The algebra of observables in Gau{\ss}ian normal spacetime coordinates
Abstract
We discuss the canonical structure of a spacetime version of the radial gauge, i.e. Gau{\ss}ian normal spacetime coordinates. While it was found for the spatial version of the radial gauge that a "local" algebra of observables can be constructed, it turns out that this is not possible for the spacetime version. The technical reason for this observation is that the new gauge condition needed to upgrade the spatial to a spacetime radial gauge does not Poisson-commute with the previous gauge conditions. It follows that the involved Dirac bracket is inherently non-local in the sense that no complete set of observables can be found which is constructed locally and at the same time has local Dirac brackets. A locally constructed observable here is defined as a finite polynomial of the canonical variables at a given physical point specified by the Gau{\ss}ian normal spacetime coordinates.
Keywords
Cite
@article{arxiv.1510.04154,
title = {The algebra of observables in Gau{\ss}ian normal spacetime coordinates},
author = {Norbert Bodendorfer and Paweł Duch and Jerzy Lewandowski and Jędrzej Świeżewski},
journal= {arXiv preprint arXiv:1510.04154},
year = {2016}
}
Comments
16 pages; discussion of the cosmological constant added; matches published version