Topological quantum field theories are powerful tools which probe the geometry and topology in three and four dimensions. Chern-Simons theory is one such theory which provides a natural framework for the study of knots and links in three dimensions. We will discuss the perturbative and non-perturbative aspects of computing the expectation value of Wilson loop operators corresponding to the knots and links. In particular, we will present the field-theoretic interpretation of the invariants of knots, links and three-manifolds in the mathematics literature.

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Chern-Simons Field Theory Invariants

  • P. Ramadevi

摘要

Topological quantum field theories are powerful tools which probe the geometry and topology in three and four dimensions. Chern-Simons theory is one such theory which provides a natural framework for the study of knots and links in three dimensions. We will discuss the perturbative and non-perturbative aspects of computing the expectation value of Wilson loop operators corresponding to the knots and links. In particular, we will present the field-theoretic interpretation of the invariants of knots, links and three-manifolds in the mathematics literature.