BF model

The BF model is a topological field theory, which when quantization (physics), becomes a topological quantum field theory. We have a 4-dimensional differentiable manifold M, a gauge group G, which has as "dynamical" fields a two-form B taking values in the adjoint representation of G, and a connection form A for G. The action (physics) :

S=\int_M K[\mathbf{B}\wedge \mathbf{F}]

where K is an invariant nondegenerate bilinear form over

\mathfrak{g}

(if G is semisimple, the Killing form will do) and F is the curvature form :

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

This action is diffeomorphism invariant and gauge invariance. Its Euler-Lagrange equations are :

d \mathbf{F}=0

(no curvature) and :

d_\mathbf{A}B=0

(the covariant exterior derivative of B is zero) Actually, we can always gauge away any local degrees of freedom, which means this model has no local degrees of freedom. That's why it's called a topological field theory. However, if M is topologically nontrivial, A and B can have nontrivial solutions globally. Quantum field theory

See other meanings of words starting from letter:

B

BA | BC | BD | BE | BF | BG | BH | BI | BJ | BK | BL | BM | BN | BO | BP | BR | BS | BT | BU | BW | BX | BY | BZ |

Words begining with BF_model:

BF_model