A contact geometry framework for field theories with dissipation

Gaset Rifà, Jordi; Gràcia Sabaté, Francesc Xavier; Muñoz Lecanda, Miguel Carlos; Rivas Guijarro, Xavier; Román Roy, Narciso

doi:10.1016/j.aop.2020.168092

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Gaset Rifà, Jordi

Gràcia Sabaté, Francesc Xavier

Muñoz Lecanda, Miguel Carlos

Rivas Guijarro, Xavier

Román Roy, Narciso

Document typeArticle

Defense date2020-03-01

Rights accessOpen Access

Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain

Abstract

We develop a new geometric framework suitable for dealing with Hamiltonian field theories with dissipation. To this end we define the notions of k-contact structure and k-contact Hamiltonian system. This is a generalization of both the contact Hamiltonian systems in mechanics and the k-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.

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CitationGaset, J. [et al.]. A contact geometry framework for field theories with dissipation. "Annals of physics", 1 Març 2020, vol. 414, p. 168092-1-168092-20.

URIhttp://hdl.handle.net/2117/343989

DOI10.1016/j.aop.2020.168092

ISSN0003-4916

Publisher versionhttps://www.sciencedirect.com/science/article/abs/pii/S0003491620300257

Other identifiershttps://arxiv.org/pdf/1905.07354.pdf

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