R matrix construction of electromagnetic models for the Painleve transcendents
Jun 14, 1994
23 pages
Published in:
- J.Math.Phys. 36 (1995) 4863-4881
e-Print:
- hep-th/9406077 [hep-th]
DOI:
Report number:
- CRM-2889
View in:
Citations per year
Abstract:
The Painlev\'e transcendents P_{\rom{I}}--P_{\rom{V}} and their representations as isomonodromic deformation equations are derived as nonautonomous Hamiltonian systems from the classical --matrix Poisson bracket structure on the dual space \wt{\frak{sl}}_R~*(2) of the loop algebra \wt{\frak{sl}}_R(2). The Hamiltonians are obtained by composing elements of the Poisson commuting ring of spectral invariant functions on \wt{\frak{sl}}_R~*(2) with a time--dependent family of Poisson maps whose images are --dimensional rational coadjoint orbits in \wt{\frak{sl}}_R~*(2). Each system may be interpreted as describing a particle moving on a surface of zero curvature in the presence of a time--varying electromagnetic field. The Painlev\'e equations follow from reduction of these systems by the Hamiltonian flow generated by a second commuting element in the ring of spectral invariants.References(7)
Figures(0)