Statistics and UV-IR Mixing with Twisted Poincare Invariance

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We elaborate on the role of quantum statistics in twisted Poincare invariant theories. It is shown that, in order to have twisted Poincare group as the symmetry of a quantum theory, statistics must be twisted. It is also confirmed that the removal of UV-IR mixing (in the absence of gauge fields) in such theories is a natural consequence.
13 pages, LaTeX; typos corrected

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