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- Title
Symmetry and Integrability of a Reduced, 3-Dimensional Self-Dual Gauge Field Model.
- Authors
Papachristou, C. J.
- Abstract
A 3-dimensional reduction of the self-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-B¨acklund 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.
- Subjects
SYMMETRY (Physics); GAUGE field theory; NUCLEAR models; ISOMORPHISM (Mathematics); GRAVITATIONAL fields; CHIRALITY of nuclear particles; YANG-Mills theory
- Publication
Electronic Journal of Theoretical Physics, 2012, Vol 9, Issue 26, p119
- ISSN
1729-5254
- Publication type
Article