What happens to conserved currents after spontaneos symmetry breaking?

In summary, the conversation discusses the conservation of current and the role of symmetry in this conservation. It is mentioned that the linear-σ model was created to show how the axial current could be partially conserved. However, it is noted that the axial current is not conserved due to the chiral anomaly, which is different from chiral symmetry breaking. The conversation also references a Nobel lecture by Nambu on this topic.
  • #1
alemsalem
175
5
should the current still be conserved? since it stills commutes with the Hamiltonian and symmetry is just hidden.

but I just read that the linear-σ model was invented to demonstrate how the axial current could be partially conserved?

Thanks!
 
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  • #2
the axial current is not conserved due to the chiral anomaly; that's different from chiral symmetry breaking, b/c for spontaneous symmetry breaking the full charge operator still commutes with the Hamiltonian H, i.e. [H,Q] = 0, whereas for an anomaly the (renormalized) operator doesn't, i.e. [H,QA] ≠ 0!

http://en.wikipedia.org/wiki/Chiral_anomaly
 
  • #3
The Nobel lecture by Nambu is quite informative in this respect:
http://www.nobelprize.org/nobel_prizes/physics/laureates/2008/nambu_lecture.pdf
 

1. What is spontaneous symmetry breaking?

Spontaneous symmetry breaking is a phenomenon in which the symmetries of a system are not reflected in its ground state, leading to a broken symmetry in the physical laws of the system.

2. How does spontaneous symmetry breaking occur?

Spontaneous symmetry breaking occurs when the interactions between particles in a system cause the particles to arrange themselves in a way that is different from the symmetries of the underlying physical laws.

3. What are conserved currents?

Conserved currents are physical quantities that remain unchanged throughout the evolution of a system, even after spontaneous symmetry breaking.

4. What happens to conserved currents after spontaneous symmetry breaking?

After spontaneous symmetry breaking, conserved currents are still present in the system, but their form may change due to the broken symmetries. This can lead to new physical phenomena and interactions within the system.

5. How does the presence of conserved currents affect the behavior of a system after spontaneous symmetry breaking?

The presence of conserved currents after spontaneous symmetry breaking can affect the dynamics and stability of a system, as well as its physical properties. They can also provide important insights into the underlying symmetries and interactions within the system.

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