Cohomology and gauge fields. While cohomology has of course many and diverse applications, in physics no less than in other fields, the role of cohomology specifically in the global description of (higher) gauge fields (“force fields”) is profound: In generalization of the seminal historical observation (“Dirac charge quantization”) that electromagnetic field configurations are globally to be identified with 2-cocycles in ordinary differential cohomology of spacetime, higher gauge field species are similarly to be identified with generalized cohomology theories whose further properties and attributes closely reflect the field’s physical nature, as indicated in the above table.
Last revised on November 16, 2024 at 09:27:55. See the history of this page for a list of all contributions to it.