The Pauli Exclusion Principle and SU(2) vs. SO(3) in Loop Quantum Gravity

TL;DR

This paper explores how the Pauli exclusion principle can reconcile the dominance of j=1 edges in loop quantum gravity with the SU(2) gauge group, addressing area quantization ambiguities.

Contribution

It introduces the idea that a Pauli principle in loop quantum gravity explains the suppression of j=1/2 punctures without changing the gauge group from SU(2) to SO(3).

Findings

Supports SU(2) gauge group with Pauli principle.

Explains dominance of j=1 edges in black hole area quantization.

Provides a physical analogy with photons and electrons.

Abstract

Recent attempts to resolve the ambiguity in the loop quantum gravity description of the quantization of area has led to the idea that j=1 edges of spin-networks dominate in their contribution to black hole areas as opposed to j=1/2 which would naively be expected. This suggests that the true gauge group involved might be SO(3) rather than SU(2) with attendant difficulties. We argue that the assumption that a version of the Pauli principle is present in loop quantum gravity allows one to maintain SU(2) as the gauge group while still naturally achieving the desired suppression of spin-1/2 punctures. Areas come from j=1 punctures rather than j=1/2 punctures for much the same reason that photons lead to macroscopic classically observable fields while electrons do not.