2000/07/12 by Sze Kui Ng, Ng, Sze Kui
Mathematics · Physics and Astronomy · #57M27(Primary) 51P05 #81T10 #81T40(secondary) #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #Quantum Mechanics and Applications #math.GT #math.QA #msc:51P05 #msc:81T10
paper · pdf · doi:10.48550/arxiv.math/0007071
17 pages, 7 figures
arxiv created 2000/07/12 · openalex publication_date 2000/07/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a gauge model of quantum electrodynamics (QED) and its nonabelian generalization from which we derive knot invariants such as the Jones polynomial. Our approach is inspired by the work of Witten who derived knot invariants from quantum field theory based on the Chern-Simon Lagrangian. From our approach we can derive new knot and link invariants which extend the Jones polynomial and give a complete classification of knots and links. From these new knot invariants we have that knots can be completely classified by the power index m of TrR-m where R denotes the R-matrix for braiding and is the monodromy of the Knizhnik-Zamolodchikov equation. A classification table of knots can then be formed where prime knots are classified by prime integer m and nonprime knots are classified by nonprime integer m.