Aspects of q-discretized Nahm equations |
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Authors: | Masaru Kamata Atsushi Nakamula |
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Affiliation: | 1. Natural Science Education, Kisarazu National College of Technology, Kisarazu, Chiba 292-0041, Japan;2. Department of Physics, School of Science, Kitasato University, Sagamihara, Kanagawa 228-8555, Japan |
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Abstract: | There is a conjecture by Ward that almost all of integrable equations are derived from (anti-)self-dual (ASD) Yang–Mills equations. This conjecture is supported by many concrete examples, e.g., the Nahm equations. In this work, we consider a situation that if the ASD conditions are slightly loosened, as to how it affects the integrability of the equations. For this purpose, we consider a q-analog of the Nahm equations, as a non-ASD system. The analysis is performed on the reduced system which is a q-analog of the Euler–Arnold top, by the singularity confinement test and the estimation of the algebraic entropy. |
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Keywords: | Discrete map Singularity confinement Algebraic entropy |
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