  We consider BF-type topological field theory coupled to non-dynamical
particle and string sources on spacetime manifolds of the form
$\IR^1\times\MT$, where $\MT$ is a 3-manifold without boundary. Canonical
quantization of the theory is carried out in the Hamiltonian formalism and
explicit solutions of the Schr\"odinger equation are obtained. We show that the
Hilbert space is finite dimensional and the physical states carry a
one-dimensional projective representation of the local gauge symmetries. When
$\MT$ is homologically non-trivial the wavefunctions in addition carry a
multi-dimensional projective representation, in terms of the linking matrix of
the homology cycles of $\MT$, of the discrete group of large gauge
transformations. The wavefunctions also carry a one-dimensional representation
of the non-trivial linking of the particle trajectories and string surfaces in
$\MT$. This topological field theory therefore provides a phenomenological
generalization of anyons to (3 + 1) dimensions where the holonomies
representing fractional statistics arise from the adiabatic transport of
particles around strings. We also discuss a duality between large gauge
transformations and these linking operations around the homology cycles of
$\MT$, and show that this canonical quantum field theory provides novel quantum
representations of the cohomology of $\MT$ and its associated motion group.
