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Is a weak violation of the Pauli principle possible

A. Yu. Ignat'ev, V.A. Kuzmin

Published Sep 1, 1987• 2 citations
OpenAlex

Abstract

We examine models in which there is a weak violation of the Pauli principle. A simple algebra of creation and annihilation operators is constructed which contains a parameter ..beta.. and describes a weak violation of the Pauli principle (when ..beta.. = 0 the Pauli principle is satisfied exactly). The commutation relations in this algebra turn out to be trilinear. A model based on this algebra is described. It allows transitions in which the Pauli principle is violated, but the probability of these transitions is suppressed by the quantity ..beta../sup 2/ (even though the interaction Hamiltonian does not contain small parameters).

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We examine models in which there is a weak violation of the Pauli principle. A simple algebra of creation and annihilation operators is constructed which contains a parameter ..beta.. and describes a weak violation of the Pauli principle (when ..beta.. = 0 the Pauli principle is satisfied exactly). The commutation relations in this algebra turn out to be trilinear. A model based on this algebra is described. It allows transitions in which the Pauli principle is violated, but the probability of these transitions is suppressed by the quantity ..beta../sup 2/ (even though the interaction Hamiltonian does not contain small parameters).
Recently Ignatiev and Kuzmin (1988) developed a theoretical model to implement small violations of the Pauli principle. The authors remark that the Pauli principle is unique among discrete symmetries, and that in consequence any apparent violation actually signals new physical degrees of freedom, with no violation of the Pauli principle. They construct an algebraic model which incorporates the algebra of Ignatiev and Kuzmin and leads to the same apparent violations, yet preserves the Pauli principle. Their algebra is that of a Jordan pair, an algebraic concept which provides a natural framework for structures that do not assume bilinear commutation relations.
I discuss the statistics of "quons" (pronounced to rhyme with muons), particles whose annihilation and creation operators obey the qqq-deformed commutation relation (the quon algebra or qqq-mutator) which interpolates between fermions and bosons. Topics discussed include representations of the quon algebra, proof of the TCP\mathrm{TCP}TCP theorem and clustering, violation of the usual locality properties, and experimental constraints on violations of the Pauli exclusion principle (i.e., Fermi statistics) and of Bose statistics.
The Pauli exclusion principle (PEP) is one of the basic principles of modern physics and, even if there are no compelling reasons to doubt its validity, it is still debated today because an intuitive, elementary explanation is still missing, and because of its unique stand among the basic symmetries of physics. The present Letter reports a new limit on the probability that PEP is violated by electrons, in a search for an anomalous K α line in copper: the presence of this line in the soft X-ray copper fluorescence would signal a transition to a ground state already occupied by 2 electrons. The obtained value, 1 2 β 2 ⩽ 4.5 × 10 −28 , improves the existing limit by almost two orders of magnitude.