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An Interpolation between Bose and Fermi Oscillators
ABSTRACT. After a brief mention of Bose and Fermi oscillators and of particles
which obey other types of statistics, including intermediate statistics,
parastatistics, paronic statistics, anyon statistics and infinite 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. I emphasize that the
operator for interaction with an external source must be an effective Bose
operator in all cases. To accomplish this for parabose, parafermi and quon
operators, I introduce parabose, parafermi and quon Grassmann numbers,
respectively. I also discuss interactions of non-relativistic quons,
quantization of quon
fields with antiparticles, calculation of vacuum matrix elements of relativistic
quon fields, demonstration of the TCP theorem, cluster decomposition, and Wick's
theorem for relativistic quon fields, and the failure of local commutativity of
observables for relativistic quon fields. I conclude with the bound on the
parameter $q$ for electrons due to the Ramberg-Snow experiment.