Covariant Hamiltonian Field Theory

Understand

A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented.

• Whereas the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation theory offers more general means for defining mappings that preserve the form of the field equations than the usual Lagrangian description.
• It is proved that Poisson brackets, Lagrange brackets, and canonical 2-forms exist that are invariant under canonical transformations of the fields.
• The technique to derive transformation rules for the fields from generating functions is demonstrated by means of various examples.