Originally posted by meteor
Chern-Simons theory is a 3d-TQFT and Crane-Yetter model is a 4d-TQFT
There exist another Topological Quantum Field Theory apart of these two models?
Originally posted by meteor
These two papers seem introductory:
http://xxx.lanl.gov/abs/hep-th/9902115
http://xxx.lanl.gov/abs/hep-th/9905057
If this interest to someone, I've discovered that the Turaev-Viro model is another TQFT
A TQFT is a mathematical framework for describing quantum systems in a topological setting. It combines concepts from quantum mechanics and topology to study the behavior of quantum systems at a large scale.
TQFTs have important applications in condensed matter physics, where they can be used to describe topological phases of matter and study their properties. They also have connections to other fields such as mathematics and quantum computing.
TQFTs are distinct from other quantum field theories in that they do not depend on a specific spacetime or metric. They are also topological in nature, meaning that they are invariant under continuous deformations of the underlying space.
Some examples of TQFTs include Chern-Simons theory, which is used to describe the quantum Hall effect, and the Witten-Reshetikhin-Turaev model, which is used in the study of knot theory and 3-manifolds.
TQFTs have potential applications in areas such as quantum computing, topological quantum information theory, and the study of topological phases of matter. They also have connections to other areas of mathematics, such as algebraic geometry and representation theory.