Properties of six-component electromagnetic field solutions of a matrix form of the Maxwell equations, analogous to the four-component solutions of the Dirac equation, are described. It is shown that the six-component equation, including sources, is invariant under Lorentz transformations. Complete sets of eigenfunctions of the Hamiltonian for the electromagnetic fields, which may be interpreted as photon wave functions, are given both for plane waves and for angular-momentum eigenstates. Rotationally invariant projection operators are used to identify transverse or longitudinal electric and magnetic fields. For plane waves, the velocity transformed transverse wave functions are also transverse, and the velocity transformed longitudinal wave functions include both longitudinal and transverse components. A suitable sum over these eigenfunctions provides a Green function for the matrix Maxwell equation, which can be expressed in the same covariant form as the Green function for the Dirac equation. Radiation from a dipole source and from a Dirac atomic transition current are calculated to illustrate applications of the Maxwell Green function.
Topological spin transport of photons: "magnetic monopole" gauge field in Maxwell equations and polarization splitting of rays in periodically inhomogeneous media
Bosonic statistics enhance Maxwell's demon in photonic experiment
MESA+ Institute for Nanotechnology, University of Twente（特温特大学 MESA+ 纳米技术研究所）；Joint Center for Quantum Information and Computer Science, NIST and University of Maryland（美国国家标准与技术研究院与马里兰大学量子信息与计算机科学联合中心）；Department of Physics, University of Maryland（马里兰大学物理系）；Department of Physics and Astronomy, University of Rochester（罗切斯特大学物理与天文学系）；Institute for Physical Science and Technology, University of Maryland（马里兰大学物理科学与技术研究所）
