Hamilton-Jacobi Theory in k-Symplectic Field Theories
M. De Le\'On, D. Mart\'In De Diego, J.C. Marrero, M. Salgado, S., Vilari\~no
TL;DR
This paper extends Hamilton-Jacobi theory from classical mechanics to classical field theories within the k-symplectic geometric framework, providing a new formalism for analyzing such systems.
Contribution
It introduces a geometric Hamilton-Jacobi formalism tailored for k-symplectic field theories, bridging a gap in the geometric understanding of classical fields.
Findings
Developed a generalized Hamilton-Jacobi equation for k-symplectic field theories.
Provided geometric tools for analyzing classical field equations.
Extended the applicability of Hamilton-Jacobi theory to field theories.
Abstract
In this paper we extend the geometric formalism of Hamilton-Jacobi theory for Mechanics to the case of classical field theories in the k-symplectic framework.
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