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arXiv:1707.05158

A generalized spin statistics theorem

Paul O’Hara

Published Jul 13, 2017• 0 citations
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Abstract

In this article we generalize the spin statistics theorem and show that a state obeys Fermi-Dirac statistics if and only if the state is invariant under the action of $SL(n,C)$. We also briefly discuss the experimental evidence and how the theorem relates to spin entanglement.

DOI
10.48550/arxiv.1707.05158

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In this article we generalize the spin statistics theorem and show that a state obeys Fermi-Dirac statistics if and only if the state is invariant under the action of SL(n,C)SL(n,C)SL(n,C). We also briefly discuss the experimental evidence and how the theorem relates to spin entanglement.
We define statistics of quantum mechanical particles, obtaining the Bose–Einstein and Fermi–Dirac varieties of indistinguishable particles. After finding the rotation and Lorentz matrices in different Lorentz representations, we describe the spin-statistics theorem, relating fermions with half-integer spin and bosons with integer spin. We explain two simple proofs and say some words on two others. We end by discussing symmetries in more generality, and we discuss the fact that internal symmetries must commute with spacetime ones, due to the Coleman–Mandula theorem.
With the advent of general relativity and quantum mechanics, physics has in many cases shifted the emphasis from dynamics to symmetry principles associated with different types of mathematical groups. We speak of the group structure of crystals, the group invariants of the equations of motion, the group classification of elementary particles, and also of the group homeomorphisms of fractals. The objective of this article is to show how the group theoretical structure of entanglement can be used to classify atomic and molecular structure. The article begins by establishing a working definition of entanglement and then using it to derive the Pauli-exclusion principle by showing that Fermi-Dirac statistics can be considered as an entangled state invariant under the action of the SL(n, C)With the advent of general relativity and quantum mechanics, physics has in many cases shifted the emphasis from dynamics to symmetry principles associated with different types of mathematical groups. We speak of the group structure of crystals, the group invariants of the equations of motion, the group classification of elementary particles, and also of the group homeomorphisms of fractals. The objective of this article is to show how the group theoretical structure of entanglement can be used to classify atomic and molecular structure. The article begins by establishing a working definition of entanglement and then using it to derive the Pauli-exclusion principle by showing that Fermi-Dirac statistics can be considered as an entangled state invariant under the action of the SL(n,C)SL(n, C)SL(n,C) group. Based on this, a group classification scheme of entangled states is proposed to distinguish atomic and molecular structures associated with chemical bonds. group. Based on this, a group classification scheme of entangled states is proposed to distinguish atomic and molecular structures associated with chemical bonds.