  A coherent state representation for the electrons of ordered antiferromagnets
is used to derive effective Hamiltonians for the dynamics of holes in such
systems. By an appropriate choice of these states, the constraint of forbidden
double occupancy can be implemented rigorously. Using these coherent states,
one arrives at a path integral representation of the partition function of the
systems, from which the effective Hamiltonians can be read off. We apply this
method to the t-J model on the square lattice and on the triangular lattice. In
the former case, we reproduce the well-known fermion-boson Hamiltonian for a
hole in a collinear antiferromagnet. We demonstrate that our method also works
for non-collinear antiferromagnets by calculating the spectrum of a hole in the
triangular antiferromagnet in the self-consistent Born approximation and by
comparing it with numerically exact results.
