The starting point for the formal classical description of electromagnetic radiation is usually Maxwell’s equations. Originally, there were 20 equations, which essentially summarized earlier works by Karl Gauss, Andre-Marie Ampere, Michael Faraday, and others. Maxwell added the idea of a "displacement current"to complete his electromagnetic theory. Many years later, the number of Maxwell’s equations was lowered to four by Oliver Heaviside. By use of the curl and divergence operators of vector calculus, he was able to produce the form of Maxwell’s equations whose vacuum formulation is familiar today (Table 1). Often overlooked and undervalued is the analysis and experimental testing of Maxwell's original equations by Heinrich Hertz, which facilitated their acceptance and advancement.
One of the key results underpinning a quantum formulation of electrodynamics is the following equation, in which a volume integral succinctly expresses the energy of any radiation field Hrad in terms of the position r-dependent electric and magnetic induction fields E(r) and B(r), respectively:
Here, the constant ε0 is the permittivity of free space.