Variant of ADHMN construction associated with \(q\)-analysis. (English) Zbl 1121.81098
Summary: A \(q\)-deformation of the ADHMN caloron construction is considered, under which the anti-self-dual (ASD) conditions of the gauge fields are preserved. It is shown that the \(q\)-dependent Nahm data with certain constraints are crucial to determine the ASD gauge fields, as in the case of ordinary caloron construction. As an application of the \(q\)-deformed ADHMN construction, we give a \(q\)-deformed caloron of Harrington-Shepard type. Some limits of the parameters are also considered.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 33D90 | Applications of basic hypergeometric functions |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
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