nLab
higher gauge field

Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Differential cohomology

Contents

Idea

A general gauge field is a cocycle in differential cohomology. The case of the electromagnetic field and the Yang-Mills fields with 2-form curvature is just a very special case of this, in general a gauge field has higher curvature forms. For instance the B-field has a curvature 3-form, the C3-field has a curvature 4-form and the RR-field has a curvature form in every even or every odd degree.

For emphasis, therefore, one sometimes speaks of higher gauge fields and higher gauge theory , where the “higher” is as in higher category theory . Indeed, where an ordinary Yang-Mills field is a connection on a bundle defined in ordinary category theory, a higher gauge field is modeled by a connection on a 2-bundle or generally by a connection on a principal infinity-bundle.

See gauge theory for more.

Examples

References

Introductory lecture notes include

For foundations of higher prequantum field theory see

For foundations of higher gauge theory in homotopy type theory see

Revised on May 24, 2013 11:53:29 by Urs Schreiber (84.153.217.1)