Re: Loop quantum gravity - loop quantum electrodynamics

whopkins_at_csd.uwm.edu
Date: 03/03/05 

Date: 3 Mar 2005 15:44:33 -0800

francoisbelfort@yahoo.fr wrote:
> The people of loop quantum gravity explain gravitation with loops,
> and always say that electrodynamics can also be described by loops.
>
> Has anybody managed to tell the story of classical electrodynamics
> - on the same level as Jackson - with loops?

Maxwell did and, in effect, originated the entire approach that the
loop approach to gauge theory (known under the misnomer of "loop
quantum gravity") is a successor to.

> How would electrodynamic loops describe the scalar
> and vector potential?
> The E and B field? Or a light beam?

Maxwell defined the differential form A.dr (yes, literally:
differential forms. He explicitly used the Grassman algebra of
differential forms in his treatise). He used it consistently in the
context of the "electromagnetic momentum", which is the integral of
A.dr around closed loops and, basically, used this to characterize the
potential, itself.

There was no explicit awareness of (dt) in his treatise, so he never
got to the point of ever considering the combination of (A.dr - phi dt).

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