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The process of quantization is supposed to assign to a classical field theory (prequantum field theory) a corresponding quantum field theory. One tends to imagine that in some cases the resulting QFT can itself be regarded as a classical field theory, roughly, and the process of quantization be applied again. One then speaks of second quantization .
In its simplest form the free second quantization (in the sense of free field theory, introducing no interaction between the second quantized quanta) is identified with the Fock space construction on a given space of quantum states.
For interacting second quantization see sigma-model -- exposition of second quantization of sigma-models.
worldvolume field theory | of fundamental branes | and their second quantization | which in perturbation theory is given by |
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worldline formalism | particle | quantum field theory | scattering amplitudes |
2d CFT correlators | string | string field theory | string scattering amplitudes |
In linear type theory, which may be regarded as quantum logic (by the discussion there), the Fock space construction may naturally be identified with the !-modality. See there for more.