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wormwoodsilver101
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- What are the continuous global symmetries before and after the spontaneous symmetry breaking of doublet of scalar fields? And what is the proof for the symmetry?
What are the global symmetries before and after symmetry breaking?
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- Thread starter wormwoodsilver101
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In summary, global symmetries are transformations that apply to an entire system and leave its properties unchanged. Symmetry breaking can cause a change or complete breaking of global symmetries in a system. A system can have global symmetries at different stages of its evolution. Global symmetries are closely related to conservation laws and can be categorized as discrete or continuous, as well as internal or external.
- #2
samalkhaiat
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The global symmetries of a Lagrangian DON’T change “after the spontaneous symmetry breaking”. The Lagrangian you wrote is invariant under the global U(1) transformation [itex]\phi \to e^{i \theta} \phi[/itex]. It is also invartiant under the global SU(2) transformation [itex]\phi \to e^{i \theta^{a} T_{a}}\phi[/itex]. So, “before and after the spontaneous symmetry breaking” the global symmetry group of [itex]\mathcal{L}[/itex] is always [itex]SU(2) \times U(1)[/itex].wormwoodsilver101 said:
1. What is symmetry breaking in physics?
Symmetry breaking is a phenomenon in physics where a system or theory exhibits different symmetries before and after a certain event or phase transition. This can result in changes to the physical properties of the system.
2. What are global symmetries?
Global symmetries refer to symmetries that are present throughout a system, regardless of location or time. They are represented by global transformation operators that act on the entire system.
3. How do global symmetries change before and after symmetry breaking?
Before symmetry breaking, a system may exhibit a larger number of global symmetries. However, after symmetry breaking, some of these symmetries may be broken or hidden, resulting in a smaller number of remaining global symmetries.
4. Can global symmetries be restored after symmetry breaking?
In some cases, global symmetries can be restored after symmetry breaking. This can occur if the system undergoes a second phase transition or if the broken symmetries are only approximate and can be restored under certain conditions.
5. How do global symmetries affect the behavior of a system?
Global symmetries play an important role in determining the physical properties and behavior of a system. They can constrain the possible states and interactions of the system, and their breaking can lead to the emergence of new phenomena and phases.
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