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| Chern-Simons theory is a topological ] in three dimensions which describes knot and ] invariants. | Chern-Simons theory is a ] ] in three dimensions which describes knot and ] invariants. | ||
| There is a correspondence to topological ], which is related to ] invariants. | There is a correspondence to topological ], which is related to ] invariants. | ||
| This theory is ] over boundary manifolds and manifolds with zero ] at their boundaries. However, this theory is gauge variant if there is no restriction on the curvature form at the boundary. This might be useful in ] mechanisms. | |||
| This terms is ] with respect to gauge invariant quantities. | |||
| The Chern-Simons term can also be added to models which aren't topological quantum field theories. In 3D, this gives rise to a massive ] if this term is added to the ]. This term can be induced by integrating over a massive charged ]. It also appears in the ]. | |||
| == See also == | == See also == | ||
Revision as of 19:17, 30 October 2005
Chern-Simons theory is a topological gauge theory in three dimensions which describes knot and three-manifold invariants.
There is a correspondence to topological string theory, which is related to Gromov-Witten invariants.
This theory is gauge-invariant over boundary manifolds and manifolds with zero curvature form at their boundaries. However, this theory is gauge variant if there is no restriction on the curvature form at the boundary. This might be useful in anomaly inflow mechanisms.
This terms is nonlocal with respect to gauge invariant quantities.
The Chern-Simons term can also be added to models which aren't topological quantum field theories. In 3D, this gives rise to a massive photon if this term is added to the Yang-Mills action. This term can be induced by integrating over a massive charged Dirac field. It also appears in the quantum Hall effect.
See also
References
Chern-simons Theory, Matrix Models, And Topological Strings (International Series of Monographs on Physics, Marcos Marino, OUP, 2005
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