Homological evolutionary vector fields in Korteweg-de Vries, Liouville, Maxwell, and several other models
Mathematical Physics
2012-02-10 v1 High Energy Physics - Theory
Differential Geometry
math.MP
Exactly Solvable and Integrable Systems
Abstract
We review the construction of homological evolutionary vector fields on infinite jet spaces and partial differential equations. We describe the applications of this concept in three tightly inter-related domains: the variational Poisson formalism (e.g., for equations of Korteweg-de Vries type), geometry of Liouville-type hyperbolic systems (including the 2D Toda chains), and Euler-Lagrange gauge theories (such as the Yang-Mills theories, gravity, or the Poisson sigma-models). Also, we formulate several open problems.
Keywords
Cite
@article{arxiv.1111.3272,
title = {Homological evolutionary vector fields in Korteweg-de Vries, Liouville, Maxwell, and several other models},
author = {Arthemy V. Kiselev},
journal= {arXiv preprint arXiv:1111.3272},
year = {2012}
}
Comments
Proc. 7th International Workshop "Quantum Theory and Symmetries-7" (August 7-13, 2011; CVUT Prague, Czech Republic), 20 pages