2011/06/10 by Frédéric Hélein, Hélein, Frédéric
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1106.2086
Variational Problems in Differential Geometry, Leeds : United Kingdom (2009)
arxiv created 2011/06/10 · arxiv updated 2011/06/13
The formulation of a relativistic dynamical problem as a system of Hamilton equations by respecting the principles of Relativity is a delicate task, because in their classical form the Hamilton equations require the use of a time coordinate, which of course contradicts the Relativity. Two interesting solutions have been proposed during the last century: the covariant phase space and the multisymplectic formalism. These two approaches were inspired at the beginning by different points of view. However, as shown by works by Kijowski-Szczyrba, Forger-Romero and Vitagliano, a synthetic vision of the two theories leads probably to the most satisfactory answer to the basic question of understanding the Hamiltonian structure of relativistic fields theory.