What is the quantum Hamiltonian in term of photon annihilation and creation operators in the Landau gauge?

For covariant canonical quantisation of the free electromagnetic
field, the gauge fixing term is usually chosen (for e.g. the Feynman
Gauge) so that one can live without the Nakanishi-Lautrup auxiliary
field. And the quantum Hamiltonian can be written in term of photon
annihilation and creation operators.

In the Landau gauge, however, the Nakanishi-Lautrup auxiliary field is
indispensable. Should one choose the Nakanishi-Lautrup auxiliary
field, instead of the time-component of gauge filed, as the canonical
variable? What is the quantum Hamiltonian in term of photon
annihilation and creation operators? Is there any textbook about
canonical (not path integral) quantisation in the Landau gauge?

-Max

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