Lie Theory suffices to understand, and Locally Resolve, the Problem of Time

Abstract

The Lie claw digraph controls Background Independence and thus the Problem of Time and indeed the Fundamental Nature of Physical Law. This has been established in the realms of Flat and Differential Geometry with varying amounts of extra mathematical structure. This Lie claw digraph has Generator Closure at its centre (Lie brackets), Relationalism at its root (implemented by Lie derivatives), and, as its leaves, Assignment of Observables (zero commutants under Lie brackets) and Constructability from Less Structure Assumed (working if generator Deformation leads to Lie brackets algebraic Rigidity). This centre is enabled by automorphisms and powered by the Generalized Lie Algorithm extension of the Dirac Algorithm (itself sufficing for the canonical subcase, for which generators are constraints). The Problem of Time's facet ordering problem is resolved.