Discovering Z Symmetry: Understanding its Role in Physics

[Safinaz]

Hi all,

Have anyone heard about a symmetry called " Z symmetry " . It's considered a discrete symmetry, in which terms at a Lagrangian for example can take "Z charges" 0, 1 or +1 to be invariant or non-invariant under this symmetry ..

I heard about before, but I try to find any reference for it. I found only rotational groups like $Z_2$ and $Z_4$.


S.

 

[ChrisVer]

what about it?

 

[Safinaz]

I need a reference about ,
also I don't remember exactly, when we give "Z charges " for the fields in a term like say : $d^c e^+ \phi$, when
this term is invariant or not invariant under this symmetry.

 

[ChrisVer]

if you try to do a discrete symmetry, in front of your terms you will have:
$(-1)^{\sum_i Q_i}$
invariant is when it's plus (so you have the same result)
not invariant if it's minus (because you got a minus in front).
It's pretty similar to a U(1) symmetry, because a broken U(1) gives you the Z2.

Now I guess, if you have a Z_N group, looking at it as the Nth root of unity, then in order to be invariant it has to belong to the identity again...