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The existence of antiparticles seems to forbid violations of statistics

A. B. Govorkov

Published Jan 1, 1993• 0 citations
OpenAlex

Abstract

I try to prove the impossibility of small violations of Fermi- and Bose-statistics even within the nonlocal quantum field theory corresponding to the infinite statistics. The existence of antiparticles plays the crucial role in this proof.

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DOES THE EXISTENCE OF ANTIPARTICLES FORBID VIOLATIONS OF STATISTICS?

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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 fˉ \bar ffˉ​ 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.
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.