A More Sensitive Lorentzian State Sum

Abstract

We give the construction modulo normalization of a new state sum model for lorentzian quantum general relativity, using the construction of Dirac's expansors to include quantum operators corresponding to edge lengths as well as the quantum bivectors of the Barrett-Crane model, and discuss the problem of its normalization. The new model gives rise to a new picture of quantum geometry in which lengths come in a discrete spectrum, while areas have a continuum of values.

11 pages latex

References in corpus (5)

• Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space
• Asymptotics of Relativistic Spin Networks
• Higher Yang-Mills Theory
• Asymptotics of 10j symbols
• Categorical representations of categorical groups

Cited by in corpus (6)

• Higher gauge theory and a non-Abelian generalization of 2-form electrodynamics
• Categorical representations of categorical groups
• 2-categorical Poincare Representations and State Sum Applications
• 2-Groups, trialgebras and their Hopf categories of representations
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Knot theory and a physical state of quantum gravity