b\u305d\u308c\u306f\u305d\u308c\u3092\u9069\u7528\u3057\u307e\u3059 th c =  –  c th {displaystyle theta c = -ctheta} \u3001 \u3057\u304b\u3057 th a = a th {displaystyle theta a = atheta} \u30b9\u30d4\u30ea\u30c3\u30c8\u30d5\u30a3\u30fc\u30eb\u30c9\u81ea\u4f53\u304c\u30b0\u30e9\u30b9\u30de\u30f3\u54c1\u8cea\u3067\u3042\u308b\u305f\u3081\u3067\u3059\u3002 2\u3064\u306eGra\u00dfmann\u6570\u306e\u7a4d\u306f\u518d\u3073\u300c\u901a\u5e38\u306e\u300d\u6570\u3067\u3042\u308b\u305f\u3081\u3001Eichfeld\u306eBRST\u5909\u63db\u306fGra\u00dfmann-Quality\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u30aa\u30fc\u30af\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u307f\u306b\u306a\u308a\u307e\u3059 a {displaystyle alpha} \u7d42\u3048\u305f th c {displaystyle theta c} \u4ea4\u63db\u3002\u30d5\u30a7\u30eb\u30df\u30aa\u30f3\u6750\u6599\u5834\u3092\u8003\u616e\u3057\u3066\u3044\u306a\u3044\u3068\u3001\u4ea4\u63db\u30eb\u30fc\u30eb\u306f\u305d\u308c\u3089\u306b\u3082\u9069\u7528\u3055\u308c\u308b\u305f\u3081\u3001\u53e4\u5178\u7684\u306a\u91cf\u5b50\u529b\u5b66\u306e\u4f4d\u76f8\u306e\u81ea\u7531\u9078\u629e\u306b\u5bfe\u5fdc\u3059\u308b\u6750\u6599\u5834\u306e\u30ad\u30e3\u30ea\u30d6\u30ec\u30fc\u30b7\u30e7\u30f3\u306e\u81ea\u7531\u306f\u3001BRST\u5bfe\u79f0\u306b\u3088\u3063\u3066\u3082\u8868\u73fe\u3067\u304d\u307e\u3059\u3002 \u30b9\u30d4\u30ea\u30c3\u30c8\u3068\u30b9\u30d4\u30ea\u30c3\u30c8\u306e\u5206\u91ce\u306e\u5909\u63db\u884c\u52d5\u306f\u7570\u306a\u308a\u307e\u3059\u304c\u3001\u7269\u8cea\u3084\u53cd\u7269\u8cea\u3068\u306f\u5bfe\u7167\u7684\u306b\u3001\u5e7d\u970a\u3068\u53cd\u30de\u30b9\u30bf\u30fc\u306e\u9593\u306b\u7269\u7406\u7684\u306a\u6587\u8108\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u305d\u306e\u305f\u3081\u3001\u3053\u308c\u306f\u7269\u7406\u5b66\u3068\u77db\u76fe\u3057\u307e\u305b\u3093\u3002 \u4e00\u822c\u7684\u306a\u30b1\u30fc\u30b9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u4e00\u822c\u306b\u3001\u30ad\u30e3\u30ea\u30d6\u30ec\u30fc\u30b7\u30e7\u30f3\u306a\u3057 r \u30d0\u30c4 {displaystyle r_ {xi}} -So -Called\u3092\u5236\u9650\u3059\u308b\u305f\u3081\u306b \u4e2d\u897f-lautrup\u30d5\u30a7\u30eb\u30c9  b {displaystyle b} \uff08\u53e4\u5178\u7684\u306a\u96fb\u6c17\u529b\u5b66\u306eB\u30d5\u30a3\u30fc\u30eb\u30c9\u3068\u306e\u8868\u8a18\u306b\u6df7\u4e71\u3057\u306a\u3044\u3067\u304f\u3060\u3055\u3044\uff09\u3002\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u5bc6\u5ea6\u306f\u305d\u3046\u3067\u3059 L= Lkin+ c\u00afa\u222b d4\u3068 \u03b4ga(A\u2032,x)\u03b4\u03b1b(y)|\u03b1=0c b\uff08 \u3068 \uff09\uff09 + b ag a+ \u03be2b ab a{displaystyle {mathcal {l}} = {mathcal {l}} _ {text {kin}}+{bar {c}} ^{a} int mathrm {d} ^{4} y\u3001{frac {delta g ^{a}\uff08a ‘\u3001x\uff09 {bigg |} _ {alpha = 0} c^{b}\uff08y\uff09+b^{a} g^{a}+{frac {xi} {2}} b^{a} b^{a}} \u3057\u305f\u304c\u3063\u3066 g {displaystyle g} \u4e00\u822c\u7684\u306a\u6761\u4ef6\u306e\u305f\u3081\u306b d g \/ d a {displaystyle delta g\/delta alpha} \u6a5f\u80fd\u6d3e\u751f\u7528\u3002 r \u30d0\u30c4 {displaystyle r_ {xi}}  – \u304b\u3089\u306e\u30b3\u30fc\u30c6\u30a3\u30f3\u30b0\u306e\u7d50\u679c g a = \u2202 m a m a {displaystyle g^{a} = partial^{mu} a_ {mu}^{a}}}} \u4e2d\u91ce\u4e38\u7530\u7551\u306e\u30aa\u30a4\u30e9\u30fc\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u65b9\u7a0b\u5f0f\u306b\u95a2\u9023\u3057\u3066 \u2202 l \/ \u2202 b a = 0 {displaystyle partial {mathcal {l}}\/partial b^{a} = 0} \u3002\u3053\u306e\u65b9\u7a0b\u5f0f\u304b\u3089\u3001\u4e2d\u56fd\u8a9elautrup\u30d5\u30a3\u30fc\u30eb\u30c9\u306f\u88dc\u52a9\u30d5\u30a3\u30fc\u30eb\u30c9\u306b\u3059\u304e\u306a\u3044\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002 BRST\u5bfe\u79f0\u64cd\u4f5c\u306e\u5834\u5408\u306b\u4e00\u822c\u7684\u306b\u6709\u52b9\u3067\u3059\u3002 r \u30d0\u30c4 {displaystyle r_ {xi}} -\u8f03\u6b63 c\u00afa\u2192c\u00afa\u2032=c\u00afa\u2212\u03b8BaBa\u2192Ba\u2032=Ba{displaystyle {begin {aligned} {bar {c}}^{a} to {{bar {c}}^{a}} ‘\uff06= {bar {c}}^{a} -theta b^{a} \\ {a} {a} {a} {a} {a} {a} }} \u7279\u306b\u3001BRST\u5bfe\u79f0\u624b\u8853\u306f\u80fd\u529b\u304c\u3042\u308a\u307e\u305b\u3093\u3002\u3053\u308c\u306f\u3001\u30d5\u30a3\u30fc\u30eb\u30c9\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u306e\u6a5f\u80fd\u306b\u3064\u3044\u3066 f [ a \u3001 b \u3001 c \u3001 c\u00af] {displaystyle f [a\u3001b\u3001c\u3001{bar {c}}]} \u306f \uff08 f ‘  –  f \uff09\uff09 ‘  –  \uff08 f ‘  –  f \uff09\uff09 = 0 {displaystyle\uff08f’-f\uff09 ‘ – \uff08f’-f\uff09= 0} \u3002 \u3042\u306a\u305f\u306f\u5b9a\u7fa9\u3057\u307e\u3059 f ‘  –  f = th s f {displaystyle f’-f = theta sf} BRST\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u3068 s {displaystyleS} \u3001\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u308c\u306f\u7c21\u5358\u306b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059 s s f = 0 {displaystyleSSF = 