Introduction to Classical and Quantum Lagrangian Field Theory

Abstract

Classical field theory may be regarded as a generalization of Lagrangian mechanics in the sense that generalized coordinates which are functions of a parameter (time) get replaced by fields which are functions of local parameters in a four-dimensional continuum, viz. spacetime coordinates. These local functions or local fields, being the generalized coordinates of the classical field theory, satisfy Euler—Lagrange equations of motion which are called field equations. The field equations result from an appropriate action principle, just as in classical mechanics.