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Physical Review Letters

Local Quantum Field Theory of Possible Violation of the Pauli Principle

Oscar Wallace Greenberg, Rabindra Nath Mohapatra

Published Nov 30, 1987• 145 citations
Publisher

Abstract

We generalize to a local relativistic quantum field theory a proposal of Ignatiev and Kuzmin for a single oscillator which has small violation of the Pauli principle and thus provide a theoretical framework which, for the first time, allows quantitative tests of the Pauli principle. Our theory provides a continuous interpolation between fully hindered parafermi statistics of order 2 ($\ensuremath{\beta}=0$), which is equivalent to Fermi statistics, and ordinary parafermi statistics of order 2 ($\ensuremath{\beta}=1$). We suggest two types of experiments which can place bounds on $\ensuremath{\beta}$.

DOI
10.1103/physrevlett.59.2507

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We generalize to a local relativistic quantum field theory a proposal of Ignatiev and Kuzmin for a single oscillator which has small violation of the Pauli principle and thus provide a theoretical framework which, for the first time, allows quantitative tests of the Pauli principle. Our theory provides a continuous interpolation between fully hindered parafermi statistics of order 2 (\ensuremathβ=0\ensuremath{\beta}=0\ensuremathβ=0), which is equivalent to Fermi statistics, and ordinary parafermi statistics of order 2 (\ensuremathβ=1\ensuremath{\beta}=1\ensuremathβ=1). We suggest two types of experiments which can place bounds on \ensuremathβ\ensuremath{\beta}\ensuremathβ.
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.
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.
A new test theory for describing tests of fundamental principles of Special and General Relativity is presented. Using a generalised Pauli equation which may be based on a generalised Dirac equation, possible violations of local Lorentz invariance and local position invariance on the quantum level are described. On the quantum level there are more possibilities to violate these principles than on the classical level. The corresponding terms can be tested by Hughes–Drever type experiments or by atom interferometry. It is proposed that an atom interferometric test of Local Position Invariance will give a three order improvement of existing estimates. 1
A new test theory for describing tests of fundamental principles of special and general relativity is presented. Using a generalized Pauli equation which may be based on a generalized Dirac equation, possible violations of local Lorentz invariance and local position invariance on the quantum level are described. On the quantum level there are more possibilities to violate these principles than on the classical level. The corresponding terms can be tested by Hughes-Drever-type experiments or by atom interferometry. It is proposed that an atom interferometric test of local position invariance will give a three orders of magnitude improvement over existing estimates.
A new test theory for describing tests of fundamental principles of special and general relativity is presented. Using a generalized Pauli equation which may be based on a generalized Dirac equation, possible violations of local Lorentz invariance and local position invariance on the quantum level are described. On the quantum level there are more possibilities to violate these principles than on the classical level. The corresponding terms can be tested by Hughes-Drever-type experiments or by atom interferometry. It is proposed that an atom interferometric test of local position invariance will give a three orders of magnitude improvement over existing estimates. PACS numbers: 0480C, 0375D, 0365