Spin-statistics transmutation in relativistic quantum field theories of dyons

We analyse spin and statistics of quantum dyon fields, i.e. fields carryingboth electric and magnetic charge, in 3+1 space-time dimensions. It has beenshown long time ago that, at the quantum mechanical level, a composite dyonmade out of a magnetic pole of charge g and a particle of electric charge epossesses half-integral spin and fermionic statistics, if the constituents arebosons and the Dirac quantization condition $eg=2\pi n$ holds, with n odd. Thisphenomenon is called spin-statistics transmutation. We show that the samephenomenon occurs at the quantum field theory level for an elementary dyon.This analysis requires the construction of gauge invariant charged dyon fields.Dirac's proposal for such fields, relying on a Coulomb-like photon cloud, leadsto quantum correlators exhibiting an unphysical dependence on the Dirac-string.Recently Froehlich and Marchetti proposed a recipe for charged dyon fields,based on a sum over Mandelstam-strings, which overcomes this problem. Usingthis recipe we derive explicit expressions for the quantum field theorycorrelators and we provide a proof of the occurrence of spin-statisticstransmutation. The proof reduces to a computation of the self-linking numbersof dyon worldlines and Mandelstam strings, projected on a fixed timethree-space. Dyon composites are also analysed. The transmutation discussed inthis paper bares some analogy with the appearance of anomalous spin andstatistics for particles or vortices in Chern-Simons theories in 2+1dimensions. However, peculiar features appear in 3+1 dimensions e.g. in thespin addition rule.Comment: 32 pages, LaTeX, no figure