higher U(1)-gauge theory
Connections on bundles
Higher abelian differential cohomology
Higher nonabelian differential cohomology
Application to gauge theory
The higher gauge theory analog of electromagnetism, including in degree 2 the B-field, in degree 3 the C-field, and so on.
Over a spacetime , a field configuration of order -gauge theory is a circle n-bundle with connection .
The action functional of the bare theory is given by
where is the field strength/curvature of , and where denotes the Hodge star operator.
The presence of background electric charge on is modeled by a fixed circle (d-n-1)-bundle with connection
where is the dimension of , and adding to the action the higher electric background charge coupling term
given by the Beilinson-Deligne cup product of the higher electromagnetic field with the background electric current, followed by fiber integration in ordinary differential cohomology.
The presence of background magnetic charge, on the other hand, is modeled by changing the configurations from circle -bundles with connection to twisted circle -bundles with connection (…)
Created on December 21, 2011 01:32:39
by Urs Schreiber