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Physical Review A

Thermodynamical implications of a violation of the Pauli principle

V. Rahal, Alessandro Campa

Published Oct 1, 1988• 18 citations
Publisher

Abstract

We suggest a mechanism allowing the introduction of a small violation of the Pauli exclusion principle. Within this framework, we compute the grand partition function for a free-electron gas in a metal. We discuss the physical implications of our results and infer an upper bound on the violation parameter.
DOI
10.1103/physreva.38.3728

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The Pauli exclusion principle can be stated as inequality ≤1\le 1≤1 for the electron density matrix ρρρ. Nowadays it is replaced by skew symmetry of the multi-electron wave function. The replacement leads to numerous additional constraints on ρρρ, which are discussed in this letter together with their physical implications, in particular for spin magnetic moment of a multi-electron system.
The modern state of the Pauli exclusion principle is shortly discussed. We describe the discovery by Pauli, his principle for electrons, and how it was generalized for all elementary particles in the framework of quantum mechanics. The motivations and theoretical conceptions that induced the experiments for verification of the Pauli exclusion principle are analyzed. The results and methodology of two different types of experiments are discussed: (1) the search of unusual atoms and nuclei in the stable non-Pauli states, and (2) the experiments in which the emitted radiation of non-Pauli transitions is measured. In conclusion, the comments on the discussed experiments that follow from the general quantum mechanical conceptions and group theory are formulated.
The Pauli exclusion principle has been tested for atomic electrons giving a lifetime for such a violation, per iodine atom, of > 2 \ifmmode\times\else\texttimes\fi{} 1027{10}^{27}1027 sec. This result is compared to a normal electromagnetic dipole transition, and a limit is set on a possible symmetric wave-function admixture to a KKK-shell electron wave function.
The Pauli exclusion principle (PEP) and, more generally, the spin-statistics connection, is at the very basis of our understanding of matter and Nature. The PEP spurs, presently, a lively debate on its possible limits, deeply rooted in the very foundations of Quantum Mechanics and Quantum Field Theory. Therefore, it is extremely important to test the limits of its validity. Quon theory provides a suitable mathematical framework of possible small violation of PEP, where the q violation parameter translates into a probability of violating PEP. Experimentally, setting a bound on PEP violation means confining the q-parameter to a value very close to either 1 (for bosons) or −1 (for fermions). The VIP (VIolation of the Pauli exclusion principle) experiment established a limit on the probability that PEP is violated by electrons, using the very clean method of searching for PEP forbidden atomic transitions in copper. We describe the experimental method, the obtained results, both in terms of the q-parameter and as probability of PEP violation, we briefly discuss the results and present plans to go beyond the actual limit by upgrading the experimental technique using vetoed new spectroscopical fast Silicon Drift Detectors. We discuss as well the possibility of using a similar experimental technique to search for X-rays generated as a signature of the spontaneous collapse of the wave function, predicted by continous spontaneous localization type theories.
In a recent paper, we proposed a ``paronic'' field-theory framework for possible small deviations from the Pauli exclusion principle. This theory cannot be represented in a positive-metric (Hilbert) space. Nonetheless, the issue of possible small violations of the exclusion principle can be addressed in the framework of quantum mechanics, without being connected with a local quantum field theory. In this paper, we discuss the phenomenology of small violations of both Fermi and Bose statistics. We consider the implications of such violations in atomic, nuclear, particle, and condensed-matter physics and in astrophysics and cosmology. We also discuss experiments that can detect small violations of Fermi and Bose statistics or place stringent bounds on their validity.