A Correction to the Immirizi Parameter of SU(2) Spin Networks

TL;DR

This paper revises the value of the Immirizi parameter in loop quantum gravity, showing it should be twice the previously suggested value when considering SU(2) symmetry and j=1 transitions as dominant.

Contribution

It demonstrates that the Immirizi parameter's value is doubled under SU(2) symmetry assumptions with j=1 dominant transitions, refining previous estimates.

Findings

The Immirizi parameter is twice the previously reported value.

SU(2) symmetry with j=1 transitions leads to a revised parameter estimate.

The asymptotic quasinormal modes obey SU(2) symmetry.

Abstract

The elegant predictions of loop quantum gravity are obscured by the free Immirizi parameter. Dreyer (2003), considering the asymptotic quasinormal modes spectrum of a black hole, proposed that the Immirizi parameter may be fixed by letting the j=1 transitions of spin networks as the dominant processes contributing to the black hole area, as opposed to the expected j=1/2 transitions. This suggested that the gauge group of the theory might be SO(3) rather than SU(2). Corichi (2003), maintaining SU(2) as the underlying gauge group, and invoking the principle of local fermion-number conservation, reported the same value of the Immirizi parameter for j=1 processes as obtained by Dreyer. In this note, preserving the SU(2) structure of the theory, and considering j=1 transitions as the dominant processes, we point out that the value of the Immirizi parameter is in fact twice the value reported by these authors. We arrive at this result by assuming the asymptotic quasinormal modes themselves as dynamical systems obeying SU(2) symmetry.