Bodendorfer N, Thiemann T, Thurn A (2013)
Publication Status: Published
Publication Type: Journal article
Publication year: 2013
Publisher: IOP PUBLISHING LTD
Book Volume: 30
Journal Issue: 4
DOI: 10.1088/0264-9381/30/4/045002
We rederive the results of our companion paper, for matching space-time and internal signature, by applying in detail the Dirac algorithm to the Palatini action. While the constraint set of the Palatini action contains second class constraints, by an appeal to the method of gauge unfixing, we map the second class system to an equivalent first class system which turns out to be identical to the first class constraint system obtained via the extension of the ADM phase space performed in our companion paper. Central to our analysis is again the appropriate treatment of the simplicity constraint. Remarkably, the simplicity constraint invariant extension of the Hamiltonian constraint, that is a necessary step in the gauge unfixing procedure, involves a correction term which is precisely the one found in the companion paper and which makes sure that the Hamiltonian constraint derived from the Palatini Lagrangian coincides with the ADM Hamiltonian constraint when Gauss and simplicity constraints are satisfied. We therefore have rederived our new connection formulation of general relativity from an independent starting point, thus confirming the consistency of this framework.
APA:
Bodendorfer, N., Thiemann, T., & Thurn, A. (2013). New variables for classical and quantum gravity in all dimensions: II. Lagrangian analysis. Classical and Quantum Gravity, 30(4). https://dx.doi.org/10.1088/0264-9381/30/4/045002
MLA:
Bodendorfer, Norbert, Thomas Thiemann, and Andreas Thurn. "New variables for classical and quantum gravity in all dimensions: II. Lagrangian analysis." Classical and Quantum Gravity 30.4 (2013).
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