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Springer eBooks

The Pauli Principle

Published May 24, 2007• 0 citations
Publisher
DOI
10.1007/978-0-387-37744-5_12

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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).

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The Pauli exclusion principle (PEP) and, more generally, the spin-statistics connection, is at the very basis of our understanding of matter. The PEP spurs, presently, a lively debate on its possible limits, deeply rooted in the very foundations of Quantum Field Theory. Therefore, it is extremely important to test the limits of its validity. Quon theory provides a suitable mathematical framework of possible 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 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 future plans to go beyond the actual limit by upgrading the experimental technique using vetoed new spectroscopic fast Silicon Drift Detectors. We mention as well the possibility of using a similar experimental technique to search for eventual X-rays generated as a signature of the spontaneous collapse of the wave function, predicted by continuous spontaneous localization type theories.

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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).
The Pauli exclusion principle (PEP) and, more generally, the spin-statistics connection, is at the very basis of our understanding of matter. The PEP spurs, presently, a lively debate on its possible limits, deeply rooted in the very foundations of Quantum Field Theory. Therefore, it is extremely important to test the limits of its validity. Quon theory provides a suitable mathematical framework of possible 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 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 future plans to go beyond the actual limit by upgrading the experimental technique using vetoed new spectroscopic fast Silicon Drift Detectors. We mention as well the possibility of using a similar experimental technique to search for eventual X-rays generated as a signature of the spontaneous collapse of the wave function, predicted by continuous spontaneous localization type theories.