  Maxwell's equations and the Dirac equation are the first-order differential
relativistic wave equation for electromagnetic waves and electronic waves
respectively. Hence, there is a notable similarity between these two wave
equations, which has been widely researched since the Dirac equation was
proposed. In this paper, we show that the Maxwell equations can be written in
an exact form of the Dirac equation by representing the four Dirac operators
with $8\times8$ matrices. Unlike the ordinary $4\times4$ Dirac equation, both
spin--1/2 and spin--1 operators can be derived from the $8\times8$ Dirac
equation, manifesting that the $8\times8$ Dirac equation is able to describe
both electrons and photons. As a result of the restrictions that the
electromagnetic wave is a transverse wave, the photon is a spin--1 particle.
The four--current in the Maxwell equations and the mass in the electronic Dirac
equation also force the electromagnetic field to transform differently to the
electronic field. We use this $8\times8$ representation to find that the
Zitterbewegung of the photon is actually the oscillatory part of the Poynting
vector, often neglected upon time averaging.
