Spin and Statistics

Catalina Curceanu, John D. Gillaspy, Robert C. Hilborn

This Resource Letter provides a guide to the literature on the spin-statistics connection and related issues such as the Pauli exclusion principle and particle indistinguishability. Journal articles and books are cited for the following topics: basic resources, general aspects of spin-statistics, the spin-statistics theorem, theories that go beyond the standard spin-statistics theorem, and experimental tests of the spin-statistics theorem and the symmetrization postulate.

Aleš Kováč

This work develops three interconnected pillars of Triadic Mesh Dynamics (TMD): emergent spin, the statistical behaviour of particles, and their unification in the TMD spin–statistics theorem.In TMD, spin arises as a local orientational rhythm of triads in the discrete network, while particle statistics follow from topological constraints on sharing orientation between triads.We show that only two stable classes of orientational dynamics exist: locked configurations corresponding to fermions and shared configurations corresponding to bosons.This dichotomy leads to a fully mechanical explanation of the link between spin and statistics, replacing the axiomatic structure of quantum field theory with a geometric–topological mechanism.The result is a physically transparent interpretation in which spin and statistics emerge from the same orientational dynamics of the triadic network.

Jason Twamley

Krzysztof Byczuk, Józef Spałek

We derive the statistical distribution functions for the Hubbard chain with infinite Coulomb repulsion among particles and for the statistical spin liquid with an arbitrary magnitude of the local interaction in momentum space. Haldane's statistical interaction is derived from an exact solution for each of the two models. In the case of the Hubbard chain, the charge (holon) and the spin (spinon) excitations decouple completely and are shown to behave statistically as fermions and bosons, respectively. In both cases the statistical interaction must contain several components; a rule for the particles with the internal symmetry.

A. Zee