${\displaystyle F_{\mu \nu }=\partial _{\mu }A_{\nu }-\partial _{\nu }A_{\mu ))$

${\displaystyle A^{\mu }=\left({\frac {\phi }{c)),{\boldsymbol {A))\right),~A_{\mu }=\eta _{\mu \nu }A^{\nu }=\left(-{\frac {\phi }{c)),{\boldsymbol {A))\right)}$

${\displaystyle \partial _{\mu }={\frac {\partial }{\partial x^{\mu ))}=\left({\frac {1}{c)){\frac {\partial }{\partial t)),\nabla \right)}$

${\displaystyle {\boldsymbol {E))=-\nabla \phi -{\frac {\partial {\boldsymbol {A))}{\partial t))}$

${\displaystyle {\boldsymbol {B))=\nabla \times {\boldsymbol {A))}$

${\displaystyle E_{j}/c=\partial _{j}A_{0}-\partial _{0}A_{j}=-F_{0j))$

${\displaystyle B_{i}\epsilon _{ijk}=\partial _{j}A_{k}-\partial _{k}A_{j}=F_{jk))$

${\displaystyle (F_{01},F_{02},F_{03})=(-E_{x}/c,-E_{y}/c,-E_{z}/c)}$

${\displaystyle (F_{23},F_{31},F_{12})=(B_{x},B_{y},B_{z})}$

${\displaystyle (F^{01},F^{02},F^{03})=(E_{x}/c,E_{y}/c,E_{z}/c)}$

${\displaystyle (F^{23},F^{31},F^{12})=(B_{x},B_{y},B_{z})}$

${\displaystyle (F_{\mu \nu })={\begin{bmatrix}0&-E_{x}/c&-E_{y}/c&-E_{z}/c\\E_{x}/c&0&B_{z}&-B_{y}\\E_{y}/c&-B_{z}&0&B_{x}\\E_{z}/c&B_{y}&-B_{x}&0\\\end{bmatrix)),}$

${\displaystyle (F^{\mu \nu })={\begin{bmatrix}0&E_{x}/c&E_{y}/c&E_{z}/c\\-E_{x}/c&0&B_{z}&-B_{y}\\-E_{y}/c&-B_{z}&0&B_{x}\\-E_{z}/c&B_{y}&-B_{x}&0\\\end{bmatrix))}$

${\displaystyle {\tilde {F))^{\mu \nu }={\frac {1}{2))\epsilon ^{\mu \nu \rho \sigma }F_{\rho \sigma ))$

${\displaystyle ({\tilde {F))^{01},{\tilde {F))^{02},{\tilde {F))^{03})=(F_{23},F_{31},F_{12})=(B_{x},B_{y},B_{z})}$

${\displaystyle ({\tilde {F))^{23},{\tilde {F))^{31},{\tilde {F))^{12})=(F_{01},F_{02},F_{03})=(-E_{x}/c,-E_{y}/c,-E_{z}/c)}$

${\displaystyle ({\tilde {F))^{\mu \nu })={\begin{bmatrix}0&B_{x}&B_{y}&B_{z}\\-B_{x}&0&-E_{z}/c&E_{y}/c\\-B_{y}&E_{z}/c&0&-E_{x}/c\\-B_{z}&-E_{y}/c&E_{x}/c&0\\\end{bmatrix))}$

${\displaystyle (G^{01},G^{02},G^{03})=(D_{x},D_{y},D_{z})}$

${\displaystyle (G^{23},G^{31},G^{12})=(H_{x}/c,H_{y}/c,H_{z}/c)}$

${\displaystyle G^{\mu \nu }={\frac {1}{Z_{0))}F^{\mu \nu }+P^{\mu \nu }={\frac {1}{c\mu _{0))}F^{\mu \nu }+P^{\mu \nu ))$

${\displaystyle (P^{01},P^{02},P^{03})=(P_{x},P_{y},P_{z})}$

${\displaystyle (P^{23},P^{31},P^{12})=(-M_{x}/c,-M_{y}/c,-M_{z}/c)}$

${\displaystyle (G^{\mu \nu })={\begin{bmatrix}0&D_{x}&D_{y}&D_{z}\\-D_{x}&0&H_{z}/c&-H_{y}/c\\-D_{y}&-H_{z}/c&0&H_{x}/c\\-D_{z}&H_{y}/c&-H_{x}/c&0\\\end{bmatrix))}$

