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Small Violations of Statistics

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Confluence of Cosmology, Massive Neutrinos, Elementary Particles, and Gravitation

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Abstract

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.

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Authors and Affiliations

  1. Center for Theoretical Physics Department of Physics, University of Maryland, College Park, MD, 20742-4111

    O. W. Greenberg

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  1. O. W. Greenberg
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Editors and Affiliations

  1. Global Foundation, Inc., Coral Gables, Florida

    Behram N. Kursunoglu

  2. Florida International University, Miami, Florida

    Stephan L. Mintz

  3. University of Miami, Coral Gables, Florida

    Arnold Perlmutter

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© 2002 Kluwer Academic Publishers

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Greenberg, O.W. (2002). Small Violations of Statistics. In: Kursunoglu, B.N., Mintz, S.L., Perlmutter, A. (eds) Confluence of Cosmology, Massive Neutrinos, Elementary Particles, and Gravitation. Springer, Boston, MA. https://doi.org/10.1007/0-306-47094-2_17

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  • DOI: https://doi.org/10.1007/0-306-47094-2_17

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-306-46208-5

  • Online ISBN: 978-0-306-47094-3

  • eBook Packages: Springer Book Archive

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