Constructing a class of solutions for the Hamilton-Jacobi equation in field theory

Details Constructing a class of solutions for the Hamilton-Jacobi equation in field theory Constructing a class of solutions for the Hamilton-Jacobi equation in field theory

2007-09-12

arxiv.org/abs/0709.1930v1

J. Math. Phys. 48, 112902 (2007)

Physics

Mathematical Physics

16 pages; submitted to J. Math. Phys

Scientific paper

10.1063/1.2804076

A new approach leading to the formulation of the Hamilton-Jacobi equation for field theories is investigated within the framework of jet-bundles and multi-symplectic manifolds. An algorithm associating classes of solutions to given sets of boundary conditions of the field equations is provided. The paper also puts into evidence the intrinsic limits of the Hamilton-Jacobi method as an algorithm to determine families of solutions of the field equations, showing how the choice of the boundary data is often limited by compatibility conditions.

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