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Problem of Time and Background Independence: classical version's higher Lie Theory by Anderson, Edward is a scholarly article available to read on EtoBox.

What is Problem of Time and Background Independence: classical version's higher Lie Theory about?

A local resolution of the Problem of Time has recently been given, alongside reformulation as a local theory of Background Independence. The classical part of this requires just Lie's Mathematics, much of which is basic: i) Lie derivatives to encode Relationalism. ii) Lie brackets for Closure giving Lie algebraic structures. iii) Observables defined by a Lie brackets relation, in the constrained canonical case as explicit PDEs to be solved using Lie's flow method, and themselves forming Lie algebras. iv) Lattices of constraint algebraic substructures induce dual lattices of observables subalgebras. The current Article focuses on two pieces of `higher Lie Theory' that are also required. Preliminarily, we extend Dirac's Algorithm for Constraint Closure to `Lie's Algorithm' for Generator Closure. 1) We then reinterpret `passing families of theories through the Dirac Algorithm' - a method used for Spacetime Construction (from space) and getting more structure from less structure assumed more generally - as the Dirac Rigidity subcase of Lie Rigidity. We also provide a Foundations of Geometry example of specifically Lie rather than Dirac Rigidity, to illustrate merit in extending from Di

Author

Anderson, Edward

Published

2019

Language

EN