In quantum physics, what theorem links half-integer spin with fermionic behavior and integer spin with bosonic behavior?

The spin–statistics theorem links half-integer spin with fermionic behavior and integer spin with bosonic behavior in relativistic quantum field theory.

Particles with half-integer spin, such as electrons and quarks, obey Fermi–Dirac statistics and are described by antisymmetric exchange behavior. Particles with integer spin, such as photons and gluons, obey Bose–Einstein statistics and have symmetric exchange behavior.

The theorem depends on core assumptions including special relativity, locality, and a positive-definite probability interpretation. It is not merely an empirical classification of particles; it follows from the mathematical structure of relativistic quantum fields.

The theorem explains why electrons obey the exclusion principle while photons can occupy the same state in large numbers. It does not say that spin is literally a tiny classical rotation. Quantum spin is an intrinsic form of angular momentum.