O. Greenberg

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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(More)
I discuss theories of violations of statistics, including intermediate statistics, parastatistics, parons, and quons. I emphasize quons, which allow small violations of statistics. I analyze the quon algebra and its representations, implications of the algebra including the observables allowed by the superselection rule separating inequivalent(More)
We consider the nonrelativistic quantum mechanics of a model of two spinless fermions interacting via a two-body potential. We introduce quantum fields associated with the two particles as well as the expansion of these fields in asymptotic " in " and " out " fields, including such fields for bound states, in principle. We limit our explicit discussion to a(More)
The star commutator of : φ(x) ⋆ φ(x) : with : φ(y) ⋆ φ(y) : fails to vanish at equal times and thus also fails to obey microcausality at spacelike separation even for the case in which θ 0i = 0. The failure to obey microcausality for this sample observable implies that this form of noncommutative field theory fails to obey microcausality in general. This(More)
G. Lüders and W. Pauli proved the CPT theorem based on Lagrangian quantum field theory almost half a century ago. R. Jost gave a more general proof based on " axiomatic " field theory nearly as long ago. The axiomatic point of view has two advantages over the Lagrangian one. First, the ax-iomatic point of view makes clear why CPT is fundamental–because it(More)
The quon algebra gives a description of particles, " quons, " that are neither fermions nor bosons. The parameter q attached to a quon labels a smooth interpolation between bosons, for which q = +1, and fermions, for which q = −1. Wigner and Ehrenfest and Oppenheimer showed that a composite system of identical bosons and fermions is a fermion if it contains(More)