Connection between the Wigner Inequalities and Analyticity and Unitarity

A lower bound on the momentum derivative of the phase shifts, $\frac{d{\delta }_l}{\mathrm{dk}}$, is derived from the combination of unitarity, crossing, and analyticity (in the domain resulting from axiomatic field theory). As an application, a lower bound for the ${\pi }^0{\pi }^0$ scattering length is deduced.