On Types of Observables in Constrained Theories

TL;DR

This paper expands the concept of observables in constrained theories beyond Kuchar's notion by introducing A-observables, which are based on algebraic substructures, applicable to a wider range of theories.

Contribution

It introduces a general notion of A-observables linked to algebraic substructures, extending the applicability of observable concepts in constrained theories.

Findings

Kuchar observables are limited to certain theories

A-observables are defined via algebraic substructures

Constrained algebraic structures form bounded lattices

Abstract

The Kuchar observables notion is shown to apply only to a limited range of theories. Relational mechanics, slightly inhomogeneous cosmology and supergravity are used as examples that require further notions of observables. A suitably general notion of A-observables is then given to cover all of these cases. `A' here stands for `algebraic substructure'; A-observables can be defined by association with each closed algebraic substructure of a theory's constraints. Both constrained algebraic structures and associated notions of A-observables form bounded lattices.