Newton's second law in field theory

Abstract

[EN]In this article we present a natural generalization of Newton’s Second Law valid in field theory, i.e., when the parameterized curves are replaced by parameterized sub-manifolds of higher dimension. For it we introduce what we have called the geodesic k-vector field, analogous to the ordinary geodesic field and which describes the iner-tial motions (i.e., evolution in the absence of forces). From this generalized Newton’s law, the corresponding Hamilton’s canonical equations of field theory (Hamilton-De Donder-Weyl equations) are obtained by a simple procedure. It is shown that solu-tions of generalized Newton’s equation also hold the canonical equations. However, unlike the ordinary case, Newton equations determined by different forces can define equal Hamilton’s equations.