scholarly journals The KZ equation and the quantum‐group difference equation in quantum self‐dual Yang–Mills theory

1996 ◽  
Vol 37 (8) ◽  
pp. 3704-3712
Author(s):  
Ling‐Lie Chau ◽  
Itaru Yamanaka
Keyword(s):  
Difference Equation ◽  
Quantum Group ◽  
Yang Mills ◽  
Kz Equation

Uq(2) YANG–MILLS THEORY

1998 ◽  
Vol 13 (04) ◽  
pp. 553-568 ◽  
Author(s):  
H. B. BENAOUM ◽  
M. LAGRAA
Keyword(s):  
Quantum Group ◽  
Gauge Fields ◽  
Yang Mills ◽  
Adequate Definition ◽  
Weinberg Angle ◽  
Definition Of

A Yang–Mills theory is presented using the Uq(2) quantum group. Unlike previous works, no assumptions are required — between the quantum gauge parameters and the quantum gauge fields (or curvature) — to get the quantum gauge variations of the different fields. Furthermore, an adequate definition of the quantum trace is presented. Such a definition leads to a quantum metric, which therefore allows us to construct a Uq(2) quantum Yang–Mills Lagrangian. The Weinberg angle θ is found in terms of this q metric to be [Formula: see text].

Gauging quantum groups: Yang–Baxter joining Yang–Mills

2016 ◽  
Vol 30 (06) ◽  
pp. 1630003 ◽  
Author(s):  
Yong-Shi Wu
Keyword(s):  
Quantum Group ◽  
Exact Solutions ◽  
Quantum Groups ◽  
2D Systems ◽  
Joint Work ◽  
Yang Mills ◽  
Gauge Models

This review is an expansion of my talk at the conference on Sixty Years of Yang–Mills Theory. I review and explain the line of thoughts that lead to a recent joint work with Hu and Geer [Hu et al., arXiv:1502.03433] on the construction, exact solutions and ubiquitous properties of a class of quantum group gauge models on a honey-comb lattice. Conceptually the construction achieves a synthesis of the ideas of Yang–Baxter equations with those of Yang–Mills theory. Physically the models describe topological anyonic states in 2D systems.

scholarly journals ASPECTS OF THE q-DEFORMED FUZZY SPHERE

2001 ◽  
Vol 16 (04n06) ◽  
pp. 361-365 ◽  
Author(s):  
HAROLD STEINACKER
Keyword(s):  
Quantum Group ◽  
Differential Calculus ◽  
Gauge Theories ◽  
Short Review ◽  
Real Structure ◽  
Fuzzy Sphere ◽  
Yang Mills ◽  
Chern Simons

These notes are a short review of the q-deformed fuzzy sphere [Formula: see text], which is a "finite" noncommutative two-sphere covariant under the quantum group U q( su (2)). We discuss its real structure, differential calculus and integration for both real q and q a phase, and show how actions for Yang–Mills and Chern–Simons-like gauge theories arise naturally. It is related to D-branes on the SU (2)k WZW model for [Formula: see text].

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