topological quantum field theory
E119326
A topological quantum field theory is a quantum field theory whose observables and correlation functions depend only on the topology of the underlying spacetime manifold rather than its geometric details, making it a powerful tool in both mathematics and theoretical physics.
All labels observed (1)
| Label | Occurrences |
|---|---|
| topological quantum field theory canonical | 1 |
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical physics concept
ⓘ
quantum field theory ⓘ topological field theory ⓘ |
| appliesTo |
cobordisms between manifolds
ⓘ
oriented manifolds ⓘ |
| axiomatizedBy | Michael Atiyah ⓘ |
| codomain | category of vector spaces ⓘ |
| dependsOn | topology of spacetime manifold ⓘ |
| developedBy | Graeme Segal ⓘ |
| dimensionVariant |
2-dimensional topological quantum field theory
ⓘ
3-dimensional topological quantum field theory ⓘ 4-dimensional topological quantum field theory ⓘ |
| domain | category of d-dimensional cobordisms ⓘ |
| example |
BF theory
ⓘ
Chern–Simons theory ⓘ Donaldson–Witten theory ⓘ Rozansky–Witten theory ⓘ |
| feature |
finite-dimensional state spaces for closed manifolds
ⓘ
metric-independent correlation functions ⓘ topological invariance under diffeomorphisms ⓘ |
| field |
mathematics
ⓘ
theoretical physics ⓘ |
| formalizedBy | Atiyah–Segal axioms ⓘ |
| goal | classification of manifolds via quantum invariants ⓘ |
| independentOf |
local geometric details of spacetime
ⓘ
metric of spacetime manifold ⓘ |
| maps | cobordism category to category of vector spaces ⓘ |
| producesInvariant |
Donaldson invariants
ⓘ
Jones polynomial ⓘ Seiberg–Witten theory ⓘ
surface form:
Seiberg–Witten invariants
Witten–Reshetikhin–Turaev invariant ⓘ |
| relatedTo |
conformal field theory
ⓘ
fusion category ⓘ modular tensor category ⓘ quantum group ⓘ supersymmetric quantum field theory ⓘ topological string theory ⓘ |
| structure | symmetric monoidal functor ⓘ |
| studies | topological invariants ⓘ |
| usedIn |
3-manifold invariants
ⓘ
4-manifold invariants ⓘ category theory ⓘ condensed matter physics ⓘ knot theory ⓘ low-dimensional topology ⓘ representation theory ⓘ topological phases of matter ⓘ topological quantum computation ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.