Atiyah–Segal axioms

E508539

axiomatic framework definition of topological quantum field theory set of mathematical axioms

The Atiyah–Segal axioms are a set of mathematical conditions that rigorously define topological quantum field theories as functorial assignments from geometric data to algebraic structures.

Try in SPARQL Jump to: Surface forms Statements Referenced by

Observed surface forms (2)

Surface form	Occurrences
Atiyah–Segal axioms for TQFT	1
Segal’s axioms for conformal field theory	1

Statements (47)

Predicate	Object
instanceOf	axiomatic framework ⓘ definition of topological quantum field theory ⓘ set of mathematical axioms ⓘ
appliesTo	closed manifolds as inputs of the theory ⓘ d-dimensional manifolds ⓘ
assigns	linear map to each d-dimensional cobordism ⓘ vector space to each closed (d−1)-manifold ⓘ
assumes	finite-dimensional state spaces in the basic formulation ⓘ
characterizes	topological quantum field theory as a symmetric monoidal functor ⓘ
clarifies	relationship between geometry of manifolds and algebra of state spaces ⓘ
codomainOfFunctor	category of Hilbert spaces ⓘ category of vector spaces ⓘ
defines	topological quantum field theory ⓘ
developedBy	Graeme Segal NERFINISHED ⓘ Michael Atiyah NERFINISHED ⓘ
domainOfFunctor	category of d-dimensional cobordisms ⓘ
ensures	invariance under diffeomorphisms ⓘ topological invariance of correlation functions ⓘ
field	category theory ⓘ mathematical physics ⓘ quantum field theory ⓘ topology ⓘ
formalizes	idea of quantum field theory as a functor from spacetime to state spaces ⓘ
generalizedBy	Baez–Dolan cobordism hypothesis NERFINISHED ⓘ
implies	duality for orientation reversal ⓘ functoriality with respect to composition of cobordisms ⓘ monoidality with respect to disjoint union ⓘ unit object corresponding to the empty manifold ⓘ
influenced	development of topological invariants from quantum field theory ⓘ mathematical study of quantum field theories ⓘ
inspired	higher-categorical formulations of quantum field theory ⓘ
introducedBy	Michael Atiyah NERFINISHED ⓘ
motivatedBy	path integral formulation of quantum field theory ⓘ
namedAfter	Graeme Segal NERFINISHED ⓘ Michael Atiyah NERFINISHED ⓘ
relatedTo	extended topological quantum field theory ⓘ functorial quantum field theory ⓘ
requires	compatibility with composition of cobordisms ⓘ compatibility with tensor product structure ⓘ
usedIn	construction of 2-dimensional TQFTs from Frobenius algebras ⓘ construction of 3-dimensional TQFTs from Chern–Simons theory ⓘ
usesConcept	cobordism ⓘ disjoint union ⓘ functor ⓘ gluing of manifolds ⓘ oriented manifold ⓘ symmetric monoidal category ⓘ

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

topological quantum field theory → formalizedBy → Atiyah–Segal axioms ⓘ

Chern–Simons theory → relatedTo → Atiyah–Segal axioms ⓘ

this entity surface form: Atiyah–Segal axioms for TQFT

Graeme Segal → notableFor → Atiyah–Segal axioms ⓘ

this entity surface form: Segal’s axioms for conformal field theory