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arXiv · 2602.11927

Bosonic and fermionic statistics in nonperturbative quantum gravity

Bekir Baytaş·Patrick L. Rodrigues·Nelson Yokomizo
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Abstract

The relation between spin and statistics in quantum field theory relies on Poincar\'e invariance, a symmetry that is lost in the presence of a gravitational field, and replaced in general relativity by the principle of general covariance. In a nonperturbative approach to quantum gravity, beyond the picture of gravitational perturbations propagating on a flat background, it is an open question whether the gravitational field must still satisfy a bosonic statistics. By implementing the principle of general covariance through the requirement of invariance under active diffeomorphisms in loop quantum gravity, we find that the space of kinematical states of the gravitational field includes not only bosonic states, but also subspaces of fermionic and mixed statistics.

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Bekir Baytaş, Patrick L. Rodrigues, Nelson Yokomizo. 2026-02-12. Bosonic and fermionic statistics in nonperturbative quantum gravity. https://arxiv.org/abs/2602.11927

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