The Pauli Exclusion Principle, Spin, and Statistics in Loop Quantum Gravity: SU(2) versus SO(3)

TL;DR

This paper explores how a Pauli principle-like mechanism in loop quantum gravity can explain the dominance of j=1 edges in black hole area quantization, favoring SU(2) over SO(3) as the gauge group.

Contribution

It proposes that a Pauli principle analogy allows SU(2) to suppress j=1/2 punctures, resolving area quantization ambiguities without changing the gauge group.

Findings

SU(2) can naturally suppress j=1/2 punctures via a Pauli principle analogy.

Macroscopic black hole areas are dominated by j=1 punctures, consistent with observations.

The approach maintains SU(2) as the gauge group while explaining area contributions.

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). We argue that the idea 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. Such an idea can be motivated by arguments from geometric quantization even though the SU(2) under consideration does not have the geometrical interpretation of rotations in 3-dimensional space, and its representation labels do not correspond to physical angular momenta. In this picture, it is natural that macroscopic areas come almost entirely from j=1 punctures rather than j=1/2 punctures, and this is for much the same reason that photons lead to macroscopic classically observable fields while electrons do not.