1. A Generalized Spin Statistics Theorem
Paul O’Hara
Istituto Universitario Sophia (FI)
Seminar organized within the project: ‘Hunt for the “impossible atoms”: the quest for a tiny violation of the Pauli Exclusion Principle. Implications for physics, cosmology and philosophy.’
ID 58158, funded by the
John Templeton Foundation
November 7, 2017

2. Contents Rotational invariance and spin-statistics
A Generalized spin-statistics theorem
Clifford Algebra and Majorana Fields
Experimental and Theoretical Evidence

3. Entangled Pairs A pair of spin entangled states is said to be coupled
Meaning of Coupling: Rotationally invariant quantum states can only occur in pairs. These pairs will be referred to as isotropically spin-correlated states (ISC) or coupled states
A system of n coupled and indistinguishable states obey the Fermi-Dirac statistics, while Bose-Einstein statistics follows if the coupling is broken.
Paired states ↔ Fermi-Dirac
Independent states ↔Bose-Einstein.

5. The structure of the statistical states
It follows from the coupling principle that multi-particles systems can be divided into two categories:
(1) Those containing Coupled Particles
(2) Those containing Decoupled (statistically independent) particles
(3) A mixture of both (para-statistics)
A statistical analysis of these categories applied to completely indistinguishable particles reduces to the Fermi-Dirac and Bose- Einstein statistics respectively.