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Hamilton-Jacobi theory in multisymplectic classical field theories

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hdl:2117/115384

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De León, Manuel
Prieto Martínez, Pedro DanielMés informació
Román Roy, NarcisoMés informacióMés informacióMés informació
Vilariño Fernández, Silvia
Document typeArticle
Defense date2017-09-01
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
Abstract
The geometric framework for the Hamilton-Jacobi theory developed in the studies of Carinena et al. [Int. J. Geom. Methods Mod. Phys. 3(7), 1417-1458 (2006)], Carinena et al. [Int. J. Geom. Methods Mod. Phys. 13(2), 1650017 (2015)], and de Léon et al. [Variations, Geometry and Physics (Nova Science Publishers, New York, 2009)] is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results.
CitationDe León, M., P.D. Prieto-Martínez, Roman-Roy, N., Vilariño Fernández, S. Hamilton-Jacobi theory in multisymplectic classical field theories. "Journal of mathematical physics", 1 Setembre 2017, vol. 58, p. 2-37. 
URIhttp://hdl.handle.net/2117/115384
DOI10.1063/1.5004260
ISSN0022-2488
Publisher versionhttp://aip.scitation.org/doi/10.1063/1.5004260
Other identifiershttps://arxiv.org/pdf/1504.02020.pdf
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