An Exterior Algebraic Derivation of the Euler–Lagrange Equations from the Principle of Stationary Action

In this paper, we review two related aspects of field theory: the modeling fields by means exterior algebra and calculus, derivation dynamics, i.e., Euler-Lagrange equations, stationary action principle. contrast to usual tensorial these equations for theories, that gives separate components, coordinate-free forms are derived. These alternative reminiscent formulae vector expressed in terms derivatives Lagrangian density. The first form is valid a generic density only depends on first-order field. second form, notation, specific case when function interior multivector As an application, generalized electromagnetic arbitrary grade postulated shown have, taking derivative density, Maxwell as Euler--Lagrange equations.