In Chapter 25 we discussed the Lagrangian method as it applied to nonrelativistic problems. We extend it now to the relativistic domain in which the relativistic wavefunctions, called classical fields, replace their nonrelativistic counterparts with the Lagrangian method formulated in the four-dimensional language.
Let ϕ represent the classical field. We write the Lagrangian density in terms ϕ and its derivative ∂μ ϕ, and express the Lagrangian as
and the action as
The corresponding ...