# nLab second quantization

Contents

### Context

#### Quantum field theory

functorial quantum field theory

# Contents

## Idea

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 theoryof fundamental branesand their second quantizationwhich in perturbation theory is given by
worldline formalismparticlequantum field theoryscattering amplitudes
2d CFT correlatorsstringstring field theorystring scattering amplitudes

## Properties

### Syntax in linear type theory

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 exponential modality. See there for more.

## References

Last revised on May 7, 2021 at 06:07:32. See the history of this page for a list of all contributions to it.