Quantum Statistics Forbids Particle Exchange Statistics beyond Bosons and Fermions in 3D

TL;DR

This paper proves a fundamental no-go theorem showing that in three-dimensional quantum systems, particles can only obey bosonic or fermionic statistics, ruling out any other exchange statistics.

Contribution

It establishes a rigorous theoretical proof that rules out exotic particle exchange statistics beyond bosons and fermions in three dimensions.

Findings

Higher-dimensional symmetric group representations do not produce new exchange statistics.

The theorem links quantum Hilbert space structure with microstate counting.

Excludes the possibility of anyonic or other non-boson/fermion statistics in 3D.

Abstract

Quantum matter in three spatial dimensions is observed to consist exclusively of bosons and fermions. Whether this empirical fact follows from basic consistency requirements of quantum theory itself or must be imposed as an additional principle has for 80 years remained a fundamental conceptual gap. Here we close this gap by establishing a no-go theorem that excludes any particle exchange statistics beyond bosons and fermions in three dimensions. We identify the consistency conditions linking the many-body Hilbert-space structure of quantum mechanics with the statistical microstate counting of indistinguishable particles. As a corollary, we demonstrate that higher-dimensional representations of the symmetric group cannot give rise to genuinely distinct particle exchange statistics in any spatial dimension.