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The BF model or BF theory is a topological field, which when quantized, becomes a topological quantum field theory. BF stands for background field B and F, as can be seen below, are also the variables appearing in the Lagrangian of the theory, which is helpful as a mnemonic device. We have a 4-dimensional differentiable manifold M, a gauge group G, which has as "dynamical" fields a 2-form B taking values in the adjoint representation of G, and a connection form A for G. The action is given by This action is diffeomorphically invariant and gauge invariant. Its Euler–Lagrange equations are and

Attributes	Values
rdfs:label	BF model (en) BF 모형 (ko) BFモデル (ja)
rdfs:comment	이론물리학에서 BF 모형(BF模型, 영어: BF model)은 시바르츠형 위상 양자장론의 간단한 예이다. 게이지 이론의 매우 간단한 형태이다. (ko) BFモデル(BF model)は、位相的場の理論であり、量子化したとき、位相的量子場の理論となる。BFモデルは背景場(background field)を基礎としている。B と F は、以下でみるように、理論のラグランジアンに現れる変数でもあり、記号的な使い方も有用である。 M は 4-次元微分可能多様体、G はゲージ群であり「力学的」場である 2-形式 B として G のリー群の随伴表現に値を持ち、A は G の接続形式である。作用は、により与えられる。ここに K は上の不変非退化双線型形式（G が半単純であればキリング形式はこれを満たす）であり、Fは曲率形式である。この作用は、微分同相不変であり、ゲージ不変である。作用のオイラー＝ラグランジュ方程式は、 (曲率が 0 ) と (B の(covariant exterior derivative)が 0 ) である。実際、任意の局所自由度をゲージ化することは常に可能であり、このことが位相的場の理論と呼ばれる理由である。しかしながら、M が位相的に非自明であれば、A と B が大域的に非自明な解を持つことも可能である。 (ja) The BF model or BF theory is a topological field, which when quantized, becomes a topological quantum field theory. BF stands for background field B and F, as can be seen below, are also the variables appearing in the Lagrangian of the theory, which is helpful as a mnemonic device. We have a 4-dimensional differentiable manifold M, a gauge group G, which has as "dynamical" fields a 2-form B taking values in the adjoint representation of G, and a connection form A for G. The action is given by This action is diffeomorphically invariant and gauge invariant. Its Euler–Lagrange equations are and (en)
dcterms:subject	Quantum field theory
Wikipage page ID	1428123 (xsd:integer)
Wikipage revision ID	1114264642 (xsd:integer)
Link from a Wikipage to another Wikipage	Nondegenerate Bilinear form Robbert Dijkgraaf Curvature form Quantum field theory Connection form Edward Witten Lagrangian (field theory) Gauge invariance Dual graviton Linking number Action (physics) Euler–Lagrange equation Barrett–Crane model Diffeomorphism Quantization (physics) Adjoint representation of a Lie group Background field method Killing form Spin foam Differentiable manifold Field (physics) Semisimple Lie algebra Plebanski action Topological quantum field theory Tetradic Palatini action 2-form Covariant exterior derivative Gauge group
Link from a Wikipage to an external page	http://math.ucr.edu/home/baez/qg-fall2000/qg2.2.html
sameAs	BF model BF model BF model BF model BF model
dbp:wikiPageUsesTemplate	dbt:Quantum_field_theories dbt:Quantum-stub dbt:Reflist
has abstract	The BF model or BF theory is a topological field, which when quantized, becomes a topological quantum field theory. BF stands for background field B and F, as can be seen below, are also the variables appearing in the Lagrangian of the theory, which is helpful as a mnemonic device. We have a 4-dimensional differentiable manifold M, a gauge group G, which has as "dynamical" fields a 2-form B taking values in the adjoint representation of G, and a connection form A for G. The action is given by where K is an invariant nondegenerate bilinear form over (if G is semisimple, the Killing form will do) and F is the curvature form This action is diffeomorphically invariant and gauge invariant. Its Euler–Lagrange equations are (no curvature) and (the covariant exterior derivative of B is zero). In fact, it is always possible to gauge away any local degrees of freedom, which is why it is called a topological field theory. However, if M is topologically nontrivial, A and B can have nontrivial solutions globally. In fact, BF theory can be used to formulate discrete gauge theory. One can add additional twist terms allowed by group cohomology theory such as Dijkgraaf–Witten topological gauge theory. There are many kinds of modified BF theories as topological field theories, which give rise to link invariants in 3 dimensions, 4 dimensions, and other general dimensions. (en) 이론물리학에서 BF 모형(BF模型, 영어: BF model)은 시바르츠형 위상 양자장론의 간단한 예이다. 게이지 이론의 매우 간단한 형태이다. (ko) BFモデル(BF model)は、位相的場の理論であり、量子化したとき、位相的量子場の理論となる。BFモデルは背景場(background field)を基礎としている。B と F は、以下でみるように、理論のラグランジアンに現れる変数でもあり、記号的な使い方も有用である。 M は 4-次元微分可能多様体、G はゲージ群であり「力学的」場である 2-形式 B として G のリー群の随伴表現に値を持ち、A は G の接続形式である。作用は、により与えられる。ここに K は上の不変非退化双線型形式（G が半単純であればキリング形式はこれを満たす）であり、Fは曲率形式である。この作用は、微分同相不変であり、ゲージ不変である。作用のオイラー＝ラグランジュ方程式は、 (曲率が 0 ) と (B の(covariant exterior derivative)が 0 ) である。実際、任意の局所自由度をゲージ化することは常に可能であり、このことが位相的場の理論と呼ばれる理由である。しかしながら、M が位相的に非自明であれば、A と B が大域的に非自明な解を持つことも可能である。 (ja)
prov:wasDerivedFrom	wikipedia-en:BF_model?oldid=1114264642&ns=0
page length (characters) of wiki page	3114 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:BF_model
is Link from a Wikipage to another Wikipage of	Index of physics articles (B) Lagrangian (field theory) Bf model Dual graviton Barrett–Crane model Self-dual Palatini action Plebanski action Topological quantum field theory BF theory
is Wikipage redirect of	Bf model BF theory
is foaf:primaryTopic of	wikipedia-en:BF_model

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