This question is still relevant since the discovery and description of photons more than 100 years ago.
If we follow QM theory, the answer is definitely no because the photon must have a positive momentum and therefore a positive frequency.
On the other hand, if we follow the classical theory of electromagnetic fields, the answer is yes but the photon itself is not defined.
QM theory is supported by Schrödinger's invincible equation while the well-established theory of electromagnetic fields is supported by the fact that the Poyentig vector of power flow P = ExH works for stationary fields of zero frequency.
The question arises: which theory do we follow at zero frequency?
Prof. Ismail Abbas
In this case, let us refer to the book on QED, namely:
"Quantum Electrodynamics" by Profs. Berestetskii, Pitaevskii, and Lifshitz. Elsevier, 2012.
On page 10, chapter 3 on photons there is an answer to your question, I quote:
There is is an electromagnetic quantum vacuum state there is a nonzero zero point energy with frequency 1/2 ω.
1. They remove the zero point energy term, and this way avoid the divergence of the infinite sum of frequencies.
2. They call it "radiation quanta" and write a short interesting discussion in the relativistic case.
So I guess that in QED somehow your question is addressed.
Best Regards.
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