Dynamic general covariance of physical systems

TL;DR

This paper explores a unique property of dynamic systems where their governing equations maintain their form under coordinate transformations, with non-covariant terms reducible through perturbation theory, supported by illustrative examples.

Contribution

It introduces the concept of dynamic general covariance in differential equations of physical systems and demonstrates its implications through examples.

Findings

Non-covariant addends are reducible by solutions of unperturbed equations.

Equations exhibit form-invariance under coordinate diffeomorphisms.

The property holds across various simple illustrative examples.

Abstract

One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations (optionally covariant) with respect to coordinate diffeomorphisms: the equations, in a sense, retain their form on their solutions. More precisely, non-covariant addends to the equations of such systems always exactly reduced in any order of perturbation theory by solutions of unperturbed (initial) equations. This property demonstrated by a set of simple illustrative examples. Various aspects of the dynamic covariance are discussed.