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On the complete integrability of the discrete Nahm equations | | Michael K. Murray
; Michael A. Singer
; | | Date: |
9 Mar 1999 | | Journal: | Commun.Math.Phys. 210 (2000) 497-519 | | Subject: | Mathematical Physics; Differential Geometry MSC-class: 39A12 (Primary), 58F07 (Secondary) | math-ph hep-th math.DG math.MP | | Abstract: | The discrete Nahm equations, a system of matrix valued difference equations, arose in the work of Braam and Austin on half-integral mass hyperbolic monopoles. We show that the discrete Nahm equations are completely integrable in a natural sense: to any solution we can associate a spectral curve and a holomorphic line-bundle over the spectral curve, such that the discrete-time DN evolution corresponds to walking in the Jacobian of the spectral curve in a straight line through the line-bundle with steps of a fixed size. Some of the implications for hyperbolic monopoles are also discussed. | | Source: | arXiv, math-ph/9903017 | | Services: | Forum | Review | PDF | Favorites | |
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