= Moduli-space approximation for solitons
{title2=$L_{\rm eff}=\tfrac12g_{ab}(q)\dot q^a\dot q^b-E_0$}
= Moduli-space approximation
{synonym}
Substitute a static soliton family with slowly time-dependent <collective coordinates> into the action. The kinetic energy induces a <Riemannian metric> $g$ on the family, after imposing any <Gauss law constraint in gauge theory> constraint and projecting out gauge directions. If its static energy is constant, the <Euler-Lagrange equations> are the <geodesic> equations of $g$. An approximately flat family instead carries a potential $V(q)$. This approximation neglects excitations of the other field modes and is justified only when their effects are small on the time and energy scales studied.
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