New variables for classical and quantum gravity in all dimensions: I. Hamiltonian analysis

Journal article


Publication Details

Author(s): Bodendorfer N, Thiemann T, Thurn A
Journal: Classical and Quantum Gravity
Publisher: IOP PUBLISHING LTD
Publication year: 2013
Volume: 30
Journal issue: 4
ISSN: 0264-9381


Abstract


Loop quantum gravity (LQG) relies heavily on a connection formulation of general relativity such that (1) the connection Poisson commutes with itself and (2) the corresponding gauge group is compact. This can be achieved starting from the Palatini or Holst action when imposing the time gauge. Unfortunately, this method is restricted to D + 1 = 4 spacetime dimensions. However, interesting string theories and supergravity theories require higher dimensions and it would therefore be desirable to have higher dimensional supergravity loop quantizations at one's disposal in order to compare these approaches. In this series of papers we take first steps toward this goal. The present first paper develops a classical canonical platform for a higher dimensional connection formulation of the purely gravitational sector. The new ingredient is a different extension of the ADM phase space than the one used in LQG which does not require the time gauge and which generalizes to any dimension D > 1. The result is a Yang-Mills theory phase space subject to Gauss, spatial diffeomorphism and Hamiltonian constraint as well as one additional constraint, called the simplicity constraint. The structure group can be chosen to be SO(1, D) or SO(D + 1) and the latter choice is preferred for purposes of quantization.



FAU Authors / FAU Editors

Bodendorfer, Norbert
Lehrstuhl für Theoretische Physik
Thiemann, Thomas Prof. Dr.
Lehrstuhl für Theoretische Physik
Thurn, Andreas
Lehrstuhl für Theoretische Physik


How to cite

APA:
Bodendorfer, N., Thiemann, T., & Thurn, A. (2013). New variables for classical and quantum gravity in all dimensions: I. Hamiltonian analysis. Classical and Quantum Gravity, 30(4). https://dx.doi.org/10.1088/0264-9381/30/4/045001

MLA:
Bodendorfer, Norbert, Thomas Thiemann, and Andreas Thurn. "New variables for classical and quantum gravity in all dimensions: I. Hamiltonian analysis." Classical and Quantum Gravity 30.4 (2013).

BibTeX: 

Last updated on 2018-19-04 at 04:11