0} \u8868\u73fe\u3059\u308b\u305f\u3081\u306b\u3002\u7279\u306b\u3001BRST\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u306e\u624b\u8853\u306e\u5834\u5408\u3001\u30ad\u30e3\u30ea\u30d6\u30ec\u30fc\u30b7\u30e7\u30f3\u6761\u4ef6\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 s g a= \u222b d4\u3068 \u03b4ga(A\u2032,x)\u03b4\u03b1b(y)|\u03b1=0c b\uff08 \u3068 \uff09\uff09 {displaystyle sg^{a} = int mathrm {d}^{4} y\u3001{frac {delta g^{a}\uff08a ‘\u3001x\uff09} {y\uff09}\uff08y\uff09} {bigg |} _ {bigg |} _ {bigg |} _ {y\uff09}\uff08y\uff09} \u305d\u306e\u7d50\u679c\u3001\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u5bc6\u5ea6\u306f\u5727\u7e2e\u3055\u308c\u307e\u3059 L= Lkin+ s \uff08 c\u00afaga+\u03be2c\u00afaBa\uff09\uff09 {displaystyle {mathcal {l}} = {mathcal {l}} _ {text {kin}}+sleft\uff08{bar {c}}^{a} g^{a}+{tfrac {xi} {2}}} {b {c}^{a}} \u66f8\u304f\u3002 Eichfelder\u306eBRST\u624b\u8853\u306f\u901a\u5e38\u306e\u30ad\u30e3\u30ea\u30d6\u30ec\u30fc\u30b7\u30e7\u30f3\u5909\u63db\u3068\u540c\u4e00\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306f\u81ea\u52d5\u7684\u306b\u9069\u7528\u3055\u308c\u307e\u3059 s L\u89aa\u65cf = 0 {displaystyle s {mathcal {l}} _ {text {kin}} = 0} \u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u5bc6\u5ea6\u306f\u30ca\u30a4\u30eb\u306e\u52b9\u529b\u306b\u3088\u308b\u3082\u306e\u3067\u3059 s {displaystyleS} Brst Operatons\u306e\u4e0b\u306e\u4e0d\u5909\u3001 s l = 0 {displaystyle s {mathcal {l}} = 0} \u3002 Eichfelder\u306e\u30ad\u30e3\u30ea\u30d6\u30ec\u30fc\u30b7\u30e7\u30f3\u306f\u3001BRST\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u306e\u5199\u771f\u306b\u3042\u308a\u307e\u3059\u3002\u305d\u308c\u306f\u5f62\u304b\u3089\u3067\u3059 s \u03c6 {displaystyle spsi} \u3002\u65b0\u3057\u3044\u30ad\u30e3\u30ea\u30d6\u30ec\u30fc\u30b7\u30e7\u30f3\u306f\u3001\u30d5\u30a9\u30fc\u30e0\u306e\u4efb\u610f\u306e\u7528\u8a9e\u3067\u9078\u629e\u3067\u304d\u307e\u3059 s d \u03c6 {displaystyle sdelta psi} \u30e9\u30b0\u30e9\u30f3\u5bc6\u5ea6\u306b\u8ffd\u52a0\u3055\u308c\u307e\u3059\u3002\u7279\u306b\u3001\u7269\u7406\u5b66\u306f\u30aa\u30fc\u30af\u5909\u63db\u306e\u4e0b\u3067\u5909\u5316\u3057\u3066\u306f\u306a\u308a\u307e\u305b\u3093\u3002 | a \u27e9 \u3001 | b \u27e9 {displaystyle |\u30a2\u30eb\u30d5\u30a1\u30e9\u30f3\u30b0\u30eb\u3001|\u30d9\u30fc\u30bf\u30e9\u30f3\u30b0\u30eb} Schwinger\u306e\u91cf\u5b50\u52b9\u679c\u306e\u539f\u5247\u306b\u3088\u308b\u3068\uff1a 0 = d \u27e8 a | b \u27e9 = \u27e8 a | \u79c1 s d \u03c6 | b \u27e9 {displaystyle 0 = delta langle alpha | beta rangle = langle alpha | mathrm {i} sdelta psi | beta rangle} \u3055\u3089\u306b\u3001\u52b9\u679c\u306e\u3042\u3089\u3086\u308b\u9023\u7d9a\u5c40\u6240\u7684\u5bfe\u79f0\u6027\u304b\u3089\u306e\u9a12\u97f3\u306e\u5f8c\u3001\u3064\u307e\u308a\u3001\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u5bc6\u5ea6\u306e\u5bfe\u79f0\u6027\u3001\u30e1\u30f3\u30c6\u30ca\u30f3\u30b9\u30b5\u30a4\u30ba\u3001\u304a\u3088\u3073\u305d\u308c\u306b\u7d9a\u304f\u9023\u7d9a\u65b9\u7a0b\u5f0f\u306e\u4e0b\u3067\u3082\u3002\u5f97\u3089\u308c\u305fBRST\u8ca0\u8377\u306e\u5145\u96fb\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u306f\u3001\u30ad\u30e3\u30ea\u30d6\u30ec\u30fc\u30b7\u30e7\u30f3\u6761\u4ef6\u306e\u9078\u629e\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002\u306e\u4e2d\u306b r \u30d0\u30c4 {displaystyle r_ {xi}} -\u5f7c\u306f Q BRST= \u222b d3\u30d0\u30c4 [ Ba(\u2202tca+fabcA0bcc)\u2212(\u2202tBa)ca+12fabc(\u2202tc\u00afa)cbcc] {displaystyle q_ {text {brst}} = int mathrm {d}^{3} x\u3001left [b^{a}\uff08partial _ {t} c^{a}+f^{abc} a_ {0}^{b} c^{c}\uff09 –  {t} {a {a ac {1} {2}} f^{abc}\uff08partial _ {t} {bar {c}}^{a}\uff09c^{b} c^{c} right]} \u4e00\u822c\u7684\u306b\u65b9\u7a0b\u5f0f\u3092\u6e80\u305f\u3057\u307e\u3059 \u79c1 s f = {QF\u2212FQF\u00a0bosonischQF+FQF\u00a0fermionisch{displaystyle mathrm {i} sf = {begin {cases} qf-fq\uff06quad f {text {bosonisch}} \\ qf+fq\uff06quad f {text {fermionisch}} end {case}}}}} \u3002 \u3057\u305f\u304c\u3063\u3066\u3001\u3059\u3079\u3066\u306e\u4f53\u8abf\u306b\u3064\u3044\u3066 \u27e8 a | Q f | b \u27e9 \u2213 \u27e8 a | f Q | b \u27e9 {displaystyle\u30e9\u30f3\u30b0\u30eb\u30a2\u30eb\u30d5\u30a1| qf |\u30d9\u30fc\u30bf\u30e9\u30f3\u30b0\u30ebmp\u30e9\u30f3\u30b0\u30eb\u30a2\u30eb\u30d5\u30a1| fq |\u30d9\u30fc\u30bf\u30e9\u30f3\u30b0\u30eb} = 0 \u3068 f = d \u03c6 {displaystyle f = delta psi} \u4f55\u3092\u9069\u7528\u3057\u307e\u3059 \u27e8 a | Q = Q | b \u27e9 = 0 {displaystyle\u30e9\u30f3\u30b0\u30eb\u30a2\u30eb\u30d5\u30a1| q = q |\u30d9\u30fc\u30bf\u30e9\u30f3\u30b0\u30eb= 0} \u7d9a\u304d\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001BRST\u8ca0\u8377\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u304c\u4f53\u8abf\u3067\u52d5\u4f5c\u3059\u308b\u5834\u5408\u3001\u7d50\u679c\u306f\u30bc\u30ed\u3067\u3059\u3002\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u3059\u3079\u3066\u306e\u7269\u7406\u72b6\u614b\u306b\u306fBRST\u8ca0\u8377\u304c\u3042\u308a\u307e\u305b\u3093\u3002 