Barbero-Immirzi parameter as a solution of the simplicity constraints

Abstract

In this paper we naturally obtain the values of the Barbero-Immirzi parameter as the solution of the simplicity constraints rather than setting it a priori. Particularly the Main theorem shows that if $\gamma =\pm i$ then the simplicity constraints require that the corresponding Lorentz group representations be necessary finite dimensional and therefore non-unitary.

The other paper was written and published, which includes this one. The result was more general

References in corpus (3)

• Introduction to Modern Canonical Quantum General Relativity
• Flipped spinfoam vertex and loop gravity
• Analog of the Peter-Weyl Expansion for Lorentz Group