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Canonical static concept record

Bosonic Fock space

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Summary

Fock space formed from symmetric tensor powers, appropriate to bosonic exchange symmetry.

Record metadata

Canonical name: Bosonic Fock space
Concept ID: symmetric_fock_space
Content version: 2.3.0
Primary field: Mathematics
Fields: Mathematics
Primary domain: Analysis
Domains: Analysis, Representation theory
Alternate terminology: No alternate terminology is currently authored for this record.
Concept type: Symmetric Fock space

Carrier(s)

one-particle Hilbert space $H$

Data

Hilbert direct sum of symmetric tensor powers $\bigoplus_{n\ge0}\mathrm{Sym}^nH$

Axioms / constraints

bosonic permutation symmetry

Canonically induces

bosonic occupation-number basis

Concept sources

Wikipedia — Fock space — Fock space · encyclopedic reference · source ID wp-fock_space
nLab — Fock space — Fock space · mathematical reference · source ID nlab-fock_space

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Fock space Bosonic Fock space

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: math_fock_space_to_symmetric_fock_space
Relation type: Impose axiom impose-axiom
Direction: source → target
Endpoint roles: source: Builds toward; target: Built from
Authored annotation: symmetric sectors

Authored explanation

Bosonic Fock space retains symmetric tensor powers.

How to interpret this relation type

Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.

Relation sources

Wikipedia — Fock space — Fock space · encyclopedic reference · source ID wp-fock_space
nLab — Fock space — Fock space · mathematical reference · source ID nlab-fock_space

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.