# nLab Fock space

### Context

#### Linear algebra

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Introductions

Definitions

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Paths and cylinders

Homotopy groups

Basic facts

Theorems

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# Contents

## Idea

In physics the symmetric tensor algebra on a space of quantum states of some quantum mechanical system is called its bosonic Fock space. This is regarded in turn as the space of quantum states of arbitrarily many copies of the system. In particular if the original system describes some bosonic particle species, then its Fock space is the space of quantum states of arbitrarily many such particles.

Similarly the exterior algebra/Grassmann algebra is called the fermionic Fock space.

The process of passing from a given space of quantum states to its Fock space is also known as (or rather: is part of) what is called second quantization.

Fock spaces hence appear as spaces of quantum states of free fields in quantum field theory. In perturbative quantum field theory they are still used indirectly in for non-free field theories.