Imposing det E > 0 in discrete quantum gravity

Abstract

We point out that the inequality det E > 0 distinguishes the kinematical phase space of canonical connection gravity from that of a gauge field theory, and characterize the eigenvectors with positive, negative and zero-eigenvalue of the corresponding quantum operator in a lattice-discretized version of the theory. The diagonalization of the operator det E is simplified by classifying its eigenvectors according to the irreducible representations of the octagonal group.

10 pages, plain TeX

Cited by in corpus (9)

• Spin Foam Models
• Discrete approaches to quantum gravity in four dimensions
• Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity I
• Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity II
• Simplifying the spectral analysis of the volume operator
• Group Theoretical Quantization and the Example of a Phase Space S^1 x R^+
• Semiclassical States in Quantum Cosmology: Bianchi I Coherent States
• Symplectic Cuts and Projection Quantization
• The Quantum Tetrahedron in 3 and 4 Dimensions