Chern Simons Theory: Intro Guide & Witten's QFT Paper

  • A
  • Thread starter shereen1
  • Start date
  • Tags
    Theory
In summary, Chern-Simons theory is a mathematical framework used in theoretical physics to describe the behavior of certain physical systems. It was first introduced by physicists Shiing-Shen Chern and James Simons in the 1970s. Witten's QFT paper, published in 1989, established a groundbreaking connection between Chern-Simons theory and knot theory, solidifying its importance in studying topological quantum field theories. The theory is a type of topological quantum field theory, meaning it describes the topological properties of a system without relying on its geometry. It involves mathematical concepts such as differential geometry, topology, and algebraic geometry, and relies heavily on the use of gauge fields. Chern-Simons theory has various applications in
  • #1
shereen1
51
1
Dear all
I am studying Chern simons Theory. If you please can anyone suggest me a book as introduction to Chern Simons theory ( also Chern Simon theory of garuge theories). In fact i will start by a paper of Witten (Quantum Field Theory and the Jones Polynomial)
 
Physics news on Phys.org
  • #2
Google for it!
 
  • #3
A discussion of a bunch of basic facts as well as a commented collection of pointers to reviews and other literature is provided at nLab:Chern-Simons theory.
 

Related to Chern Simons Theory: Intro Guide & Witten's QFT Paper

1. What is Chern-Simons theory?

Chern-Simons theory is a mathematical framework used in theoretical physics to describe the behavior of certain physical systems, such as topological quantum field theories and quantum Hall systems. It was first introduced by physicists Shiing-Shen Chern and James Simons in the 1970s.

2. What is the significance of Witten's QFT paper on Chern-Simons theory?

Witten's QFT paper, titled "Quantum Field Theory and the Jones Polynomial," was published in 1989 and provided a groundbreaking connection between Chern-Simons theory and knot theory. This paper helped establish Chern-Simons theory as a powerful tool for studying topological quantum field theories and its applications in other areas of physics and mathematics.

3. How does Chern-Simons theory relate to topological quantum field theories?

Chern-Simons theory is a type of topological quantum field theory, meaning that it describes the topological properties of a physical system without depending on the specific details of its geometry. In other words, Chern-Simons theory is a topological theory that is independent of the metric or curvature of the space it is defined on.

4. What are the main mathematical concepts involved in Chern-Simons theory?

Chern-Simons theory involves several mathematical concepts, including differential geometry, topology, and algebraic geometry. The theory also heavily relies on the use of gauge fields, which are mathematical objects used to describe the interactions between particles in certain physical systems.

5. What are some applications of Chern-Simons theory?

Chern-Simons theory has found many applications in theoretical physics, including in the study of quantum Hall systems, topological insulators, and string theory. It has also been used in mathematics to study knot theory and topological invariants. Additionally, Chern-Simons theory has been applied to condensed matter physics, cosmology, and other areas of physics.

Similar threads

A Chern Simons Theory: Is it the same as Topologically Massive Yang Mills?
    • Beyond the Standard Models
Replies
1
Views
1K
A First Order in Time Derivatives + Phase Space
    • Quantum Physics
Replies
1
Views
736
Can Lattice Formulations Accommodate Modern Quantum Field Theories?
    • Beyond the Standard Models
Replies
4
Views
2K
A Hodge decomposition of a 1-form on a torus
    • Differential Geometry
Replies
2
Views
1K
I Witten’s paper: "A Note On The Canonical Formalism for Gravity" LQG
    • Beyond the Standard Models
Replies
13
Views
2K
A The double copy of (2,0) theory
    • Beyond the Standard Models
Replies
1
Views
2K
A Eric WEinstein's Geometric Unity theory
    • Beyond the Standard Models
Replies
12
Views
6K
A Phases Of Adjoint QCD_3 And Dualities
    • High Energy, Nuclear, Particle Physics
Replies
1
Views
1K
Books about Kähler manifolds, Ricci flatness and other things
    • Science and Math Textbooks
Replies
2
Views
1K
Does Ads/CFT correspondence apply to LQG Kodama state?
    • Beyond the Standard Models
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top