A correction to the Immirzi parameter of SU ( 2 ) spin networks

摘要

The elegant predictions of loop quantum gravity are obscured by the free Immirzi parameter ( γ ). Dreyer (2003), considering the asymptotic quasinormal modes spectrum of a black hole, proposed that γ 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 γ 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 γ 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.