Quantum fields intertwining diffeomorphism group representations describing spinning particles
Canonical creation and annihilation fields describe particles obeying the statistics of bosons, fermions, and (in two-dimensional space) anyons. These fields can be constructed so as to intertwine, in the most geometrically natural way, unitary representations of a diffeomorphism group of physical space induced by characters of symmetric groups or braid groups. They then satisfy commutation relations, anticommutation relations, or $q$-commutation relations respectively. This talk will describe ongoing work with D. H. Sharp on the construction of quantum fields that intertwine diffeomorphism group representations describing particles with spin, induced by unitary representations of the general linear group.