Poisson bracket in classical field theory as a derived bracket

Abstract

We construct a Leibniz bracket on the space ${\Omega }^{\bullet }(J^k(\pi ))$ of all differential forms over the finite-dimensional jet bundle $J^k(\pi )$. As an example, we write Maxwell equations with sources in the covariant finite-dimensional hamiltonian form.

4 pages

References in corpus (3)

• Derived brackets
• The Poisson Bracket for Poisson Forms in Multisymplectic Field Theory
• The bracket and the evolution operator in covariant Hamiltonian field theory