Lagrangian density

Summary

A Lagrangian density is a function of a point of spacetime, the values of the fields there and their first derivatives. Its integral over a region of spacetime is the action of the field configuration. The field equations of a classical field theory are the Euler–Lagrange equations of this action. It plays for fields the role that the Lagrangian of Lagrangian mechanics plays for systems with finitely many degrees of freedom.