BRST\u30ed\u30fc\u30c9\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u306e\u4e2d\u6838\u306b\u3042\u308a\u307e\u3059\u3002\u4e00\u65b9\u3001\u30b4\u30fc\u30b9\u30c8\u3068\u30a2\u30f3\u30c1\u30de\u30b9\u30bf\u30fc\u306fBRST\u8ca0\u8377\u3092\u6301\u3063\u3066\u3044\u308b\u306e\u3067\u3001\u3053\u308c\u306f\u7269\u7406\u7684\u72b6\u614b\u3092\u8aac\u660e\u3057\u3066\u3044\u306a\u3044\u3068\u3044\u3046\u4e8b\u5b9f\u3068\u306f\u7570\u306a\u308b\u8a00\u8449\u9063\u3044\u3067\u3059\u3002 \u3055\u3089\u306b\u3001\u30ca\u30a4\u30eb\u306e\u52b9\u529b\u304b\u3089\u7d9a\u304d\u307e\u3059 s {displaystyleS} BRST\u8ca0\u8377\u6f14\u7b97\u5b50\u306e\u6b63\u65b9\u5f62\u306f\u3001\u30bc\u30ed\u307e\u305f\u306fID\u306e\u3044\u305a\u308c\u304b\u3067\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002\u305f\u3060\u3057\u3001BRST\u30ed\u30fc\u30c9\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u306b\u306f\u30b4\u30fc\u30b9\u30c8Quantums\u304c\u6d88\u3048\u3066\u3044\u306a\u3044\u305f\u3081\u3001 Q 2 = 0 {displaystyle q^{2} = 0} \u306a\u308c\u3002\u3053\u308c\u306f\u3001\u30d5\u30a9\u30fc\u30e0\u306e\u72b6\u614b\u30d9\u30af\u30c8\u30eb\u306b\u3088\u3063\u30662\u3064\u306e\u540c\u4e00\u306e\u7269\u7406\u7684\u6761\u4ef6\u3092\u4f7f\u7528\u3067\u304d\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059 Q | … \u27e9 {displaystyle q |\u30c9\u30c3\u30c8\u30e9\u30f3\u30b0\u30eb} \u5dee\u5225\u5316\u3057\u307e\u3059\u3002 ManfredB\u00f6hm\u3001Ansgar Denner\u3001Hans Joos\uff1a \u5f37\u529b\u3067\u30a8\u30ec\u30af\u30c8\u30ea\u30c3\u30af\u76f8\u4e92\u4f5c\u7528\u306e\u6e2c\u5b9a\u7406\u8ad6 \u3002 3.\u30a8\u30c7\u30a3\u30b7\u30e7\u30f3\u3002 Teubner\u3001Stuttgart Leipzig Wiesbaden 2001\u3001ISBN 3-519-23045-3\uff08\u82f1\u8a9e\uff09\u3002  Matw D. Schwartz\uff1a \u91cf\u5b50\u30d5\u30a3\u30fc\u30eb\u30c9\u7406\u8ad6\u3068\u6a19\u6e96\u30e2\u30c7\u30eb \u3002\u30b1\u30f3\u30d6\u30ea\u30c3\u30b8\u5927\u5b66\u51fa\u7248\u5c40\u3001\u30b1\u30f3\u30d6\u30ea\u30c3\u30b82014\u3001ISBN 978-1-107-03473-0\uff08\u82f1\u8a9e\uff09\u3002  \u30b9\u30c6\u30a3\u30fc\u30d6\u30f3\u30ef\u30a4\u30f3\u30d0\u30fc\u30b0\uff1a \u30d5\u30a3\u30fc\u30eb\u30c9\u306e\u91cf\u5b50\u7406\u8ad6Volume II\uff1a\u6700\u65b0\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3 \u3002 Cambridge University Press\u3001Cambridge 1996\u3001ISBN 0-521-55002-5\uff08\u82f1\u8a9e\uff09\u3002       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/7872#breadcrumbitem","name":"Brst Symmetry-Wikipedia"}}]}]