A Local Resolution of the Problem of Time. VII. Constraint Closure

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.

23 pages including 7 figures. v2 improves concepts for, and presentation of, our temporal-relationally modified Dirac Algorithm

References in corpus (7)

• Revisiting observables in generally covariant theories in the light of gauge fixing methods
• Constraints and gauge transformations: Dirac's theorem is not always valid
• Problem of Time and Background Independence: the Individual Facets
• Does relationalism alone control geometrodynamics with sources?
• TRiPoD (Temporal Relationalism incorporating Principles of Dynamics)
• A Local Resolution of the Problem of Time. V. Combining Temporal and Configurational Relationalism for Finite Theories
• A Local Resolution of the Problem of Time. IX. Spacetime Constructability

Cited by in corpus (4)

• Problem of Time and Background Independence: classical version's higher Lie Theory
• Lie Theory suffices to understand, and Locally Resolve, the Problem of Time
• A Local Resolution of the Problem of Time. VIII. Assignment of Observables
• Comparative Theory of Background Independence