General conservation law for a class of physics field theories

Abstract

In this paper we form a general conservation law that unifies a class of physics field theories. For this we first introduce the notion of a general field as a formal sum differential forms on a Minkowski manifold. Thereafter, we employ the action principle to define the conservation law for such general fields. By construction, particular field notions of physics, such as electric field strength, stress, strain etc. become instances of the general field. Hence, the differential equations that constitute physics field theories become also instances of the general conservation law. Accordingly, the general field and the general conservation law together correspond to a large class of physics field models. The approach creates solid foundations for multi-physics analysis and is critical in developing software systems for scientific computing; the unifying structure shared by the class of field models makes it possible to implement software systems which are not restricted to finite lists of admissible problems.