Symmetries + Conserved currents of SM

In summary, the standard model contains continuous symmetries such as SU(3)C x SU(2)L x U(1)Y gauge symmetries and chiral symmetries for fermions. While there is no comprehensive list of all continuous symmetries, it is believed that these are the only ones present in the standard model. The conserved currents associated with these symmetries are related to charge conservation and fermion number conservation, but are complicated by the presence of the Higgs boson. To find detailed information about these symmetries and their associated currents, one can refer to the Coleman Mandula theorem and use the Noether's theorem to calculate the conserved currents from the generators of the symmet
  • #1
michael879
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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 don't know what they are.
 
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  • #3
Bill_K said:
Hm, you could take a look at this paper.

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.
 
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  • #4
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...
 

FAQ: Symmetries + Conserved currents of SM

1. What are symmetries in the Standard Model (SM)?

Symmetries in the SM refer to the properties of the laws of physics that remain unchanged under certain transformations. These transformations can be in the form of rotations, translations, or changes in reference frame. In the SM, there are three types of symmetries: gauge symmetry, chiral symmetry, and flavor symmetry.

2. How are symmetries related to conserved currents in the SM?

Conserved currents are mathematical quantities that are associated with symmetries in the SM. These currents are conserved, meaning they do not change over time, and are related to the symmetries of the system. For example, the conserved current for gauge symmetry is the electromagnetic current, while the conserved current for chiral symmetry is the axial vector current.

3. What is the significance of conserved currents in the SM?

Conserved currents play a crucial role in the SM as they are associated with the conservation laws of the fundamental interactions. For instance, the conservation of electric charge is related to the conserved electromagnetic current, and the conservation of baryon number is related to the conserved baryon current.

4. How do symmetries and conserved currents affect the behavior of particles in the SM?

Symmetries and conserved currents dictate the interactions between particles in the SM. For example, the gauge symmetry of the strong force leads to the conservation of color charge, while the chiral symmetry of the weak force leads to the conservation of lepton number.

5. Can symmetries and conserved currents be violated in the SM?

While symmetries and conserved currents are fundamental principles of the SM, they can be violated under certain circumstances. For example, the weak force violates chiral symmetry through the phenomenon of parity violation. Additionally, some theories beyond the SM predict the violation of other symmetries, such as baryon and lepton number conservation.

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