We discuss generalizations of the well known concept of canonical transformations for symplectic structures to the case of hyperkahler structures. Different characterizations, which are equivalent in the symplectic case, give rise to non-equivalent notions in the hyperkahler framework; we will thus distinguish between hyperkahler and canonical transformations. We also discuss the properties of hyperhamiltonian dynamics in this respect.
Canonical transformastions for hyperkahler structures and hyperhamiltonian dynamics / G. Gaeta, M.A. Rodriguez. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 55:5(2014), pp. 052901.1-052901.26.
Canonical transformastions for hyperkahler structures and hyperhamiltonian dynamics
G. GaetaPrimo
;
2014
Abstract
We discuss generalizations of the well known concept of canonical transformations for symplectic structures to the case of hyperkahler structures. Different characterizations, which are equivalent in the symplectic case, give rise to non-equivalent notions in the hyperkahler framework; we will thus distinguish between hyperkahler and canonical transformations. We also discuss the properties of hyperhamiltonian dynamics in this respect.
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