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Background

So according to Greiner's Book - Relativistic Quantum Mechanics one can perfectly proceed without second quantization of the Dirac Equation. The gist of which is captured in Chapter $12$:

Let us stress the point that the hole theory is a many-body theory, describing particles with positive and negative charge. Indeed, infinitely many electrons are needed to constitute the Dirac sea. The simple probability interpretation of the wave functions acclaimed in a single-particle theory cannot be true any longer, because the creation and annihilation of electron—positron pairs must be taken into account in the wave functions.

I've also seen examples of first quantized gravity as well (I'm suggesting one goes into a non-inertial frame as shown in the example)

Question

This begs the question: does a version of Hawking's information paradox without second quantization exist? (A counter proof why it can't exist will suffice as well)

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    Note that one can consider interacting many-body systems without resorting to second quantization. It may be not common in QFT, but rather commonplace in solid state physics. – Roger V. Jul 25 '21 at 08:42

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