English

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 kk-contact structure and kk-contact Hamiltonian system. This is a generalization of both the contact Hamiltonian systems in mechanics and the kk-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.

Keywords

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

R2 v1 2026-06-23T09:10:58.863Z