A Generalized Spin Statistics Theorem

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Presentation transcript:

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

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

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.

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.