The Electrodynamics of Material Media

摘要: The general equations of a gauge invariant, classical theory the electrodynamics material media are obtained. invariance is insured by taking $\ensuremath{\nabla}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{D}=\ensuremath{\rho}, \ensuremath{\nabla}\ifmmode\times\else\texttimes\fi{}\mathrm{H}\ensuremath{-}{\mathrm{D}}^{\ensuremath{'}}=\mathrm{J}$ as conditions auxiliary to variation principle $\ensuremath{\delta}\ensuremath{\int}\ensuremath{\int}{L+\ensuremath{\Sigma}\stackrel{}{n}{\ensuremath{\theta}}_{n}[{{N}_{n}}^{\ensuremath{'}}+\ensuremath{\nabla}\ifmmode\cdot\else\textperiodcentered\fi{}({N}_{n}{\mathrm{V}}_{n})]dvdt}=0.$ Lagrangian function, $L$, depends on D, H, ${N}_{n}$, ${\mathrm{V}}_{n}$, ${\ensuremath{\theta}}_{n}$ and possibly their derivatives; here ${N}_{n}$ numerical density atoms in state $n$, ${\mathrm{V}}_{n}$ macroscopic or average velocity, variable that functions velocity potential some cases has dimensions action. electromagnetic potentials enter multipliers only.