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touqra
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Can someone explain what's Z2 symmetry ? Is it necessary to have it in a model, even SM ?
BenTheMan said:Z2 is usually a symmetry like something goes to - something.
So, for example, I can write this lagrangian:
[tex]\mathcal{L} = \frac{1}{2}\partial_{\mu} \phi \partial^{\mu} \phi+\lambda\phi^4[/tex]
The Z2 symmetry is manifest---that is I can always take [tex]\phi[/tex] to [tex]-\phi[/tex] and get the same lagrangian back.
As far as necessarily needing it for anything, I don't know, but I don't suspect there's anything particularly deep about it.
touqra said:What does it mean to have a [tex]-\phi[/tex] field ?
Z2 symmetry, also known as discrete or binary symmetry, is a type of symmetry that involves only two possible values or states. In physics, it is often used to describe systems that exhibit a property where the system remains unchanged after a certain transformation, such as a reflection or a rotation by 180 degrees.
Z2 symmetry is relevant in models because it can simplify and constrain the behavior of a system. By imposing Z2 symmetry, certain interactions or terms in the model can be forbidden, leading to a more elegant and predictive model. Z2 symmetry is commonly used in particle physics, condensed matter physics, and other fields of physics.
One example is the Ising model, which describes the behavior of ferromagnetic materials and uses Z2 symmetry to constrain the orientation of spins. Another example is the Higgs mechanism in particle physics, where the Higgs field is assumed to have Z2 symmetry. This symmetry breaking leads to the spontaneous generation of the masses of particles.
Z2 symmetry can be broken in two ways: explicitly or spontaneously. Explicit breaking occurs when the symmetry is not present in the model or when certain terms are added that violate the symmetry. Spontaneous breaking occurs when the symmetry is present, but the system chooses a particular state that is not symmetric. This can lead to the appearance of new phenomena, such as mass generation in the Higgs mechanism.
Understanding Z2 symmetry in models can provide insights into the behavior and properties of physical systems. It allows for the simplification and prediction of complex systems, and can also lead to the discovery of new phenomena. Additionally, understanding Z2 symmetry can help bridge the gap between theoretical models and experimental observations, leading to a better understanding of the natural world.