Quantization of the Maxwell field

4-potential of the photon field satisfies the wave equation (30), 

The 4-potential can be expanded in terms of harmonic components in the form 

This solution, due to Gupta and Bleuler [48, [ 3-2], eliminates the problem in a covariant manner. The effect is that only photons with polarization transverse to k contribute to the number of photons 

The causal photon propagator in Coulomb gauge can be defined, in a similar manner to (62), by 

The 00-component simplifies to give the instantaneous Coulomb interaction between charges 

---