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A interacting theory that violates CPT invariance necessarily violates Lorentz invariance. On the other hand, CPT invariance is not sufficient for out-of-cone Lorentz invariance. Theories that violate CPT by having different particle and antiparticle masses must be nonlocal.

- O W Greenberg
- 1999

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)

- O W Greenberg
- 2000

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)

- O W Greenberg
- 1997

I show that the spin-statistics theorem has been confused with another theorem that I call the spin-locality theorem. I also argue that the spin-statistics theorem properly depends on the properties of asymptotic fields which are free fields. In addition, I discuss how ghosts evade both theorems, give the basis of the spin-statistics theorem for fields… (More)

- S R Corley, O W Greenberg
- 1996

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)

- O W Greenberg
- 2005

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)

- O W Greenberg
- 2003

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)

- O W Greenberg
- 2008

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… (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)

- O W Greenberg
- 2004

We formulate Lorentz covariance of a quantum field theory in terms of covariance of time-ordered products (or other Green's functions). This formulation of Lorentz covariance implies spacelike local commutativity or anticom-mutativity of fields, sometimes called microscopic causality or microcausality. With this formulation microcausality does not have to… (More)