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arXiv:quant-ph/0101135

Rotational invariance and the Pauli exclusion principle

Paul O’Hara

Published Jan 29, 2001• 2 citations
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Abstract

In this article, the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This will be referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and those that do not. Surprisingly, it would seem that Fermi-Dirac statistics follows as a consequence of this coupling while the Bose-Einstein follows by breaking it. Finally, the experimental evidence to justify the above classification will be discussed. Pacs: 3.65.Bz, 5.30 d, 12.40.Ee

DOI
10.48550/arxiv.quant-ph/0101135

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In this article, the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This will be referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and those that do not. Surprisingly, it would seem that Fermi-Dirac statistics follows as a consequence of this coupling while the Bose-Einstein follows by breaking it. Finally, the experimental evidence to justify the above classification will be discussed. Pacs: 3.65.Bz, 5.30 d, 12.40.Ee
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 uses 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 SLnC group. A group classification scheme of entangled states is proposed to distinguish atomic and molecular bonds in chemistry. We conclude by discussing the possible use of interferometry in quantum computing.
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.
The spin-statistics theorem is generalized to include quantum entanglement. Specifically, within the context of spin entanglement, we prove that isotropically spin-correlated (ISC) states must occur in pairs. This pairing process can be composed of parallel or anti-parallel states. Consequently, the article proposes using ISC states as a unifying principle to explain better Bose-Einstein condensates, the theory of superconductivity, and molecular and atomic orbitals, all of which involve a pairing process. The theoretical framework is established in sections 1 and 2. The other qualitative sections focus primarily on the experimental evidence to support the theory.
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In the framework of recently developed description of the non-relativistic constrained quantum mechanics of systems of NNN-Coulombically interacting electrons [Phys. Rev. {\bf A} 78, 032503 (2008)], we study the relation between spin and statistics in two-electron systems. We find that that the Fermi-Dirac statistics implies lowering of the spatial SO(3) symmetry of the wave-functions of electronic states to Abelian SO(2) rotational subgroup, which is accompanied by reduction of the number of spatial degrees-of-freedom from 6 to 5. We find that the relation between spin and statistics is necessarily related to the anti-symmetry of the relative phase of the spatial part of the two-electron wave-function. We find that it leads to distinct classification of the electronic states according to their relative orbital parity (−1)m(-1)^m(−1)m and total spin S={0,1}S=\{0,1\}S={0,1}. We also find that the Pauli exclusion principle is realized dynamically due to Coulombic interaction between the particles. We find that the broken rotation symmetry of the wave-functions of the electronic states can be restored dynamically, due to conservation of the Laplace-Runge-Lenz vector. We demonstrate that the proposed theoretical description is internally consistent and predictive, and we find the non-equivalence of the above mention representation to the conventional Schr\{o}dinger picture for the description of the quantum dynamics in Coulombic systems with more than one electron.