Some new conservation laws

Abstract

It is shown that field theories possessing a certain type of nonlinearity, termed intrinsic, also possess a new type of conservation law in which the conserved quantity is an integer even in the unquantized theory. For the example of general relativity the conserved quantity is shown to assume the values M = 0, ±1, ±2, …. This conservation law (“conservation of metricity”) is valid regardless of any interaction of the metric field with other fields and regardless even of the equation of motion assumed for the metric field itself. The basis of the work is the principle that a quantity which is unchanged in value by an arbitrary continuous deformation is a fortiori unchanged in value by the passage of time. Some properties of metricity and of its carrier are given.