Hamilton-Jacobi theory in multisymplectic classical field theories
Tipo de documentoReport de recerca
Fecha de publicación2015-04-08
Condiciones de accesoAcceso abierto
The geometric framework for the Hamilton-Jacobi theory developed in [14, 17, 39] is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problema 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.
Citaciónde León, M., P.D. Prieto-Martínez, Roman-Roy, N., Vilariño, S. "Hamilton-Jacobi theory in multisymplectic classical field theories". 2015.
Versión del editorhttp://arxiv.org/pdf/1504.02020v1.pdf