Types of quantum field thories
With denoting the Hodge star operator with respect to the corresponding pseudo-Riemannian metric on , the right hand of
If is globally hyperbolic and is any spacelike hyperslice, then
Notice that due to the above equation , so that is independent of the choice of . When unwrapped into separate space and time components, the expression may be expressed as
which is a statement of the physical phenomenon of charge conservation .
While electric current is modeled by just a differential form, magnetic charge has a more subtle model. See magnetic charge .
The above has a straightforward generalization to higher abelian gauge fields such as the Kalb-Ramond field and the supergravity C-field: for a field modeled by a degree Deligne cocycle the electric current is the right hand of
electric charge, magnetic charge