Is Hidden Symmetry Broken In Linear and Nonlinear Sigma Model?

In summary, the conversation discusses the concept of symmetry breaking in linear and nonlinear sigma models. It is stated that symmetry breaking may or may not occur depending on the parameters in the Lagrangian, and is only guaranteed if the expectation value of the field is non-vanishing. There are also degenerate ground states with vanishing expectation value of the field, but the presence of symmetry breaking results in a larger number of degenerate ground states.
  • #1
ndung200790
519
0
Please teach me this:
In linear and nonlinear sigma model, the spontaneous symmetry broken is inevitable happened or it may be happened and it may be not happened?Because the expectation value of field may be zero or may be not zero,then it seem that sometimes the hidden symmetry broken not happened?
Thank you very much in advance.
 
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  • #2


Whether symmetry is broken or not depends on the parameters in the Lagrangian.
Symmetry is not always broken in a linar sigma model. Only if the expectation value of the field is non-vanishing, the symmetry is broken.
 
  • #3


Actually, if a symmetry is broken, there are an infinity of degenerate ground states and among those are also states with vanishing expectation value of the field. However only if the symmetry is broken, there are degenerate ground states at all and in some of them the expectation value of the field is non-vanishing.
 

1. What is a linear and nonlinear sigma model?

A linear and nonlinear sigma model is a theoretical framework used in quantum field theory to describe the behavior of elementary particles. It is based on the concept of spontaneous symmetry breaking, where the symmetry of a system is broken at low energies, resulting in the emergence of new particles and interactions.

2. What is the hidden symmetry breaking in a linear and nonlinear sigma model?

The hidden symmetry breaking in a linear and nonlinear sigma model refers to the breaking of symmetry that is not apparent in the original form of the model. This can happen due to quantum effects or other factors, and it results in the emergence of new phenomena that were not predicted by the original model.

3. Why is hidden symmetry breaking considered inevitable in a linear and nonlinear sigma model?

Hidden symmetry breaking is considered inevitable in a linear and nonlinear sigma model because of the way the model is constructed. It is based on the concept of spontaneous symmetry breaking, which suggests that any symmetries in a system will eventually be broken at low energies. This means that even if a symmetry is hidden in the original model, it will still be broken as the system evolves.

4. What are some examples of hidden symmetry breaking in linear and nonlinear sigma models?

One example of hidden symmetry breaking in a linear and nonlinear sigma model is the Higgs mechanism, where the symmetry between the electromagnetic and weak nuclear forces is broken, resulting in the creation of the Higgs boson particle. Another example is the chiral symmetry breaking in quantum chromodynamics, which gives rise to the masses of quarks and other particles.

5. What are the implications of hidden symmetry breaking in linear and nonlinear sigma models?

The implications of hidden symmetry breaking in linear and nonlinear sigma models are far-reaching. It can lead to the emergence of new particles and interactions, which can help us understand the fundamental forces of nature. It also plays a crucial role in our current understanding of the universe and the behavior of matter at the smallest scales.

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