Pitts, James (2019) What Are Observables in Hamiltonian EinsteinMaxwell Theory? [Preprint]

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Abstract
Is change missing in Hamiltonian EinsteinMaxwell theory? Given the most common definition of observables (having weakly vanishing Poisson bracket with each firstclass constraint), observables are constants of the motion and nonlocal. Unfortunately this definition also implies that the observables for massive electromagnetism with gauge freedom (Stueckelberg) are inequivalent to those of massive electromagnetism without gauge freedom (Proca). The alternative PonsSalisburySundermeyer definition of observables, aiming for HamiltonianLagrangian equivalence, uses the gauge generator G, a tuned sum of firstclass constraints, rather than each firstclass constraint separately, and implies equivalent observables for equivalent massive electromagnetisms.
For General Relativity, G generates 4dimensional Lie derivatives for solutions. The Lie derivative compares different spacetime points with the same coordinate value in different coordinate systems, like 1 a.m. summer time vs. 1 a.m. standard time, so a vanishing Lie derivative implies constancy rather than covariance. Requiring equivalent observables for equivalent formulations of massive gravity confirms that G must generate the 4dimensional Lie derivative (not 0) for observables.
These separate results indicate that observables are invariant under internal gauge symmetries but covariant under external gauge symmetries, but can this bifurcated definition work for mixed theories such as EinsteinMaxwell theory? Pons, Salisbury and Shepley have studied G for EinsteinYangMills. For EinsteinMaxwell, both the electromagnetic field strength F and the metric g are invariant under electromagnetic gauge transformations and covariant (changing by a Lie derivative) under 4dimensional coordinate transformations. Using the bifurcated definition, these quantities count as observables, as one would expect on nonHamiltonian grounds.
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Item Type:  Preprint  

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Additional Information:  Forthcoming in _Foundations of Physics_  
Keywords:  gauge freedom, constrained Hamiltonian dynamics, problem of time, observables  
Subjects:  General Issues > Scientific Metaphysics Specific Sciences > Physics > Cosmology General Issues > Operationalism/Instrumentalism Specific Sciences > Physics > Quantum Gravity Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances 

Depositing User:  Dr. Dr. J. Brian Pitts  
Date Deposited:  24 Jul 2019 02:41  
Last Modified:  24 Jul 2019 02:41  
Item ID:  16252  
Subjects:  General Issues > Scientific Metaphysics Specific Sciences > Physics > Cosmology General Issues > Operationalism/Instrumentalism Specific Sciences > Physics > Quantum Gravity Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances 

Date:  July 2019  
URI:  https://philsciarchive.pitt.edu/id/eprint/16252 
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