When identical particles cease to be indistinguishable: violation of statistics in quantum spacetime

Abstract

Quantum gravity may modify the fundamental symmetries that govern identical particles. In particular, noncommutative spacetime frameworks predict deformations of Bose and Fermi statistics. Here we develop a relativistic quantum field theory based on the most general oscillator algebra compatible with $\theta$-deformed Poincaré symmetry. This construction generalizes twisted statistics to a class of quon-like deformations allowing non-involutive particle exchange. We show that the resulting theory is consistent at both the free and interacting levels and derive its implications for atomic systems. Purely twisted statistics predicts Pauli-forbidden atomic transitions at rates incompatible with experiments. By contrast, a class of quon deformations suppresses such processes by powers of the noncommutativity scale, but only if superselection rules between permutation-symmetry sectors are violated. This implies an effective breakdown of particle indistinguishability and provides theoretical motivation for high-precision experimental tests of the Pauli exclusion principle.