A contact geometry framework for field theories with dissipation
Mathematical Physics
2020-02-25 v3 High Energy Physics - Theory
Differential Geometry
math.MP
Abstract
We develop a new geometric framework suitable for dealing with Hamiltonian field theories with dissipation. To this end we define the notions of -contact structure and -contact Hamiltonian system. This is a generalization of both the contact Hamiltonian systems in mechanics and the -symplectic Hamiltonian systems in field theory. The concepts of symmetries and dissipation laws are introduced and developed. Two relevant examples are analyzed in detail: the damped vibrating string and Burgers' equation.
Cite
@article{arxiv.1905.07354,
title = {A contact geometry framework for field theories with dissipation},
author = {Jordi Gaset and Xavier Gràcia and Miguel C. Muñoz-Lecanda and Xavier Rivas and Narciso Román-Roy},
journal= {arXiv preprint arXiv:1905.07354},
year = {2020}
}
Comments
26 pp. Minor corrections. The bibliography has been updated