Explicit partial and functional differential equations for beables or observables

Abstract

We provide explicit partial differential equations - in finite cases - and functional differential equations - in field-theoretic cases - which determine observables or beables in the senses of Kucha\v{r} and of Dirac. These cover a wide range of relational mechanics models as well as Electromagnetism, Yang--Mills Theory and General Relativity. We give an underlying reason why pure-configuration Kucha\v{r} observables are already well-known: various types of shape, E-fields, B-fields, loops and 3-geometries. The partial differential equations or functional differential equations for pure-momentum observables are also posed, as are those for observables which have a mixture of configuration and momentum functional dependence.