Chern–Simons forms

E856766

differential form mathematical object secondary characteristic class

Chern–Simons forms are secondary characteristic classes in differential geometry that arise from connections on principal bundles and play a central role in topological quantum field theories.

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Observed surface forms (1)

Surface form	Occurrences
Chern–Simons form	0

Statements (48)

Predicate	Object
instanceOf	differential form ⓘ mathematical object ⓘ secondary characteristic class ⓘ
appearsAs	Lagrangian density in Chern–Simons gauge theory ⓘ
application	quantum Hall effect models ⓘ topological phases of matter ⓘ
arisesFrom	transgression in characteristic class theory ⓘ
associatedWith	Lie algebra of the structure group ⓘ curvature form ⓘ
constructedFrom	connection 1-form ⓘ curvature 2-form ⓘ invariant polynomial on a Lie algebra ⓘ
context	Cheeger–Simons differential characters NERFINISHED ⓘ differential cohomology ⓘ secondary characteristic class theory ⓘ
definedOn	principal bundle ⓘ
degreeExample	(2n−1)-form ⓘ 3-form ⓘ 5-form ⓘ
dependsOn	connection on a principal bundle ⓘ
dimension	odd degree ⓘ
example	3-dimensional Chern–Simons action functional ⓘ
field	algebraic topology ⓘ differential geometry ⓘ mathematical physics ⓘ topological quantum field theory ⓘ
invariantUnder	bundle isomorphism up to exact forms ⓘ
isSecondaryTo	primary characteristic class ⓘ
namedAfter	James Harris Simons NERFINISHED ⓘ Shiing-Shen Chern NERFINISHED ⓘ
property	gauge invariant modulo exact forms ⓘ its exterior derivative is a characteristic form ⓘ locally defined from a connection ⓘ not gauge invariant as a form ⓘ
relatedConcept	Abelian Chern–Simons theory NERFINISHED ⓘ eta invariant ⓘ gravitational Chern–Simons term ⓘ non-Abelian Chern–Simons theory NERFINISHED ⓘ
relatedTo	Chern class NERFINISHED ⓘ Pontryagin class NERFINISHED ⓘ
satisfies	d(CS) = characteristic class representative ⓘ
usedIn	3-manifold invariants ⓘ Chern–Simons theory NERFINISHED ⓘ anomaly cancellation in quantum field theory ⓘ gauge theory ⓘ index theory ⓘ knot invariants ⓘ topological quantum field theory NERFINISHED ⓘ

Referenced by (2)

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

Chern–Simons theory → hasMathematicalOriginIn → Chern–Simons forms ⓘ

Chern character → relatesTo → Chern–Simons forms ⓘ