Equivalence of general relativistic field theories

Abstract

A theorem of Aczel and Golab is strengthened and simplified. According to the new theorem any local geometric object psi A(x) may be expressed as a differential concomitant of a suitable set of local scalars SB(x). As a consequence, it is proved that any generally covariant field theory may be described in terms of scalar fields, i.e. that the set of all general covariant field theories is equivalent to its subset of scalar field theories.