Can Non-Commutative Geometry Describe Gluons?

[topsquark]

In Germany it's also apples and pears. However, due to the universality of gravitation, Newton would have found the universal law of the gravitational interaction also, if he had sat under a pear tree instead of the famous apple tree in Woolthourpe ;-).

It's a good thing he wasn't sitting under a crate at a dockyard...

-Dan

 

[mitchell porter]

This thread is a bit confused, e.g. equivocating between color SU(3) and flavor SU(3), or between a change in the basis of the gluon fields, and a change in the gauge group itself.

However, since the questioner did ask if a discrete group like the dihedral group could substitute for the gauge group: I will point out that this is (or was?) done in some lattice simulations, in which the Wilson lines are only given values from a discrete subgroup of SU(3), rather than from full SU(3). But this does result in deviations from actual QCD in certain regimes, as discussed in the introduction to a 2019 paper.

 

[casparov]

You're kinda asking for rude answers. Yes I saw on wikipedia you can consider the dihedral group also as subgroup of $SO(3)$ but that is very different from $SU(3)$ (dimensions 3 versus 8). Also a double cover of the dihedral group has $4n$ elenents whereas both $SO(3)$ and $SU(3)$ are continuous and therefore infinite groups.

Do you remember which dihedral group this is, or is that related to every dihedral group (and about the double cover comment) ? Cause there are quite a few.
A 3D dimensional manifold, which SO(3) is too, seems to me that it fits the best to reality ?

 

[casparov]

This thread is a bit confused, e.g. equivocating between color SU(3) and flavor SU(3), or between a change in the basis of the gluon fields, and a change in the gauge group itself.

However, since the questioner did ask if a discrete group like the dihedral group could substitute for the gauge group: I will point out that this is (or was?) done in some lattice simulations, in which the Wilson lines are only given values from a discrete subgroup of SU(3), rather than from full SU(3). But this does result in deviations from actual QCD in certain regimes, as discussed in the introduction to a 2019 paper.

Thank you very much for your info sir. Very much appreciated, the paper gave me some great ideas

 

[Structure seeker]

However, notation Dn is also used for a subgroup of SO(3) which is also of abstract group type Dn: the proper symmetry group of a regular polygon embedded in three-dimensional space (if n ≥ 3). Such a figure may be considered as a degenerate regular solid with its face counted twice. Therefore, it is also called a dihedron (Greek: solid with two faces), which explains the name dihedral group (in analogy to tetrahedral, octahedral and icosahedral group

The crux seems to be that reflections in 2D can be represented as rotations in 3D.

 

[AndreasC]

Pears and apples in Croatia.

If we are doing this, in Greece we say "you confused the d*** with the brush".

And the the pear and apple thing. But also the brush thing.

 

[malawi_glenn]

Thank you very much for your info sir. Very much appreciated, the paper gave me some great ideas

Ideas for what?

Also, they usage of sir is ancient, don't assume everyone who knows math and physics are male ;)

 

[casparov]

Ideas for what?

Also, they usage of sir is ancient, don't assume everyone who knows math and physics are male ;)

I saw that the paper employed some numerical programming methods that I am aware of, and that might be fruitful to try out and test, possibly some have never been tried before with certain groups for the gauge/gluons. Maybe some cool bachelor project or more.

Yes I know quite some females are in the field especially now, but the male name does suggest it for me. I use sir a lot at my work its all fine thanks for the heads up though ;)

I also want to thank you for the books, so helpful!!