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Z symmetry

  1. Sep 13, 2014 #1
    Hi all,

    Have any one 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##.

  2. jcsd
  3. Sep 13, 2014 #2


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    what about it?
  4. Sep 13, 2014 #3
    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.
  5. Sep 14, 2014 #4


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    if you try to do a discrete symmetry, in front of your terms you will have:
    [itex](-1)^{\sum_i Q_i}[/itex]
    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...
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