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If the field of electromagnetism serves as a background gauge field for electrically charged quantum particles it is subject to various quantization conditions. These say that outside the locus of any magnetic charge – for instance a magnetic monopole topological defect – the electromagnetic field is a circle bundle with connection and the first Chern class of the underlying $U(1)$-principal bundle is the discrete measure for the units of magnetic charge.
On the locus of the magnetic charge itself the situation is more complex. There the magnetic current is given by a cocycle in ordinary differential cohomology of degree 3 (with compact support) and now the electromagnetic field is a connection on a twisted bundle.
See at electromagnetic field – charge quantization.
The concept is named after
Review is for instance in
Theodore Frankel, section 16.4e of The Geometry of Physics - An Introduction
L. Mangiarotti, Gennadi Sardanashvily, Connections in Classical and Quantum Field Theory, World Scientific, 2000
Daniel Freed, section 2 of Dirac charge quantization and generalized differential cohomology
Last revised on November 22, 2018 at 02:32:27. See the history of this page for a list of all contributions to it.