カレントの同時刻交換関係を計算するときに便利な公式
フェルミオンの場合
![\begin{align} &\delta(x_0)\, [q^\dagger(x) \Gamma_1 \Lambda_1 q(x),\; q^\dagger(0) \Gamma_2 \Lambda_2 q(0)] \\\\
&=\frac{1}{2}\delta^4(x) q^\dagger(0)([\Gamma_1, \Gamma_2]\{\Lambda_1, \Lambda_2\}
+ \{\Gamma_1, \Gamma_2\} [\Lambda_1, \Lambda_2]) q(0) \end{align}](https://chart.apis.google.com/chart?cht=tx&chl=%20%5Cbegin%7Balign%7D%20%20%26%5Cdelta%28x_0%29%5C%2C%20%5Bq%5E%5Cdagger%28x%29%20%5CGamma_1%20%5CLambda_1%20q%28x%29%2C%5C%3B%20%20q%5E%5Cdagger%280%29%20%5CGamma_2%20%5CLambda_2%20q%280%29%5D%20%5C%5C%5C%5C%0A%20%20%26%3D%5Cfrac%7B1%7D%7B2%7D%5Cdelta%5E4%28x%29%20q%5E%5Cdagger%280%29%28%5B%5CGamma_1%2C%20%5CGamma_2%5D%5C%7B%5CLambda_1%2C%20%5CLambda_2%5C%7D%0A%20%20%20%2B%20%5C%7B%5CGamma_1%2C%20%5CGamma_2%5C%7D%20%5B%5CLambda_1%2C%20%5CLambda_2%5D%29%20q%280%29%20%5Cend%7Balign%7D)
はディラックガンマ行列, 
はSU(N)行列を表す.
出典は G.A Christos, Phys. Rep. 116, 251 (1984) P260.
ボソンの場合
![\begin{align}
&\ \delta(x_0)\, [\pi(x)\Lambda_1 \phi(x), \;\pi(0)\Lambda_2 \phi(0)]
= i\delta^4(x) \pi(0) [\Lambda_1,\Lambda_2] \phi(0)
\end{align}](https://chart.apis.google.com/chart?cht=tx&chl=%20%5Cbegin%7Balign%7D%0A%20%26%5C%20%5Cdelta%28x_0%29%5C%2C%20%5B%5Cpi%28x%29%5CLambda_1%20%5Cphi%28x%29%2C%20%5C%3B%5Cpi%280%29%5CLambda_2%20%5Cphi%280%29%5D%20%20%0A%3D%20%20i%5Cdelta%5E4%28x%29%20%5Cpi%280%29%20%5B%5CLambda_1%2C%5CLambda_2%5D%20%5Cphi%280%29%0A%5Cend%7Balign%7D%20)
は 
の正準共役. 出典は R. Jackiw, Field theoretic investigation in current algebra P87 , in Current Algebra and Anomalies, World Scientific, 1985.
