Re: Loop quantum gravity - loop quantum electrodynamics

From: Tom Roberts (tjroberts_at_lucent.com)
Date: 03/02/05 

Date: Wed, 02 Mar 2005 14:56:50 -0600

francoisbelfort@yahoo.fr wrote:
> Has anybody managed to tell the story of classical electrodynamics
> - on the same level as Jackson - with loops?

Yes. In several different but equivalent ways.

Kaluza-Klein theory posits a 5-d spacetime in which one dimension has the
topology of a circle and is unmeasurably small. An appropriate GR-like theory on
such a manifold yields GR + classical electrodynamics.

QED is a gauge theory of electrodynamics with gauge group U(1), which is
isomorphic to rotations around the unit circle. The modern interpretation of
this is as a fiber bundle with fiber U(1), which essentially assigns a "tiny
circle" to each point of spacetime.

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

In QED the position on the loop represents a quantum mechanical phase. The
selected representation of U(1) represents a particle's charge (naturally
quantized as a product of a unit charge times any integer). The phenomena we
interpret as E and B fields, radiation, etc., come about through quantum
interference.

> Are there any references?

Google is your friend. For an excellent, nonmathematical introduction to QED
this book cannot be beat: Feynman, _QED_.

Tom Roberts tjroberts@lucent.com

Relevant Pages

  • Re: Loop quantum gravity - loop quantum electrodynamics
    ... Kaluza-Klein theory posits a 5-d spacetime in which one dimension has the ... topology of a circle and is unmeasurably small. ... such a manifold yields GR + classical electrodynamics. ... quantized as a product of a unit charge times any integer). ...
    (sci.physics)
  • Re: Loop quantum gravity - loop quantum electrodynamics
    ... Kaluza-Klein theory posits a 5-d spacetime in which one dimension has the ... topology of a circle and is unmeasurably small. ... such a manifold yields GR + classical electrodynamics. ... quantized as a product of a unit charge times any integer). ...
    (sci.physics.particle)
  • Re: Loop quantum gravity - loop quantum electrodynamics
    ... >> Has anybody managed to tell the story of classical electrodynamics ... > QED is a gauge theory of electrodynamics with gauge group U, ... > isomorphic to rotations around the unit circle. ... > this is as a fiber bundle with fiber U, ...
    (sci.physics)
  • Re: Loop quantum gravity - loop quantum electrodynamics
    ... >> Has anybody managed to tell the story of classical electrodynamics ... > QED is a gauge theory of electrodynamics with gauge group U, ... > isomorphic to rotations around the unit circle. ... > this is as a fiber bundle with fiber U, ...
    (sci.physics.relativity)
  • Re: Loop quantum gravity - loop quantum electrodynamics
    ... >> Has anybody managed to tell the story of classical electrodynamics ... > QED is a gauge theory of electrodynamics with gauge group U, ... > isomorphic to rotations around the unit circle. ... > this is as a fiber bundle with fiber U, ...
    (sci.physics.particle)