We calculate nonperturbatively and for small $Q$ the cross section $\sigma \mathrm{}\left(Q\right)\mathrm{}$ for a scattering process to occur with loss of four-momentum $Q$ to unobserved photons, a quantity which may be measured by observing the net recoil to all other particles. The calculation proceeds by means of a threshold theorem which asserts that for small $Q$, $\sigma \mathrm{}\left(Q\right)\mathrm{}\sim {\sigma }_{0}P\left(Q\right)\mathrm{}$, where ${\sigma }_0$ is independent of $Q$, and $P\left(Q\right)\mathrm{}$ is the spectral of the coherent state $\Psi$ of bremsstrahlung photons defined by $a^{\mu }\mathrm{}\left(k\right)\mathrm{}\Psi =i{\left(2\mathrm{}\pi \right)}^{-\frac{3}{2}}\Sigma a^{}{u}_a^{\mu }{\left(u_a·k\right)}^{-1\mathrm{}}\Psi$, where $a^{\mu }\mathrm{}\left(k\right)\mathrm{}$ is the annihilation operator for a photon of four-momentum $k$, and $e_a$ and $u_a$ are the charges and four-velocities of the scattered charged particles. Although $\Psi$ is not in the Fock space, the evaluation of $P\left(Q\right)=〈\Psi ,{\delta }^4(Q-P_{\mathrm{op}})\Psi 〉$, where $P_{\mathrm{op}}$ is the operator of total electromagnetic four-momentum, is straightforward. The resulting function $P\left(Q\right)\mathrm{}$ simplifies if $Q$ is near the light cone, where the bulk of the probability is in fact located, $P\left(Q\right)\mathrm{}\sim \theta \left(Q^0\right)\theta \left(Q^2\right){\left[\Gamma \mathrm{}\right(1+B\left)\right]}^{-1\mathrm{}}B{\left(\frac{Q^2}{2}\right)}^{B-1\mathrm{}}{I}_0\mathrm{}\left(Q\right)\mathrm{}\exp \mathrm{}\left[F\right(Q\left)\right]$, where $I_0\mathrm{}\left(Q\right)=-{\left(2\mathrm{}\pi \right)}^{-3\mathrm{}}{\left[\Sigma a^{}{e}_a{u}_a{\left(u_a·Q\right)}^{-1\mathrm{}}\right]}^2>0\mathrm{}$, $B=\int d\hat{k} I_0(Q^0=1, \overrightarrow{Q}=\hat{k})$, and $F\left(Q\right)\mathrm{}$ is given explicitly in the text, satisfies $F\left(\lambda Q\right)=F\left(Q\right)-B \ln \lambda$, and is a smooth function as the light cone is approached. The spectral function exhibits two scaling laws, one governing the approach to the origin along a ray ${\lim }_{\lambda \to 0}{\lambda }^{4-B}\sigma \left(\lambda Q\right)={\sigma }_{0}P\left(Q\right)\mathrm{}$, the other governing the approach to the light cone at fixed energy $Q^0=E$ and angle $\hat{k}{\lim }_{\mathrm{}\left|Q\right|\mathrm{}\to E}\left[{\mathrm{}(E-|\mathrm{}\overrightarrow{Q}\mathrm{}\left|\right)\mathrm{}}^{1-B}P\right(E,\overrightarrow{Q}\left)\right]=\mathrm{const}\times {\left[\Gamma \mathrm{}\right(1+B\left)\right]}^{-1\mathrm{}}B{E}^{B-1\mathrm{}}{I}_0\mathrm{}\left(k\right)\mathrm{}\exp \mathrm{}\left[F\right(k\left)\right]$, where $k=(E,E\hat{k})$. For $e^{+}-e^{-}$ annihilation at 3 on 3 Gev, $\exp \mathrm{}\left[F\right(k\left)\right]=E^{-B}\exp \left[F\right(\hat{k}\left)\right]$ produces a 30% angular modulation.

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