1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Potencial as a representation of S3

  1. Mar 3, 2008 #1
    1. The problem statement, all variables and given/known data
    I am asked to write the most general real scalar potencial (without SU(2)xU(1) structure and without spin) with a irreducible representation of the symmetric group [itex]S_3[/itex]. I am suppose to write it with:

    i) one singlet and one doublet of [itex]S_3[/itex]
    ii)two doublets of [itex]S_3[/itex]

    2. Relevant equations

    3. The attempt at a solution

    Well, I now already that the [itex]S_3[/itex] as 2 one-dimensional irreducible representations and 1 two-dimensional irreducible representations (irrep). I also know the basis of the invariant space which form each irrep. My question now, is how can a form a scalar field with this.
    For exemple, for i), I got,


    where the [itex]\phi_S[/itex] is the singlet and the other two terms forms the doublet. With this I get in fact a three-dimensional representation of [itex]S_3[/itex] which can be decomposed in [itex]D^{1}(S_3)\otimes D^{2}(S_3)[/itex], being the first a one-dimensional irrep and the second a two-dimensional irrep.
    Is that correct? I have no faith in this result...

    Thanks for any help.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted