Homological evolutionary vector fields in Korteweg-de Vries, Liouville, Maxwell, and several other models

Details Homological evolutionary vector fields in Korteweg-de Vries, Liouville, Maxwell, and several other models Homological evolutionary vector fields in Korteweg-de Vries, Liouville, Maxwell, and several other models

2011-11-14

arxiv.org/abs/1111.3272v1

J.Phys.: Conf. Ser. 343 (2012) 012058, 1-20

Physics

Mathematical Physics

Proc. 7th International Workshop "Quantum Theory and Symmetries-7" (August 7-13, 2011; CVUT Prague, Czech Republic), 20 pages

Scientific paper

10.1088/1742-6596/343/1/012058

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.

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