Gauging Quantum Groups: Yang–Baxter Joining Yang–Mills

2016 ◽  
Author(s):  
Yong-Shi Wu
Keyword(s):  
Quantum Groups ◽  
Yang Mills

scholarly journals Uq(N) GAUGE THEORIES

1994 ◽  
Vol 09 (30) ◽  
pp. 2835-2847 ◽  
Author(s):  
LEONARDO CASTELLANI
Keyword(s):  
Quantum Groups ◽  
Differential Calculus ◽  
Gauge Theories ◽  
Space Time ◽  
Yang Mills ◽  
Commutation Relations ◽  
Transformation Rules ◽  
Field Strengths

Improving on an earlier proposal, we construct the gauge theories of the quantum groups U q(N). We find that these theories are also consistent with an ordinary (commuting) space-time. The bicovariance conditions of the quantum differential calculus are essential in our construction. The gauge potentials and the field strengths are q-commuting "fields," and satisfy q-commutation relations with the gauge parameters. The transformation rules of the potentials generalize the ordinary infinitesimal gauge variations. For particular deformations of U (N) ("minimal deformations"), the algebra of quantum gauge variations is shown to close, provided the gauge parameters satisfy appropriate q-commutations. The q-Lagrangian invariant under the U q(N) variations has the Yang–Mills form [Formula: see text], the "quantum metric" gij being a generalization of the Killing metric.

q-trace for quantum groups and q-deformed Yang-Mills theory

1992 ◽  
Vol 281 (3-4) ◽  
pp. 271-278 ◽  
Author(s):  
A.P. Isaev ◽  
Z. Popowicz
Keyword(s):  
Quantum Groups ◽  
Yang Mills

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.

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