正規順序積
φ ( + ) ( x ) = ∫ d 3 k ( 2 π ) 3 2 k 0 k 0 a ( k ) e i k x , φ ( − ) ( x ) = ∫ d 3 k ( 2 π ) 3 2 k 0 k 0 a † ( k ) e − i k x {\displaystyle \phi ^{(+)}(x)=\int {\frac {d^{3}\mathbf {k} }{(2\pi )^{3}2k_{0}}}k_{0}a(k)e^{ikx},\,\phi ^{(-)}(x)=\int {\frac {d^{3}\mathbf {k} }{(2\pi )^{3}2k_{0}}}k_{0}a^{\dagger }(k)e^{-ikx}}
と消滅演算子だけを含むφ(x)と生成演算子だけを含むφ(x)に分けると、
N [ φ ( + ) ( x ) φ ( − ) ( y ) ] = N [ φ ( − ) ( y ) φ ( + ) ( x ) ] = φ ( − ) ( x ) φ ( + ) ( y ) {\displaystyle N[\phi ^{(+)}(x)\phi ^{(-)}(y)]=N[\phi ^{(-)}(y)\phi ^{(+)}(x)]=\phi ^{(-)}(x)\phi ^{(+)}(y)}