Discovering Z Symmetry: Understanding its Role in Physics

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In summary, the conversation discusses a symmetry called "Z symmetry" which is a discrete symmetry with Z charges of 0, 1, or +1. The group is similar to rotational groups like Z2 and Z4. The group affects terms in the Lagrangian and can be determined by the formula (-1)^{\sum_i Q_i}. It is compared to a U(1) symmetry, and a broken U(1) symmetry can give a Z2 symmetry. The conversation also mentions the need for a reference about the symmetry and the criteria for invariance.
  • #1
Safinaz
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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.
 
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  • #2
what about it?
 
  • #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.
 
  • #4
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...
 

1. What is Z symmetry?

Z symmetry, also known as Z2 symmetry, is a type of symmetry found in physics and mathematics. It refers to the invariance of a system under a discrete transformation, meaning that the system looks the same before and after the transformation is applied.

2. How is Z symmetry explored in science?

Z symmetry is explored through various experiments and theoretical models in fields such as particle physics, condensed matter physics, and cosmology. Scientists use mathematical equations and principles to study the effects of Z symmetry on different systems and phenomena.

3. What are some real-world applications of Z symmetry?

Z symmetry has many practical applications, including in the development of new materials and technologies. For example, Z symmetry can be used to design and create more efficient solar cells or to study the properties of topological insulators.

4. How does Z symmetry relate to other types of symmetries?

Z symmetry is closely related to other types of symmetries, such as rotational symmetry and translational symmetry. It is also linked to the concept of time-reversal symmetry, which describes the invariance of a system under the reversal of time.

5. Are there any current research developments in the study of Z symmetry?

Yes, there are ongoing research efforts to further understand and explore the implications of Z symmetry in different fields. Some recent developments include the discovery of new topological phases of matter and the study of the role of Z symmetry in the early universe.

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