# Symmetries + Conserved currents of SM

1. ### michael879

663
Can anyone give or point me to a list of ALL continuous symmetries in the standard model, and the conserved currents associated with them? I've spent a lot of time looking and for the most part everything I find is very abstract, where as I want the specific details to the SM (i.e. SU(N) gauge symmetries and chiral symmetries for massless/higgsless fields which are idealizations of the SM).

The continuous symmetries I am aware of are: SU(1)xSU(2)xSU(3) gauge symmetries and chiral symmetries for each fermion. As I haven't found an exhaustive list, I'm not sure if there are others.

I believe the conserved currents associated with these symmetries are RELATED to charge conservation and fermion number conservation. However, the higgs complicates the actual form of these currents and I dont know what they are.

2. ### Bill_K

4,160
Hm, you could take a look at this paper.

3. ### michael879

663
Bill thank you, and I will check it out to confirm this, but I suspect its not what I'm looking for. I think I actually came across this paper in my search, but it does not include local symmetries.

"I present an overview of the standard model, concentrating on its global continuous symmetries, both exact and approximate"

The BEST reference I've found for the SM is: http://einstein-schrodinger.com/Standard_Model.pdf
However it is not comprehensive and only gives the gauge symmetries (and does not explicitly give their corresponding currents)

*edit* that is a very interesting paper, thank you (and it's a very well written, thorough description of the entire SM). It does have some of what I'm looking for, but it doesn't have the associated conserved currents that arise from the symmetries.

Last edited: Nov 14, 2013
4. ### ChrisVer

By Coleman Mandula's theorem, we know that the symmetries are Spacetime X gauge... so in explicity, Poincare and Gauge Symmetries...So...
First of all the Standard Model is a Yang Mills gauge theory of SU(3)C x SU(2)L x U(1)Y, so I don't think you can find more kind of gauge symmetries in it. Of course you can go around playing with them, imposing some symmetries for the theory you want to make (eg impose a Z symmetry to forbid the decay of protons).

A physical theory though should also be Lorentz invariant, so you can also impose the Poincare symmetry.

As for the conserved currents now, you need to know the generators of your symmetries. For example in the Lorentz Group you have rotations and boosts (corresponding to conserved current for momentum and "generalized" angular momentum). The Lorentz group leads to chiral symmetries, since the proper orthochronous Lorentz Group is isomorphic to SU(2)xSU(2).
For seeing the conserved currents, just use your group generators in exponential, try an infinitesimal transformation of the field and use the Noether's theorem to find the conserved current as well as the conserved charge.
I have never tried it, so I can only guess.. The thing that must not change is the charge (combination of SU2 and U1), the color, and maybe something with the isospin...