Types of quantum field thories
By definition, every differential cohomology theory comes with a characteristic curvature form morphism
the (generalized) Chern character.
For a cocycle representing a gauge field in gauge theory, its image is the field strength of the gauge field. If we think of this cocycle as being (a generalization of) a connection on a bundle, this is essentially the curvature of that connection.
Often gauge fields are named after their field strength. For instance the field strength of the electromagnetic field is the -form whose components are the electric and the magnetic fields.
gauge field: models and components
|physics||differential geometry||differential cohomology|
|gauge field||connection on a bundle||cocycle in differential cohomology|
|instanton/charge sector||principal bundle||cocycle in underlying cohomology|
|gauge potential||local connection differential form||local connection differential form|
|field strength||curvature||underlying cocycle in de Rham cohomology|
|minimal coupling||covariant derivative||twisted cohomology|
|BRST complex||Lie algebroid of moduli stack||Lie algebroid of moduli stack|
|extended Lagrangian||universal Chern-Simons n-bundle||universal characteristic map|