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| Format: | Preprint |
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2011
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| Online Access: | https://arxiv.org/abs/1103.3966 |
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| _version_ | 1866929476689985536 |
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| author | Papachristou, C. J. |
| author_facet | Papachristou, C. J. |
| contents | A 3-dimensional reduction of the seld-dual Yang-Mills (SDYM) equation, named SDYM3, is examined from the point of view of its symmetry and integrability characteristics. By using a non-auto-Backlund transformation, this equation is connected to its potential form (PSDYM3) and a certain isomorphism between the Lie algebras of symmetries of the two systems is shown to exist. This isomorphism allows us to study the infinite-dimensional Lie algebraic structure of the "potential symmetries" of SDYM3 by examining the symmetry structure of PSDYM3 (which is an easier task). By using techniques described in a recent paper, the recursion operators for both SDYM3 and PSDYM3 are derived. Moreover, a Lax pair and an infinite set of nonlocal conservation laws for SDYM3 are found, reflecting the fact that SDYM3 is a totally integrable system. This system may physically represent gravitational fields or chiral fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1103_3966 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | Symmetry and Integrability of a Reduced, 3-Dimensional Self-Dual Gauge Field Model Papachristou, C. J. Mathematical Physics 37K10, 37K15, 37K30, 37K35 A 3-dimensional reduction of the seld-dual Yang-Mills (SDYM) equation, named SDYM3, is examined from the point of view of its symmetry and integrability characteristics. By using a non-auto-Backlund transformation, this equation is connected to its potential form (PSDYM3) and a certain isomorphism between the Lie algebras of symmetries of the two systems is shown to exist. This isomorphism allows us to study the infinite-dimensional Lie algebraic structure of the "potential symmetries" of SDYM3 by examining the symmetry structure of PSDYM3 (which is an easier task). By using techniques described in a recent paper, the recursion operators for both SDYM3 and PSDYM3 are derived. Moreover, a Lax pair and an infinite set of nonlocal conservation laws for SDYM3 are found, reflecting the fact that SDYM3 is a totally integrable system. This system may physically represent gravitational fields or chiral fields. |
| title | Symmetry and Integrability of a Reduced, 3-Dimensional Self-Dual Gauge Field Model |
| topic | Mathematical Physics 37K10, 37K15, 37K30, 37K35 |
| url | https://arxiv.org/abs/1103.3966 |