• DOI:10.1088/0264-9381/23/4/003
• Corpus ID: 16944390

Testing the master constraint programme for loop quantum gravity: III. models

@article{Dittrich2004TestingTM,
  title={Testing the master constraint programme for loop quantum gravity: III. models},
  author={Bianca Dittrich and Thomas Thiemann},
  journal={Classical and Quantum Gravity},
  year={2004},
  volume={23},
  pages={1089 - 1120}
}

• B. Dittrich, T. Thiemann
• Published 29 November 2004
• Mathematics
• Classical and Quantum Gravity

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 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 ℏ2 which can be interpreted as a normal ordering constant arising from first class constraints (while second class systems lead to ℏ normal ordering constants). The physical Hilbert space can then be obtained after subtracting this normal ordering correction.