Some First Order Linear Operators in Physics

Abstract

It is well known that among the main tools to find fields equations are the variational principles. In this introduction we wish to sketch some general underlying ideas. Suppose considering a physical system which requires several fields ø^j(x), j = 1,…, n to be specified We can suppose that the field ø^j(x) is real (if it is complex the procedure can be repeated taking into account both the real and imaginary parts). The index j may label the components of the same field, for example the components of a vector potential, or it can refer to different independent fields.