Quantization of the Electromagnetic Field: the Photon

Understanding the classical field theory of coupled dynamical scalar fields and vector potentials is rather difficult, with the quantized theory even more so, due to the fact that the Hamiltonian is no longer quadratic in the field variables and the field equations are nonlinear. Simplifying the problem by ignoring the scalar fields and only considering the vector potentials gives a theory with quadratic Hamiltonian that can be readily understood and quantized.