  We use a quantum loop expansion to derive sum rule constraints on polarized
photoabsorption cross sections in the Standard Model, generalizing earlier
results obtained by Altarelli, Cabibbo, and Maiani. We show that the
logarithmic integral of the spin-dependent photoabsorption cross section
$\int^\infty_{\nu_{th}} {d\nu\over \nu} \Delta \sigma_{\rm Born}(\nu) $
vanishes for any $2 \to 2$ Standard Model or supersymmetric process $\gamma a
\to b c$ in the classical, tree-graph approximation. Here $\nu = {p \cdot q}/M$
and $\Delta \sigma(\nu) = \sigma_P(\nu)- \sigma_A(\nu)$ is the difference
between the photoabsorption cross section for parallel and antiparallel photon
and target helicities. Tests of the sum rule for the reactions $\gamma e \to W
\nu$ and $\gamma \gamma \to W^+ W^-$ can provide new tests of the canonical
magnetic and quadrupole couplings of the Standard Model. We also extend the sum
rule to certain virtual photon processes.
