Particle spin from representations of the diffeomorphism group

The semidirect productI∧K of Schwartz' spaceI of functions on ?³ with the groupK of diffeomorphisms of ?³ provides a model for quantum theory based on local currents. Certain unitary representations of ?^K are induced by representations of \(\overline {{\text{SL(3, }}\mathbb{R}{\text{)}}}\) . From the local currents in these representations, we construct the generators of local rigid rotations, with respect to which the Hilbert space decomposes into invariant subspaces of fixed spin carrying representations of local SU(2). The physical interpretation of this procedure is discussed.