Covariant Hamiltonian field theory

Summary

Covariant Hamiltonian field theory is a Hamiltonian formulation of classical field theory that treats all spacetime coordinates alike. Each field component gets one conjugate momentum for every spacetime direction, called polymomenta, instead of one momentum conjugate to the time derivative. The field equations become first-order covariant Hamilton equations on a finite-dimensional phase space, the Legendre bundle over spacetime. It extends Hamiltonian mechanics to fields without choosing a time coordinate, and it is related to multisymplectic and polysymplectic geometry.