Talk:Gauge theory

• Can we have an intro paragraph for, say, the reader with only first year undergraduate physics, rather than this somewhat last-year mathematical physics student level.... also a roadmap for subjects to read about first (differential geometry, tensors...) ?

IMHO, first-year undergraduate level is rather a tough order -- but I am trying my best to divide this thing into an intro paragraph with the bare physical idea, a short historical note, and a section with a physics example - maybe SU(N) or something like that, followed by the heavy duty diffgeom. Would be nice to get some backup here - Amar 08:01, Jun 12, 2004 (UTC)

Contents

1 Help ! Images 2 Re mathematical formalism 3 Correction? 4 Correction

Help ! Images

• Just added an image that I drew to the classical theory section. Very evidently, it's kind of clunky - can someone with better artistic skills advise/add a better picture ? - Amar 09:57, Jun 19, 2004 (UTC)

what's a feynman diagram doing in the classical theory section? Feynman diagrams are objects in the quantum theory. and why not use LaTeX feynman diagrams instead of hand-drawn? -Lethe | Talk

The Yang-Mills action is NOT the most general gauge invariant action out there... Phys 05:48, 14 Aug 2004 (UTC)

I would like to rotate the diagram by 90 degrees. As this is a spacetime diagram, the current orientation depicts particles travelling backward in time ("downward" motion = time reversal). If the diagram is re-oriented, then the gauge interaction occurs at some known time (height above the x-axis) which how Feynman would have drawn this. Ancheta Wis 13:13, 28 Sep 2004 (UTC) Thinking about it, the particles need to be bosons, so the straight lines need to be wavy lines. What about the interaction with the gauge boson, now, does it make sense for a collision to occur, or is it simply a decay? Ancheta Wis 21:59, 28 Sep 2004 (UTC)

Re mathematical formalism

Maybe there should be some mention that the gauge group <math>G<math> is the structure group of the vector or spinor bundle in question, whereas the group of gauge transformations is the group of <math>G<math>-bundle automorphisms, i.e. those bundle automorphisms whose induced isomorphism on the fibres lies within the gauge group <math>G<math>.

I would further welcome some examples of gauge groups and groups of gauge transformations for a few theories, e.g. Relativity or QED...

I have added a parragraph on gauge fixing, I wonder if it should be more detailed, jointly with some expansion on the classical invariances of a force field lagrangian (A.R.)

Correction?

I think the expression for the Noether current(O(n) scalar theory) in the article is wrong. The current should not have the i index.I think the correct expression would be

<math>\ J^{a}_{\mu} = \imath\sum_{ij}\partial_\mu \varphi_i T^{a}_{ij}\varphi_j<math>

-Vatsa Jan 29, 2005

This article isn't consistent. It "defines" A with a factor of 1/g but has a 1/4g² coefficient for the Yang-Mills term. Phys 06:53, 3 Feb 2005 (UTC)

Correction

It's not true that the sections of a principal bundle form a group! So, this is not a good definition of the group of gauge transformations. I was confused about this for a long time myself. To get a group, you need the sections of the bundle associated to the principal bundle P by means of the adjoint action of G on itself. I don't have the energy to write a clear explanation of this for people who don't know this sort of stuff. But, I wanted to point out that the description of gauge transformations as sections of a principal bundle is wrong.

(I'll be amazed if this correction actually shows up;I have no clue how Wiki works. Sorry!)

- John Baez, February 3rd 2005