Pitts, J. Brian (2019) What Are Observables in Hamiltonian EinsteinMaxwell Theory? [Preprint]
This is the latest version of this item.

Text
ObservablesEinsteinMaxwellFOPRevArXiV.pdf  Accepted Version Download (127kB)  Preview 
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.
Export/Citation:  EndNote  BibTeX  Dublin Core  ASCII/Text Citation (Chicago)  HTML Citation  OpenURL 
Social Networking: 
Available Versions of this Item
 What Are Observables in Hamiltonian EinsteinMaxwell Theory? (deposited 25 Jul 2019 04:01) [Currently Displayed]
Monthly Views for the past 3 years
Monthly Downloads for the past 3 years
Plum Analytics
Actions (login required)
View Item 