  Solitons in classical field theories correspond to states in quantum field
theories. If the spatial dimension is infinite, then momentum eigenstates are
not normalizable. This leads to infrared divergences, which are generally
regularized via wave packets or by compactification. However, in some
applications both possibilities are undesirable. In the present note, we
introduce a finite inner product on translation-invariant kink states that
allows us to compute probabilities involving these nonnormalizable states.
Essentially, it is the quotient of the usual inner product by the translation
group. We present a surprisingly simple formula for the reduced inner product,
which requires no knowledge of the zero-mode dependence of the states but
includes a correction which accounts for the mixing between zero modes and
normal modes as the kink moves. As an application, we show that initial and
final state corrections to meson multiplication vanish. However, we find that
the pole of the subleading term in the initial state requires an infinitesimal
imaginary shift.
