The question of a canonical quantization of the electromagnetic field as a system with two primary constraints is analyzed. Attention is focused on the following aspects of the problem: 1) the conditions on physical states; 2) the ``old'' and ``new'' Gupta formalisms; 3) the interpretation of the operators $\hat\alpha_0$, $\hat\alpha_0^+$; 4) the vacuum in quantum electrodynamics. The starting point for the analysis is Dirac's quantization recipe for systems with constraints. It is shown that the Fermi formalism with a condition on the physical states is completely correct.

@article{Prokhorov:1988,
	author = {L. V. Prokhorov},
	title = {Quantization of the electromagnetic field},
	publisher = {Physics-Uspekhi},
	year = {1988},
	journal = {Phys. Usp.},
	volume = {31},
	number = {2},
	pages = {151-162},
	url = {https://ufn.ru/en/articles/1988/2/d/},
	doi = {10.1070/PU1988v031n02ABEH005699}
}