  K\"ahler's geometric approach in which relativistic fermion fields are
treated as differential forms is applied in three spacetime dimensions. It is
shown that the resulting continuum theory is invariant under global
U($N)\otimes$U($N)$ field transformations, and has a parity-invariant mass
term, both symmetries shared in common with staggered lattice fermions. The
formalism is used to construct a version of the Thirring model with contact
interactions between conserved Noether currents. Under reasonable assumptions
about field rescaling after quantum corrections, a more general interaction
term is derived, sharing the same symmetries but now including terms which
entangle spin and taste degrees of freedom, which exactly coincides with the
leading terms in the staggered lattice Thirring model in the long-wavelength
limit. Finally truncated versions of the theory are explored; it is found that
excluding scalar and pseudoscalar components leads to a theory of six-component
fermion fields describing particles with spin 1, with fermion and antifermion
corresponding to states with definite circular polarisation. In the UV limit
only transverse states with just four non-vanishing components propagate.
Implications for the description of dynamics at a strongly interacting
renormalisation-group fixed point are discussed.
