Quantization of the electromagnetic field

After quantization of the electromagnetic field, the EM (electromagnetic) field consists of discrete energy parcels, photons. Photons are massless particles of definite energy, definite momentum, and definite spin.

In order to explain the photoelectric effect, Einstein assumed heuristically in 1905 that an electromagnetic field consists of parcels of energy hν, where h is Planck's constant and ν is the wave frequency. In 1927 Paul A. M. Dirac was able to weave the photon concept into the fabrics of the new quantum mechanics and to describe the interaction of photons with matter. He applied a technique which is now generally called second quantization, although this term is somewhat of a misnomer for EM fields, because they are, after all, solutions of the classical Maxwell equations. In Dirac's theory the fields are quantized for the first time and it is also the first time that Planck's constant enters the expressions. In his original work, Dirac took the phases of the different EM modes (Fourier components of the field) and the mode energies as dynamic variables to quantize (i.e., he reinterpreted them as operators and postulated commutation relations between them). At present it is more common to quantize the Fourier components of the vector potential. This is what will be done below.

A quantum mechanical photon state ${\displaystyle |\mathbf {k} ,\mu \rangle }$ belonging to mode ${\displaystyle (\mathbf {k} ,\mu )}$ will be introduced. It will be shown that it has the following properties

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