  A field theory describing the low-energy, long-wavelength sector of an
incommensurate, spiral magnetic phase is derived from a spin-fermion model that
is commonly used as a microscopic model for high-temperature superconductors.
After integrating out the fermions in a path-integral representation, a
gradient expansion of the fermionic determinant is performed. This leads to an
O(3)$\otimes$O(2)-symmetric quantum nonlinear $\sigma$ model, where the doping
dependence is explicitly given by generalized fermionic susceptibilities which
enter into the coupling constants of the $\sigma$ model and contain the
fermionic band-structure that results from the spiral background. A stability
condition of the field theory self-consistently determines the spiral
wavevector as a function of the doping concentration. Furthermore, terms of
topological nature like the $\theta$-vacuum term in (1+1)-dimensional nonlinear
$\sigma$ models are obtained for the plane of the spiral.
