3-fold degeneracy: what is it?

[gioialorusso]

Hi everybody,
I apologize for my trivial question, I'm reading a paper by Freedman and Kitaev and, when describing anyons and quantum Hall Effect with v=1/3, they say that "the ground state of electron liquid on the torus is 3-fold degenerate". What is the meaning? It means that there are 3 levels with the same energy? I'm sorry, I'm italian and sometimes it's hard to understand english math words.
Is there any paper you would suggest me on TQC for beginners?
Thank you so much,
best regards,
Gioia

 

[Einj]

Hi Gioia, I'm from Italy too (I think I must however answer in English). However I'm not an expert in anyons, but usually when someone speak about a n-fold degenerate ground state it means exactly what you said. It means that there are n states that have the same energy.
It's the same thing that happen, for example, in hydrogen atom when, for any given value of the quantum number L you have many values of m (between -L and L) that share the same energy.
I hope I haven't writter stupid things.

Einj

 

[gioialorusso]

Thank you so much, Einj.

Gioia