# nLab higher gauge field

## Surveys, textbooks and lecture notes

#### Differential cohomology

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.

## 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)