BF theory
E508541
BF theory is a topological quantum field theory defined in terms of a gauge connection and an auxiliary field, notable for its role in describing topological aspects of gauge theories and gravity.
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
gauge theory
ⓘ
topological quantum field theory ⓘ |
| appearsIn | Plebanski action for general relativity as constrained BF theory NERFINISHED ⓘ |
| appliesTo | topological aspects of gravity ⓘ |
| canBeDiscretizedAs | lattice BF theory ⓘ |
| canBeFormulatedIn | any spacetime dimension ⓘ |
| definedOn | principal G-bundle ⓘ |
| dependsOnMetric | false ⓘ |
| describes | topological aspects of gauge theories ⓘ |
| fieldContent |
auxiliary field B
ⓘ
gauge connection ⓘ |
| generalizes | Schwarz-type topological field theories NERFINISHED ⓘ |
| hasAction | ∫ Tr(B ∧ F) ⓘ |
| hasCoupling | B field coupled linearly to curvature F ⓘ |
| hasEquationOfMotion |
DB = 0 (covariant constancy of B)
ⓘ
F = 0 (flat connection condition) ⓘ |
| hasGaugeGroup | Lie group G ⓘ |
| hasProperty |
background independent
ⓘ
finite number of degrees of freedom on compact manifolds ⓘ gauge invariant ⓘ |
| hasSymmetry |
local gauge symmetry
ⓘ
topological shift symmetry of B field ⓘ |
| hasVariant |
3-dimensional BF theory
ⓘ
4-dimensional BF theory NERFINISHED ⓘ BF theory with cosmological term ⓘ constrained BF theory ⓘ |
| influenced | spin foam models for loop quantum gravity ⓘ |
| isTopological | true ⓘ |
| mathematicallyRelatedTo |
category theory and higher gauge theory
ⓘ
cohomology of the underlying manifold ⓘ topological invariants of manifolds ⓘ |
| quantizationMethod |
canonical quantization
ⓘ
path integral quantization ⓘ |
| relatedTo |
Chern–Simons theory
NERFINISHED
ⓘ
Plebanski formulation of general relativity NERFINISHED ⓘ lattice gauge theory ⓘ spin foam models of quantum gravity ⓘ |
| studiedIn |
high energy theoretical physics
ⓘ
mathematical physics ⓘ quantum topology ⓘ |
| usedIn |
knot invariants and link invariants
ⓘ
quantum gravity research ⓘ topological phases of matter ⓘ |
| usedToConstruct |
state sum models
ⓘ
topological invariants via partition functions ⓘ |
| usesCurvature | field strength F of the gauge connection ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.