Extends classical Lie theory with Lie's Algorithm and a commuting pentagon invariance criterion to locally resolve the Problem of Time via background independence.
A Local Resolution of the Problem of Time. VII. Constraint Closure
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abstract
We now set up Constraint Closure in a manner consistent with Temporal and Configurational Relationalism. This requires modifying the Dirac Algorithm - which addresses the Constraint Closure Problem facet of the Problem of Time piecemeal - to the TRi-Dirac Algorithm. This is a member of the wider class of Dirac-type algorithms that enjoys the property of being Temporal Relationalism implementing (TRi). Constraint algebraic structures ensue. We include examples of types of constraint, outcomes of the Dirac Algorithm and different kinds of Constraint Closure Problems. Enough new Principles of Dynamics is required to support this venture that an Appendix on it is provided: differential Hamiltonians, anti-Routhians, and the brackets, state spaces and morphisms corresponding to these.
fields
gr-qc 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Problem of Time and Background Independence: classical version's higher Lie Theory
Extends classical Lie theory with Lie's Algorithm and a commuting pentagon invariance criterion to locally resolve the Problem of Time via background independence.