ダランベール演算子
並びに、先進グリーン関数
D adv ( x − x ′ ) = 1 4 π | x − x ′ | δ ( c t − c t ′ + | x − x | ) = 1 ( 2 π ) 4 ∫ − ∞ ∞ e i k ( x − x ′ ) k 2 − ( k 0 − i ε ) 2 d 4 k {\displaystyle {\begin{aligned}D_{\text{adv}}(x-x')&={\frac {1}{4\pi |\mathbf {x} -\mathbf {x} '|}}\delta (ct-ct'+|\mathbf {x} -\mathbf {x} |)\\&={\frac {1}{(2\pi )^{4}}}\int _{-\infty }^{\infty }{\frac {e^{ik(x-x')}}{\mathbf {k} ^{2}-(k_{0}-i\epsilon )^{2}}}d^{4}k\end{aligned}}}