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

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.