  We consider the O(3) or CP(1) nonlinear sigma model as an effective field
theory in a derivative expansion, with the most general Lagrangian that obeys
O(3), parity and Lorentz symmetry. We work out the complete list of possible
operators (terms) in the Lagrangian and eliminate as many as possible using
integrations by parts. We further show at the four-derivative level, that the
theory can be shown to avoid the Ostrogradsky instability, because the
dependence on the d'Alembertian operator or so-called box, can be eliminated by
a field redefinition. Going to the six-derivative order in the derivative
expansion, we show that this can no longer be done, unless we are willing to
sacrifice Lorentz invariance. By doing so, we can eliminate all dependence on
double time derivatives and hence the Ostrogradsky instability or ghost,
however, we unveil a remaining dynamical instability that takes the form either
as a spiral instability or a runaway instability and estimate the critical
field norm, at which the instability sets off.
