BF model

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

The action is given by

${\displaystyle S=\int _{M}K[\mathbf {B} \wedge \mathbf {F} ]}$

where K is an invariant

over ${\displaystyle {\mathfrak {g}}}$ (if G is

${\displaystyle \mathbf {F} \equiv d\mathbf {A} +\mathbf {A} \wedge \mathbf {A} }$

This action is

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.^[1] 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.^[2]

See also

• Background field method
• Barrett–Crane model
• Dual graviton
• Plebanski action
• Spin foam
• Tetradic Palatini action

References

External links

• http://math.ucr.edu/home/baez/qg-fall2000/qg2.2.html

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