De Donder–Weyl theory

Summary

De Donder–Weyl theory is the covariant Hamiltonian form of a first-order Lagrangian field theory, named after Théophile De Donder and Hermann Weyl. It assigns to each field component one polymomentum for every spacetime direction. It replaces the Euler–Lagrange equations by first-order equations for the fields and the polymomenta. It is the basic example of covariant Hamiltonian field theory. It applies when the Lagrangian density is regular, that is, when the polymomenta determine the field derivatives.