In theoretical physics, Hamiltonian field theory is the field-theoretic analogue to classical Hamiltonian mechanics. It is a formalism in classical field theory alongside See more

The fields φi and conjugates πi form an infinite dimensional phase space, because fields have an infinite number of degrees of freedom. See more

For two functions which depend on the fields φi and πi, their spatial derivatives, and the space and time coordinates,
and the fields are … See more

Covariant Hamiltonian field theory is the relativistic formulation of Hamiltonian field theory.
Hamiltonian field … See more

The Hamiltonian for a system of discrete particles is a function of their generalized coordinates and conjugate momenta, and possibly, time. For … See more

The equations of motion for the fields are similar to the Hamiltonian equations for discrete particles. For any number of fields:
where again the overdots are partial time derivatives, the variational derivative with respect to the fields See more

The following results are true if the Lagrangian and Hamiltonian densities are explicitly time-independent (they can still have implicit time … See more