Complex Form of Classical and Quantum Electrodynamics
  We consider a complex covariant form of the macroscopic Maxwell equations, in a moving medium or at rest, following the original ideas of Minkowski. A compact, Lorentz invariant, derivation of the energy-momentum tensor and the corresponding differential balance equations are given. Conservation laws and quantization of electromagnetic field will be discussed in this covariant approach elsewhere. 
Sergey I. Kryuchkov, Nathan A. Lanfear, and Sergei K. Suslov
math-ph math.MP