A State Sum Model for (2+1) Lorentzian Quantum Gravity

Abstract

A state sum model based on the group SU(1,1) is defined. Investigations of its geometry and asymptotics suggest it is a good candidate for modelling (2+1) Lorentzian quantum gravity.

Figures (18)

• Figure 1: The 2-2 Pachner move. Two triangles sharing a common edge are transformed into two different triangles sharing a common edge.
• Figure 2: The 3-1 Pachner move. Three triangles, each sharing a common edge, are transformed into one triangle by removing the internal vertex and associated edges.
• Figure 3: A labeled tetrahedron. The edge $e_{kl}$ is determined by deleting the $k$-th and $l$-th vertices.
• Figure 4: The 3-2 Pachner move. Three tetrahedra sharing a common edge are replaced by two tetrahedra sharing a common face.
• Figure 5: The 4-1 Pachner move caused by adding or removing an internal vertex

Theorems & Definitions (36)

• Definition 2.1: Atiyah
• Proposition 3.1
• Proposition 3.2
• Theorem 3.3: Gauss
• Proposition 4.1: Orthogonality
• Proposition 4.2: Biedenharn-Elliot
• Proposition 4.3: Four to One
• Theorem 4.4
• Theorem 4.5: Laplace IntegralsAsymp
• Theorem 4.6: Stationary PhaseAsymp