In physics, a Dirac string is a hypothetical one-dimensional curve in space, conceived of by the physicist Paul Dirac, stretching between two Dirac magnetic monopoles with opposite magnetic charges, or from one magnetic monopole out to infinity. The gauge potential cannot be defined on the Dirac string, but it is defined everywhere else. The Dirac string acts as the solenoid in the Aharonov–Bohm effect, and the requirement that the position of the Dirac string should not be observable implies the Dirac quantization rule: the product of a magnetic charge and an electric charge must always be an integer multiple of
The Dirac string is the only way to incorporate magnetic monopoles into Maxwell's equations, since the magnetic flux running along the interior of the string maintains their validity. If Maxwell equations are modified to allow magnetic charges at the fundamental level then the magnetic monopoles are no longer Dirac monopoles, and do not require attached Dirac strings.
Details
The quantization forced by the Dirac string can be understood in terms of the cohomology of the fibre bundle representing the gauge fields over the base manifold of space-time. The magnetic charges of a gauge field theory can be understood to be the group generators of the cohomology group