Electronic International Standard Serial Number (EISSN)
1879-1662
abstract
We analyse the problem of defining a Poisson bracket structure on the space of solutions of the equations of motions of first order Hamiltonian field theories. The cases of Hamiltonian mechanical point systems ¿ as a (0+1)-dimensional field ¿ and more general field theories without gauge symmetries are addressed by showing the existence of a symplectic (and, thus, a Poisson) structure on the space of solutions. Also the easiest case of gauge theory, namely free electrodynamics, is considered: within this problem, a pre-symplectic tensor on the space of solutions is introduced, and a Poisson structure is induced in terms of a flat connection on a suitable bundle associated to the theory.
Classification
keywords
field theories; multisymplectic geometry; peierls brackets; poisson brackets; space of solutions