Topological spin-statistics relation in quantum field theory

A. P. Balachandran, Alan Daughton, Zixuan Gu +3 more

A spin-statistics theorem for spinning particles in d is proved without using relativity or field theory, but assuming the existence of antiparticles. The theorem excludes nonabelian statistics such as parastatistics of order 2 and more for d ⩾ 3 and statistics based on nonabelian representations of the braid groups for d = 2.

Thomas Klein Kvorning

Andreas Wipf

A. P. Balachandran

We review the theory of statistics of identical systems in terms of the properties of the classical configuration space. Special emphasis is placed on the influence of the connectivity of this space on quantum statistics. The theory shows that exotic statistical systems, such as those obeying fractional statistics, can occur in all dimensions. Particle statistics in one dimension involves novel features particular to this dimension and these are briefly described. The proof of a topological spin-statistics theorem which avoids field theory or relativity is also outlined.

Sami M. Al-Jaber

Michael I Aksman

The Spin-Statistics Theorem and the Pauli Exclusion Principle are conventionally introducedas irreducible phenomenological axioms of relativistic quantum field theory, proved via thePCT theorem and the connection between spin and commutation relations. This paperpresents a complete, rigorous geometric derivation of fermionic antisymmetry directly fromthe macroscopic hydrodynamics of the DSM-861 vacuum. All topological constraints andN-particle statistics are identically derived without open conjectures.