Fock model
E860125
The Fock model is a realization of certain group representations on a Fock space of quantum states, widely used in mathematical physics and representation theory to study structures like the Weil representation.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical construction
ⓘ
realization of group representation ⓘ representation-theoretic model ⓘ |
| appliesTo |
group representations
ⓘ
oscillator representations ⓘ unitary representations ⓘ |
| associatedWith |
Heisenberg group
NERFINISHED
ⓘ
metaplectic group NERFINISHED ⓘ oscillator representation ⓘ symplectic group NERFINISHED ⓘ |
| basedOn | quantum states ⓘ |
| constructionMethod |
canonical commutation relations
ⓘ
creation and annihilation operators ⓘ holomorphic realization ⓘ |
| contrastedWith | Schrödinger model NERFINISHED ⓘ |
| dependsOn |
complex structure on phase space
ⓘ
symplectic vector space ⓘ |
| field |
mathematical physics
ⓘ
representation theory ⓘ |
| formalism |
Hilbert space formalism
ⓘ
operator formalism ⓘ |
| generalizationOf | Schrödinger model of the Weil representation NERFINISHED ⓘ |
| hasProperty |
graded by particle number
ⓘ
lowest weight representation structure ⓘ unitary action of groups ⓘ |
| mathematicalArea |
functional analysis
ⓘ
operator algebras ⓘ |
| realizedOn |
Hilbert space
ⓘ
bosonic Fock space ⓘ space of holomorphic functions ⓘ space of square-integrable holomorphic functions ⓘ |
| relatedConcept |
Bargmann–Fock space
NERFINISHED
ⓘ
Segal–Bargmann space NERFINISHED ⓘ coherent states ⓘ holomorphic discrete series ⓘ |
| relatedTo | Weil representation NERFINISHED ⓘ |
| underlies | second quantization formalism ⓘ |
| usedFor |
constructing explicit models of representations
ⓘ
geometric representation theory ⓘ harmonic analysis on groups ⓘ quantization ⓘ realizing Weil representation ⓘ studying Weil representation ⓘ |
| usedIn |
quantum field theory
NERFINISHED
ⓘ
quantum harmonic oscillator NERFINISHED ⓘ theory of automorphic forms ⓘ theta correspondence NERFINISHED ⓘ |
| uses | Fock space ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.