${\displaystyle (P^{\mu \nu })={\begin{bmatrix}0&P_{x}&P_{y}&P_{z}\\-P_{x}&0&-M_{z}/c&M_{y}/c\\-P_{y}&M_{z}/c&0&-M_{x}/c\\-P_{z}&-M_{y}/c&M_{x}/c&0\\\end{bmatrix))}$

${\displaystyle A_{\mu }=\left(-{\frac {\phi }{c)),A_{r},rA_{\theta },rA_{\varphi }\sin \theta \right)}$

${\displaystyle (F_{\mu \nu })={\begin{bmatrix}0&-E_{r}/c&-rE_{\theta }/c&-rE_{\varphi }\sin \theta /c\\E_{r}/c&0&rB_{\varphi }&-rB_{\theta }\sin \theta \\rE_{\theta }/c&-rB_{\varphi }&0&r^{2}B_{r}\sin \theta \\rE_{\varphi }\sin \theta /c&rB_{\theta }\sin \theta &-r^{2}B_{r}\sin \theta &0\\\end{bmatrix))}$

${\displaystyle \eta _{\mu \nu }=\operatorname {diag} (-1,1,r^{2},r^{2}\sin ^{2}\theta )}$

${\displaystyle \eta ^{\mu \nu }=\operatorname {diag} (-1,1,{\tfrac {1}{r^{2))},{\tfrac {1}{r^{2}\sin ^{2}\theta )))}$

${\displaystyle (F^{\mu \nu })={\begin{bmatrix}0&E_{r}/c&E_{\theta }/cr&E_{\varphi }/cr\sin \theta \\-E_{r}/c&0&B_{\varphi }/r&-B_{\theta }/r\sin \theta \\-E_{\theta }/cr&-B_{\varphi }/r&0&B_{r}/r^{2}\sin \theta \\-E_{\varphi }/cr\sin \theta &B_{\theta }/r\sin \theta &-B_{r}/r^{2}\sin \theta &0\\\end{bmatrix))}$

${\displaystyle (F^{\mu \nu })={\begin{bmatrix}0&{\frac {1}{4\pi \epsilon _{0}c)){\frac {q}{r^{2))}&0&0\\-{\frac {1}{4\pi \epsilon _{0}c)){\frac {q}{r^{2))}&0&0&0\\0&0&0&0\\0&0&0&0\\\end{bmatrix))}$

${\displaystyle \partial _{\rho }F_{\mu \nu }+\partial _{\mu }F_{\nu \rho }+\partial _{\nu }F_{\rho \mu }=0}$

${\displaystyle \partial _{\mu }{\tilde {F))^{\mu \nu }={\frac {1}{2))\epsilon ^{\mu \nu \rho \sigma }\partial _{\mu }F_{\rho \sigma }=0}$

${\displaystyle \nabla \cdot {\boldsymbol {B))=0}$

${\displaystyle \nabla \times {\boldsymbol {E))+{\frac {\partial {\boldsymbol {B))}{\partial t))=\mathbf {0} }$

${\displaystyle \partial _{\mu }F^{\mu \nu }=-{\frac {Z_{0)){c))\,j^{\nu }=-\mu _{0}j^{\nu ))$

${\displaystyle \nabla \cdot {\boldsymbol {E))={\frac {\rho }{\epsilon _{0))))$

${\displaystyle \nabla \times {\boldsymbol {B))-{\frac {1}{c^{2))}{\frac {\partial {\boldsymbol {E))}{\partial t))=\mu _{0}{\boldsymbol {j))}$

${\displaystyle \partial _{\mu }G^{\mu \nu }=-{\frac {1}{c))\,j^{\nu ))$

${\displaystyle \nabla \cdot {\boldsymbol {D))=\rho }$

${\displaystyle \nabla \times {\boldsymbol {H))-{\frac {\partial {\boldsymbol {D))}{\partial t))={\boldsymbol {j))}$

${\displaystyle {\dot {p))_{\mu }=-q{\dot {X))^{\nu }F_{\nu \mu }(X)}$

${\displaystyle F_{\mu \nu }={\mathcal {D))_{\mu }A_{\nu }-{\mathcal {D))_{\nu }A_{\mu }=\partial _{\mu }A_{\nu }-\partial _{\nu }A_{\mu ))$

${\displaystyle {\mathcal {D))_{\mu }F^{\mu \nu }=-{\frac {Z_{0)){c))\,j^{\nu ))$