Conservation of weak isospin

[RedX]

How is weak isospin conserved?

Before spontaneous symmetry breaking, it's conserved - by construction.

Afterwards, the vacuum expectation value of the Higgs breaks the symmetry.

It's the mass terms, and interactions of the Higgs field, where the symmetry is broken, and so there is no conservation for these processes.

The mass terms, however, can appear in interaction calculations through propagators and spinors, and so anywhere there is mass should there not be non-conservation of isospin?

 

[azntoon]

Yes, weak isospin is not conserved in interactions involving the Higgs field. This includes interactions with fermions, and all other interactions that involve the Higgs. However, for interactions not involving the Higgs field, weak isospin is still conserved.

 

[Entropia]

The conservation of weak isospin is a fundamental principle in the Standard Model of particle physics. It is one of the three fundamental symmetries in the electroweak interaction, along with weak hypercharge and electric charge. Weak isospin is a quantum number that describes the behavior of particles under the weak interaction, which is responsible for radioactive decay and certain types of nuclear reactions.

The conservation of weak isospin is a result of the underlying gauge symmetry of the electroweak interaction. This means that the laws of physics are invariant under a transformation of the weak isospin quantum number. This symmetry is broken by the vacuum expectation value of the Higgs field, which gives mass to the W and Z bosons and breaks the symmetry between the weak isospin up and down components.

The mass terms in the Higgs field do not violate the conservation of weak isospin because they are a result of the symmetry breaking, not the cause of it. The interactions of the Higgs field, however, do not conserve weak isospin because they are not governed by the underlying gauge symmetry. This is why weak isospin is not conserved in processes involving the Higgs field.

In calculations involving particles with mass, such as propagators and spinors, weak isospin is not conserved. This is because these calculations involve the interactions of the particles, which are not governed by the underlying gauge symmetry. However, in processes where only the gauge bosons (such as the W and Z bosons) are involved, weak isospin is conserved.

In summary, the conservation of weak isospin is a fundamental principle in the Standard Model of particle physics, resulting from the underlying gauge symmetry of the electroweak interaction. While the interactions of the Higgs field do not conserve weak isospin, it is still a useful concept in understanding the behavior of particles under the weak interaction.