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The Jordanian \(U_h(2)\) Yang-Mills theory. (English) Zbl 1022.81038
The purpose of the paper is to extend the Yang-Mills theory to the case of a Jordanian group. It is shown that the Woronowicz prescription using a bimodule constructed out of a tensorial product of a bimodule and its conjugate and a bi-invariant singlet leads to a trivial differential calculus. Still, a nontrivial calculus is shown to emerge when using Karimipour’s method, working under the assumption that the bicovariant bimodules are generated as left modules by the differentials of the Jordanian group generators, and constrained by the requirement that the bicovariance is preserved.
The \(h\)-trace is computed; this leads to the Jordanian quantum \(h\)-metric - essential for the construction of the \(U_h(2)\) Yang-Mills Lagrangian. As well, the Weinberg angle is determined in terms of the Jordanian \(h\)-metric.

MSC:
81T13 Yang-Mills and other gauge theories in quantum field theory
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
81R15 Operator algebra methods applied to problems in quantum theory
20G42 Quantum groups (quantized function algebras) and their representations
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