SDiff(2) Toda equation -- hierarchy, $τ$ function, and symmetries

Details SDiff(2) Toda equation -- hierarchy, $τ$ function, and symmetries SDiff(2) Toda equation -- hierarchy, $τ$ function, and symmetries

1991-12-17

arxiv.org/abs/hep-th/9112042v1

Lett.Math.Phys. 23 (1991) 205-214

Physics

High Energy Physics

High Energy Physics - Theory

16 pages (``vanilla.sty" is attatched to the end of this file after ``\bye" command)

Scientific paper

10.1007/BF01885498

A continuum limit of the Toda lattice field theory, called the SDiff(2) Toda equation, is shown to have a Lax formalism and an infinite hierarchy of higher flows. The Lax formalism is very similar to the case of the self-dual vacuum Einstein equation and its hyper-K\"ahler version, however now based upon a symplectic structure and the group SDiff(2) of area preserving diffeomorphisms on a cylinder $S^1 \times \R$. An analogue of the Toda lattice tau function is introduced. The existence of hidden SDiff(2) symmetries are derived from a Riemann-Hilbert problem in the SDiff(2) group. Symmetries of the tau function turn out to have commutator anomalies, hence give a representation of a central extension of the SDiff(2) algebra.

Affiliated with

Also associated with

No associations

Rating

SDiff(2) Toda equation -- hierarchy, $τ$ function, and symmetries does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with SDiff(2) Toda equation -- hierarchy, $τ$ function, and symmetries, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and SDiff(2) Toda equation -- hierarchy, $τ$ function, and symmetries will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-77556