nLab
Fock space

Context

Linear algebra

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Algebraic Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory: classical, pre-quantum, quantum, perturbative quantum

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

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.

References

Named after Vladimir Aleksandrovich Fock.

General

A textbook account with an eye towards perturbative algebraic quantum field theory is in

See also

In linear type theory

The Fock space construction may be axiomatized as the !-modality in linear type theory. This is discussed in the following articles.

Last revised on December 23, 2017 at 12:38:29. See the history of this page for a list of all contributions to it.