Extending the Symmetry Group: Even/Odd Z2 Symmetry?

Thread starter amrashed
Start date Jun 8, 2011
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Group Symmetry

In summary, the purpose of extending the symmetry group with even/odd Z2 symmetry is to further classify and categorize physical systems based on their symmetries. The even/odd Z2 symmetry group is defined as a mathematical group that contains two elements - even and odd. Some examples of systems that exhibit even/odd Z2 symmetry include crystals, atomic nuclei, and molecules. The even/odd Z2 symmetry of a system can determine its properties and can be extended to other symmetry groups through the use of group theory.

Jun 8, 2011

amrashed

I am extending the standard model symmetry group by introducing discrete symmetry (Z2). The group could be (I, G) or (I, -G). Is that called even and odd Z2 symmetry? What is the difference of considering either of them?

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Jun 8, 2011

chrispb

There is exactly one finite group of order 2.

Related to Extending the Symmetry Group: Even/Odd Z2 Symmetry?

1. What is the purpose of extending the symmetry group with even/odd Z2 symmetry?

The purpose of extending the symmetry group with even/odd Z2 symmetry is to further classify and categorize physical systems based on their symmetries. This allows for a more comprehensive understanding of the underlying principles and behaviors of these systems.

2. How is the even/odd Z2 symmetry group defined?

The even/odd Z2 symmetry group is defined as a mathematical group that contains two elements - even and odd. These elements represent the two possible values of a quantity under the operation of symmetry.

3. What are some examples of systems that exhibit even/odd Z2 symmetry?

Some examples of systems that exhibit even/odd Z2 symmetry include crystals, atomic nuclei, and molecules. In these systems, the even/odd Z2 symmetry is related to the parity or spatial inversion symmetry.

4. How does the even/odd Z2 symmetry affect the properties of a system?

The even/odd Z2 symmetry of a system can determine its properties such as the energy levels, magnetic properties, and stability. It can also affect the selection rules for allowed transitions between different states in the system.

5. How does the concept of even/odd Z2 symmetry extend to other symmetry groups?

The concept of even/odd Z2 symmetry can be extended to other symmetry groups through the use of group theory. By combining different symmetry operations, more complex symmetry groups can be formed, providing a deeper understanding of the symmetries present in a system.