Testing the master constraint programme for loop quantum gravity: III. SL(2, R) models

Journal article


Publication Details

Author(s): Thiemann T, Dittrich B
Journal: Classical and Quantum Gravity
Publisher: IOP PUBLISHING LTD
Publication year: 2006
Volume: 23
Journal issue: 4
Pages range: 1089-1120
ISSN: 0264-9381


Abstract


This is the third paper in our series of five in which we test the master constraint programme for solving the Hamiltonian constraint in loop quantum gravity. In this work, we analyse models which, despite the fact that the phase space is finite dimensional, are much more complicated than in the second paper. These are systems with an SL(2, R) gauge symmetry and the complications arise because non-compact semisimple Lie groups are not amenable (have no finite translation invariant measure). This leads to severe obstacles in the refined algebraic quantization programme (group averaging) and we see a trace of that in the fact that the Spectrum of the master constraint does not contain the point zero. However, the minimum of the spectrum is of order h 2 which can be interpreted as a normal ordering constant arising from first class constraints (while second class systems lead to h normal ordering constants). The physical Hilbert space can then be obtained after subtracting this normal ordering correction.



FAU Authors / FAU Editors

Thiemann, Thomas Prof. Dr.
Lehrstuhl für Theoretische Physik


How to cite

APA:
Thiemann, T., & Dittrich, B. (2006). Testing the master constraint programme for loop quantum gravity: III. SL(2, R) models. Classical and Quantum Gravity, 23(4), 1089-1120. https://dx.doi.org/10.1088/0264-9381/23/4/003

MLA:
Thiemann, Thomas, and Bianca Dittrich. "Testing the master constraint programme for loop quantum gravity: III. SL(2, R) models." Classical and Quantum Gravity 23.4 (2006): 1089-1120.

BibTeX: 

Last updated on 2018-08-08 at 10:53