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Modern Physics Letters A

DOES THE EXISTENCE OF ANTIPARTICLES FORBID VIOLATIONS OF STATISTICS?

A. B. Govorkov

Published Aug 30, 1992• 7 citations
Publisher

Abstract

We consider a field theory based on the bilinear q-mutator relations and continuously transforming into the usual theory. For the free fields we show that the violations of usual (Fermi- or Bose-) statistics even within this "slightly" nonlocal theory are incompatible with the existence of antiparticles and the positive definiteness of norms of the state vectors in the Fock representation.

DOI
10.1142/s0217732392003815

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We consider a field theory based on the bilinear q-mutator relations and continuously transforming into the usual theory. For the free fields we show that the violations of usual (Fermi- or Bose-) statistics even within this "slightly" nonlocal theory are incompatible with the existence of antiparticles and the positive definiteness of norms of the state vectors in the Fock representation.
I discuss the statistics of "quons" (pronounced to rhyme with muons), particles whose annihilation and creation operators obey the qqq-deformed commutation relation (the quon algebra or qqq-mutator) which interpolates between fermions and bosons. Topics discussed include representations of the quon algebra, proof of the TCP\mathrm{TCP}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.
Conventional proofs of the spin–statistics theorem either use relativistic quantum field theory or concern field theory solitons. We here construct new proofs of this theorem for spinning particles. They are extensions of previous work on spinless particles and require neither relativity nor field theory. They do, however, assume certain continuity conditions involving the existence of antiparticles. Non-Abelian statistics, such as parastatistics and braid statistics of order 2 or more, are excluded in our framework.
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.