Topological quantum field theories

In summary, Chern-Simons theory is a 3d-TQFT that is gauge invariant and independent of the background metric. It relates to knot theory and the Turaev-Viro model is another TQFT.
  • #1
meteor
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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?
 
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  • #2
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?

Meteor you would be doing me a favor if you could explain a little about Chern-Simons theory and perhaps give some web links---all at very introductory level if possible.
 
  • #3
Sorry, I'm not an expert on it, so what I'm going to say is probably known to you:
Chern-Simons theory (a.k.a. Chern-Simons gauge theory) is a gauge theory. It's gauge invariant and Lorentz invariant
One of the most important features of Chern-Simons theory is that is independent of the background metric that you choose for the spacetime
In Chern-Simons theory, the field is a connection
Ed Witten discovered in 1989 that exists some relationship between knot theory and Chern-Simons theory
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
 
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  • #4

What is a topological quantum field theory (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.

What is the significance of topological quantum field theories?

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.

How are topological quantum field theories different from other quantum field theories?

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.

What are some examples of topological quantum field theories?

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.

What are the potential applications of topological quantum field theories?

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.

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