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.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.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsApr 1, 1989113 citations

Particles with small violations of Fermi or Bose statistics

Oscar Wallace Greenberg

I discuss the statistics of "quons" (pronounced to rhyme with muons), particles whose annihilation and creation operators obey the $q$ -deformed commutation relation (the quon algebra or $q$ -mutator) which interpolates between fermions and bosons. Topics discussed include representations of the quon algebra, proof of the $\mathrm{TCP}$ 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.I discuss the statistics of "quons" (pronounced to rhyme with muons), particles whose annihilation and creation operators obey the $q$-deformed commutation relation (the quon algebra or $q$-mutator) which interpolates between fermions and bosons. Topics discussed include representations of the quon algebra, proof of the $\mathrm{TCP}$ 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.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsJun 15, 1991376 citations

Quantum statistics of interacting particles

Elliot W. Montroll, John Ward

Il Nuovo CimentoMar 1, 195810 citations

Elementary particle statistics reconsidered

Domenico Costantini, Ubaldo Garibaldi

Physics Letters ADec 1, 198813 citations

Small Violations of Statistics

Oscar Wallace Greenberg

There are two motivations to consider statistics that are neither Bose nor Fermi: (1) to extend the framework of quantum theory and of quantum field theory, and (2) to provide a quantitative measure of possible violations of statistics. After reviewing tests of statistics for various particles, and types of statistics that are neither Bose nor Fermi, I discuss quons, particles characterized by the parameter q, which permit a smooth interpolation between Bose and Fermi statistics; q=1 gives bosons, q=−1 gives fermions. The new result of this talk is work by Robert C. Hilborn and myself that gives a heuristic argument for an extension of conservation of statistics to quons with trilinear couplings of the form $\bar f$ fb , where f is fermion-like and b is boson-like. We showed that q f 2=q b. In particular, we related the bound on qg for photons to the bound on q e for electrons, allowing the very precise bound for electrons to be carried over to photons. An extension of our argument suggests that all particles are fermions or bosons to high precision.There are two motivations to consider statistics that are neither Bose nor Fermi: (1) to extend the framework of quantum theory and of quantum field theory, and (2) to provide a quantitative measure of possible violations of statistics. After reviewing tests of statistics for various particles, and types of statistics that are neither Bose nor Fermi, I discuss quons, particles characterized by the parameter q, which permit a smooth interpolation between Bose and Fermi statistics; q=1 gives bosons, q=−1 gives fermions. The new result of this talk is work by Robert C. Hilborn and myself that gives a heuristic argument for an extension of conservation of statistics to quons with trilinear couplings of the form $$ \bar f$$ fb , where f is fermion-like and b is boson-like. We showed that q f 2=q b. In particular, we related the bound on qg for photons to the bound on q e for electrons, allowing the very precise bound for electrons to be carried over to photons. An extension of our argument suggests that all particles are fermions or bosons to high precision.

arXiv:quant-ph/9903069Kluwer Academic Publishers eBooksDec 19, 20053 citations

I discuss the statistics of "quons" (pronounced to rhyme with muons), particles whose annihilation and creation operators obey the

q

-deformed commutation relation (the quon algebra or

q

-mutator) which interpolates between fermions and bosons. Topics discussed include representations of the quon algebra, proof of the

\mathrm{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.

\bar f

fb , where f is fermion-like and b is boson-like. We showed that q f 2=q b. In particular, we related the bound on qg for photons to the bound on q e for electrons, allowing the very precise bound for electrons to be carried over to photons. An extension of our argument suggests that all particles are fermions or bosons to high precision.