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We describe paths in the configuration space of (3+1) dimensional QED whoserelative quantum phase (or relative phase in the functional integral) dependson the value of the theta angle. The final configurations on the two paths arerelated by a gauge transformation but differ in magnetic helicity orChern-Simons number. Such configurations must exhibit gauge potentials thatfall off no faster than 1/r in some region of finite solid angle, although theyneed not have net magnetic charge (i.e., are not magnetic monopoles). Therelative phase is proportional to theta times the difference in Chern-Simonsnumber. We briefly discuss some possible implications for QCD and the strong CPproblem.

Theta terms and asymptotic behavior of gauge potentials in (3+1) dimensions